package org.matheclipse.core.system; import static org.junit.Assert.assertEquals; import static org.junit.Assert.fail; import java.math.BigDecimal; import java.math.BigInteger; import org.apfloat.Apfloat; import org.apfloat.ApfloatContext; import org.apfloat.ApfloatMath; import org.apfloat.OverflowException; import org.junit.Test; import org.matheclipse.core.basic.Config; import org.matheclipse.core.eval.EvalEngine; import org.matheclipse.core.expression.ApcomplexNum; import org.matheclipse.core.expression.ApfloatNum; import org.matheclipse.core.expression.BuiltinFunctionCalls; import org.matheclipse.core.expression.F; import org.matheclipse.core.expression.ID; import org.matheclipse.core.expression.data.ByteArrayExpr; import org.matheclipse.core.interfaces.IAST; import org.matheclipse.core.interfaces.IASTMutable; import org.matheclipse.core.interfaces.IInteger; import org.matheclipse.parser.client.Parser; import org.matheclipse.parser.client.ParserConfig; import org.matheclipse.parser.client.ast.ASTNode; /** Tests built-in functions */ public class LowercaseTestCase extends ExprEvaluatorTestCase { @Test public void test001() { // syntax error in relaxed mode // check("Sin[x]", ""); check("1.2345678*^5", // "123456.8"); check("1.2345678*^6", // "1.23457*10^6"); check("1.2345678*^7", // "1.23457*10^7"); check("1.23456789*^8", // "1.23457*10^8"); // github #66 Double d = Double.parseDouble("1231231236123216361256312631627.12312312"); checkNumeric("1231231236123216361256312631627.12312312", // d.toString()); checkNumeric("N(1231231236123216361256312631627.12312312,50)", // "1.2312312361232163E30"); check("f[[1,2]]", // "f[[1,2]]"); check("-cos(x)", // "-Cos(x)"); check("expand((a+b)^3)", // "a^3+3*a^2*b+3*a*b^2+b^3"); check("expand((a+b)^8)", // "a^8+8*a^7*b+28*a^6*b^2+56*a^5*b^3+70*a^4*b^4+56*a^3*b^5+28*a^2*b^6+8*a*b^7+b^8"); check("expand((a+b+c)^3)", // "a^3+3*a^2*b+3*a*b^2+b^3+3*a^2*c+6*a*b*c+3*b^2*c+3*a*c^2+3*b*c^2+c^3"); check("f(g(x),{x,-1.5`,1.5`},{y,-1.5`,1.5`})", // "f(g(x),{x,-1.5,1.5},{y,-1.5,1.5})"); } @Test public void testTildeOperator() { check("a~b~c", // "b(a,c)"); check("a~b~c~d~e", // "d(b(a,c),e)"); } @Test public void testAbort() { check("Print(\"a\"); Abort(); Print(\"b\")", // "$Aborted"); } @Test public void testAbs() { check("Abs((0.5)^z)", // "0.5^Re(z)"); check("Abs(2^z*Log(2*z))", // "2^Re(z)*Abs(Log(2*z))"); check("Abs(I^(2*Pi))", // "1"); check("Abs(Undefined)", // "Undefined"); check("Abs(Indeterminate)", // "Indeterminate"); // Integer.MIN_VALUE check("Abs(-2147483648)", // "2147483648"); // Long.MIN_VALUE check("Abs(-9223372036854775808)", // "9223372036854775808"); // Integer.MIN_VALUE check("Abs(11/-2147483648 )", // "11/2147483648"); // Long.MIN_VALUE check("Abs(-9223372036854775808/11)", // "9223372036854775808/11"); check("Abs(x*Sign(x))", // "Abs(x*Sign(x))"); check("Abs(Abs(x))", // "Abs(x)"); check("Abs(E-Pi)", // "-E+Pi"); check("Abs(x^2)", // "Abs(x)^2"); check("Abs(1/2*x)", // "Abs(x)/2"); check("Abs(1/2*E^(\\[ImaginaryJ]*\\[Pi]/4))", // "1/2"); check("Abs(-x^(a + b))", // "Abs(x^(a+b))"); check("Abs(-x)", // "Abs(x)"); check("Abs(Conjugate(z))", // "Abs(z)"); check("Abs(3*a*b*c)", // "3*Abs(a*b*c)"); // check("Abs(x^(-3))", "1/Abs(x)^3"); check("Abs((1+I)/Sqrt(2))", // "1"); check("Abs(0)", // "0"); check("Abs(10/3)", // "10/3"); check("Abs(-10/3)", // "10/3"); check("Abs(Indeterminate)", // "Indeterminate"); check("Abs(Infinity)", // "Infinity"); check("Abs(-1*Infinity)", // "Infinity"); check("Abs(ComplexInfinity)", // "Infinity"); check("Abs(I*Infinity)", // "Infinity"); check("Abs(Sqrt(Pi))", // "Sqrt(Pi)"); check("Abs(-3*Sqrt(Pi))", // "3*Sqrt(Pi)"); check("Abs(E)", // "E"); } @Test public void testAbsArg() { check("AbsArg(z)", // "{Abs(z),Arg(z)}"); check("AbsArg(-2*z)", // "{2*Abs(z),Arg(-z)}"); check("AbsArg(2*z)", // "{2*Abs(z),Arg(z)}"); check("AbsArg({a, {b, c}})", // "{{Abs(a),Arg(a)},{{Abs(b),Arg(b)},{Abs(c),Arg(c)}}}"); check("AbsArg({{1, -1, 0}, {0, 1}})", // "{{{1,0},{1,Pi},{0,0}},{{0,0},{1,0}}}"); check("AbsArg(Gamma(-1/2))", // "{2*Sqrt(Pi),Pi}"); check("AbsArg({1, I, 0})", // "{{1,0},{1,Pi/2},{0,0}}"); check("AbsArg(z) /. z -> {1, I, 0}", // "{{1,1,0},{0,Pi/2,0}}"); } @Test public void testAbsoluteTiming() { // check("AbsoluteTiming(x = 1; Pause(x); x + 3)[[1]]>1", // // "True"); // check("Timing(x = 1; Pause(x); x + 3)[[1]]<1", // // "True"); } @Test public void testAbsoluteCorrelation() { check("AbsoluteCorrelation({5, 3/4, 1}, {2, 1/2, 1})", // "91/24"); check("AbsoluteCorrelation({1.5, 3, 5, 10}, {2, 1.25, 15, 8})", // "40.4375"); check("AbsoluteCorrelation(N({1, 2, 5, 6}, 20), N({2, 3, 6, 8}, 20))", // "21.5"); check("AbsoluteCorrelation({2 + I, 3 - 2*I, 5 + 4* I}, {I, 1 + 2*I, 10 - 5*I})", // "10+I*55/3"); } @Test public void testAccumulate() { check("Accumulate({{a, b}, {c, d}, {e, f}})", // "{{a,b},{a+c,b+d},{a+c+e,b+d+f}}"); check("Accumulate({})", // "{}"); check("Accumulate({a})", // "{a}"); check("Accumulate({a, b})", // "{a,a+b}"); check("Accumulate({a, b, c, d})", // "{a,a+b,a+b+c,a+b+c+d}"); check("Accumulate(f(a, b, c, d))", // "f(a,a+b,a+b+c,a+b+c+d)"); } @Test public void testAddTo() { // print: AddTo: d is not a variable with a value, so its value cannot be changed. check("d += 7", // "d+=7"); // print: AddTo: test is not a variable with a value, so its value cannot be changed. check("\"test\" += 7", // "test+=7"); // print: Part: Part specification k[[2]] is longer than depth of object. check("k[[2]] += x", // "k[[2]]+=x"); check("a = 10", // "10"); check("a += 2", // "12"); check("a", // "12"); check("index={1,2,3,4,5,6,7,8,9}", // "{1,2,3,4,5,6,7,8,9}"); check("index[[3]]+=y", // "3+y"); check("index", // "{1,2,3+y,4,5,6,7,8,9}"); } @Test public void testAlternatives() { // http://mathematica.stackexchange.com/a/44084 check("f(a_Integer|b_Real) := {1,a,2,b,3}", // ""); check("f(100)", // "{1,100,2,3}"); check("f(100.0)", // "{1,2,100.0,3}"); check("g(a_Real | b_Integer, x_) := (x*a)^b", // ""); check("g(100,a)", // "a^100"); check("g(100.0,a)", // "100.0*a"); check("a+b+c+d/.(a|b)->t", // "c+d+2*t"); check("a+b+c+d/.Except(b,(a|c))->t", // "b+d+2*t"); } @Test public void testApart() { // see github #856 check("Apart((4+3*Sqrt(2)+Sqrt(3)+Sqrt(6))/(2+Sqrt(2)+Sqrt(3)),x)", // "1+Sqrt(2)"); // check("Factor(x^2 - y^2 )", "(x-y)*(x+y)"); // check("Solve(x^2 - y^2==0, y)", "{{y->-x},{y->x}}"); // TODO handle multiple variables: // check("Apart(1 / ((x + a) (x + b) (x + c)))", // // "1/(2*(x-y)*y)-1/(2*y*(x+y))"); check("Apart(1 / (x^2 - y^2), x)", // "1/(2*(x-y)*y)-1/(2*y*(x+y))"); check("Apart(1/(a*b+a*c),x)", // "1/(a*(b+c))"); // TODO return 1/b - a/(b*(a + b*x)) check("Apart((x/(a+(b*x))),x)", // "x/(a+b*x)"); check("Apart((3*x-8)/((x+1)*(x-5)),x)", // "7/6*1/(-5+x)+11/6*1/(1+x)"); check("Apart((a + b)^3)", // "a^3+3*a^2*b+3*a*b^2+b^3"); check("Apart(1 / (x^2 - y^2))", // "1/(x^2-y^2)"); check("Apart(x/(2*x + a^2))", // "x/(a^2+2*x)"); check("Apart(y/(x + 2)/(x + 1),x)", // "y/(1+x)-y/(2+x)"); check("Sin(1 / (x ^ 2 - y ^ 2)) // Apart", // "Sin(1/(x^2-y^2))"); check("Apart(1 / (x^2 + 5*x + 6))", // "1/(2+x)-1/(3+x)"); check("Apart(1 / (x^2 - y^2), x)", // "1/(2*(x-y)*y)-1/(2*y*(x+y))"); check("Apart(1/((1 + x)*(5 + x)))", // "1/(4*(1+x))-1/(4*(5+x))"); check("Apart(1 < (x + 1)/(x - 1) < 2)", // "1<1+2/(-1+x)<2"); check("Apart(1/((1 + x)*(5 + x)))", // "1/(4*(1+x))-1/(4*(5+x))"); check("Apart((x)/(x^2-1))", // "1/(2*(-1+x))+1/(2*(1+x))"); check("Apart((x+3)/(x^2-3*x-40))", // "11/13*1/(-8+x)+2/13*1/(5+x)"); check("Apart((10*x^2+12*x+20)/(x^3-8))", // "7/(-2+x)+(4+3*x)/(4+2*x+x^2)"); check("Apart((3*x+5)*(1-2*x)^(-2))", // "13/2*1/(1-2*x)^2+3/2*1/(-1+2*x)"); check("Apart((10*x^2+12*x+20)/(x^3-8))", // "7/(-2+x)+(4+3*x)/(4+2*x+x^2)"); check("Apart((10*x^2-63*x+29)/((x+2)*(x+3)^5))", // "195/(2+x)-308/(3+x)^5-185/(3+x)^4-195/(3+x)^3-195/(3+x)^2-195/(3+x)"); } @Test public void testAppend() { check("Append({1, 2, 3}, 4) ", // "{1,2,3,4}"); check("Append(f(a, b), c)", // "f(a,b,c)"); check("Append({a, b}, {c, d}) ", // "{a,b,{c,d}}"); check("Append(a, b)", // "Append(a,b)"); } @Test public void testAppendTo() { check("w = f({1}, {2}, {3});w[[2]]={2,a}", // "{2,a}"); check("w", // "f({1},{2,a},{3})"); check("w = f({1}, {2}, {3});AppendTo(w[[2]], a)", // "{2,a}"); check("w", // "f({1},{2,a},{3})"); check("AppendTo(Null,1)", // "AppendTo(Null,1)"); check("s = {}", // "{}"); check("AppendTo(s, 1)", // "{1}"); check("s", // "{1}"); check("y = f()", // "f()"); check("AppendTo(y, x)", // "f(x)"); check("y", // "f(x)"); check("AppendTo({}, 1)", // "AppendTo({},1)"); check("AppendTo(a, b)", // "AppendTo(a,b)"); check("$l = {1, 2, 4, 9};appendto($l, 16)", // "{1,2,4,9,16}"); check("$l = {1, 2, 4, 9};appendto($l, 16);$l", // "{1,2,4,9,16}"); } @Test public void testAppelF1() { check("AppellF1(a, b1, b2, c, 0, 0) ", // "1"); check("AppellF1(a, b1, b2, c, z1, 0) ", // "Hypergeometric2F1(a,b1,c,z1)"); check("AppellF1(a, b1, b2, c, 0, z2) ", // "Hypergeometric2F1(a,b2,c,z2)"); check("AppellF1(a, b1, b2, c, z1, 1) ", // "Hypergeometric2F1(a,b1,-b2+c,z1)*Hypergeometric2F1(a,b2,c,1)"); check("AppellF1(a, b1, b2, c, z1, z1) ", // "Hypergeometric2F1(a,b1+b2,c,z1)"); check("AppellF1(a, b1, b1, c, z1, -z1) ", // "HypergeometricPFQ({1/2+a/2,a/2,b1},{1/2+c/2,c/2},z1^2)"); check("AppellF1(a, b1, b2, b1+b2, z1, z2) ", // "(1-z2)^a*Hypergeometric2F1(a,b1,b1+b2,(z1-z2)/(1-z2))"); } @Test public void testApply() { check("(Count(#, Last(#))&) @@ {{1, 2},{3, 4}}", // "1"); check("Apply(f)[p(x, y)]", // "f(x,y)"); check("Apply(f)[aaa]", // "aaa"); // check("Apply(f, p[x][q[y]], {1}, Heads -> True)", // "f(x)[f(y)]"); check("Apply(f, p[x][q[y]], {1}, Heads -> False)", // "p(x)[f(y)]"); check("Apply(f, p[x][q[y]], {1})", // "p(x)[f(y)]"); check("Apply(f, 1+2+3, {1}, Heads -> True)", // "6"); check("List @@@ (1+2+3)", // "6"); check("f@ g@ h@ i", // "f(g(h(i)))"); // github issue #40 check("((#+##&) @@#&) /@{{1,2},{2,2,2},{3,4}}", // "{4,8,10}"); check("Times @@ {1, 2, 3, 4}", // "24"); check("f @@ {{a, b}, {c}, d}", // "f({a,b},{c},d)"); check("apply(head, {3,4,5})", // "Head(3,4,5)"); check("apply(f, a)", // "a"); check("apply(f, {a, \"string\", 3}, {-1})", // "{a,string,3}"); check("table(i0^j, ##) & @@ {{i0, 3}, {j, 4}}", // "{{1,1,1,1},{2,4,8,16},{3,9,27,81}}"); check("apply(f, {{a, b, c}, {d, e}})", // "f({a,b,c},{d,e})"); check("apply(f, {{a, b, c}, {d, e}}, {1})", // "{f(a,b,c),f(d,e)}"); check("apply(f, {{a, b, c}, {d, e}}, {0, 1})", // "f(f(a,b,c),f(d,e))"); // Apply down to level 2 (excluding level 0): check("apply(f, {{{{{a}}}}}, 2)", // "{f(f({{a}}))}"); check("apply(f, {{{{{a}}}}}, {0, 2})", // "f(f(f({{a}})))"); check("apply(f, {{{{{a}}}}}, Infinity)", // "{f(f(f(f(a))))}"); check("apply(f, {{{{{a}}}}}, {0, Infinity})", // "f(f(f(f(f(a)))))"); check("apply(f, {{{{{a}}}}}, -1)", // "{f(f(f(f(a))))}"); check("apply(f, {{{{{a}}}}}, -2)", // "{f(f(f(f(a))))}"); check("apply(f, {{{{{a}}}}}, -3)", // "{f(f(f({a})))}"); check("apply(f, {{{{{a}}}}}, {2, -3})", // "{{f(f({a}))}}"); check("apply(f, h0(h1(h2(h3(h4(a))))), {2, -3})", // "h0(h1(f(f(h4(a)))))"); check("Apply(List,1+2+3)", // "6"); check("f @@ {1, 2, 3}", // "f(1,2,3)"); check("Plus @@ {1, 2, 3}", // "6"); check("f @@ (a + b + c)", // "f(a,b,c)"); check("Apply(f, {a + b, g(c, d, e * f), 3}, {1})", // "{f(a,b),f(c,d,e*f),3}"); check("f @@@ {a + b, g(c, d, e * f), 3}", // "{f(a,b),f(c,d,e*f),3}"); check("Apply(f, {a, b, c}, {0})", // "f(a,b,c)"); check("Apply(f, {{{{{a}}}}}, {2, -3})", // "{{f(f({a}))}}"); check("Apply(List, a + b * c ^ e * f(g), {0, Infinity})", // "{a,{b,{c,e},{g}}}"); check("Apply(f, {a, b, c}, x+y)", // "Apply(f,{a,b,c},x+y)"); } @Test public void testArcCos() { // see https://github.com/mtommila/apfloat/issues/18 checkNumeric("N(ArcCos(-2),30)", // "3.1415926535897932384626433832+I*(-1.3169578969248167086250463473)"); checkNumeric("N(ArcCos(2),30)", // "I*1.3169578969248167086250463473"); checkNumeric("ArcCos(-2.0)", // "3.141592653589793+I*(-1.3169578969248166)"); checkNumeric("ArcCos(2.0)", // "I*(-1.3169578969248166)"); check("ArcCos(Cos(-1/2))", // "1/2"); check("ArcCos(Cos(-1))", // "1"); check("ArcCos(Cos(1))", // "1"); check("ArcCos(Cos(-42))", // "-42+14*Pi"); check("ArcCos(Cos(42))", // "-42+14*Pi"); check("ArcCos(Cos(Pi/4))", // "Pi/4"); check("ArcCos(Cos(5))", // "-5+2*Pi"); check("ArcCos(0)", // "Pi/2"); check("ArcCos(1)", // "0"); check("Integrate(ArcCos(x), {x, -1, 1})", // "Pi"); check("arccos(-11)", // "ArcCos(-11)"); check("arccos(-x)", // "ArcCos(-x)"); check("D(ArcCos(x),x)", // "-1/Sqrt(1-x^2)"); check("diff(ArcCos(x),x)", // "-1/Sqrt(1-x^2)"); } @Test public void testArcCosh() { check("ArcCosh(0)", // "I*1/2*Pi"); checkNumeric("ArcCosh(0.0)", // "I*1.5707963267948966"); checkNumeric("ArcCosh(1.4)", // "0.867014726490565"); check("ArcCosh(-x)", // "ArcCosh(-x)"); check("D(ArcCosh(x),x)", // "1/Sqrt(-1+x^2)"); check("ArcCosh(-Infinity)", // "Infinity"); check("ArcCosh(I*Infinity)", // "Infinity"); } @Test public void testArcCot() { check("ArcCot(Cot(-1/2))", // "-1/2"); check("ArcCot(Cot(-1))", // "-1"); check("ArcCot(Cot(1))", // "1"); check("ArcCot(Cot(-42))", // "-42+13*Pi"); check("ArcCot(Cot(42))", // "42-13*Pi"); check("ArcCot(Cot(Pi/4))", // "Pi/4"); check("ArcCot(Cot(5))", // "5-2*Pi"); check("ArcCot(0)", // "Pi/2"); check("ArcCot(1)", // "Pi/4"); check("arccot(complexinfinity)", // "0"); check("arccot(0)", // "Pi/2"); check("arccot(-11)", // "-ArcCot(11)"); check("arccot(-x)", // "-ArcCot(x)"); check("D(ArcCot(x),x)", // "-1/(1+x^2)"); } @Test public void testArcCoth() { check("ArcCoth(1/Sqrt(5))", // "ArcCoth(1/Sqrt(5))"); check("ArcCoth(0)", // "I*1/2*Pi"); // TODO fails in bitbucket pipelines // check("ArcCoth(0.0)", "I*1.5707963267948966"); // check("ArcCoth(0.5)", "0.5493061443340549+I*(-1.5707963267948966)"); check("ArcCoth(-x)", // "-ArcCoth(x)"); check("ArcCoth(-1)", // "-Infinity"); check("D(ArcCoth(x),x)", // "1/(1-x^2)"); } @Test public void testArcCsc() { check("ArcCsc(-1+I)", // "-I*ArcCsch(1+I)"); check("ArcCsc(3.5)", // "0.289752"); check("ArcCsc(1.0+3.5*I)", // "0.073021+I*(-0.261854)"); check("ArcCsc(1)", // "Pi/2"); check("ArcCsc(-1)", // "-Pi/2"); check("arccsc(0)", // "ComplexInfinity"); check("arccsc(-x)", // "-ArcCsc(x)"); check("D(ArcCsc(x),x)", // "-1/(Sqrt(1-1/x^2)*x^2)"); } @Test public void testArcCsch() { check("ArcCsch(-1+I)", // "-I*ArcCsc(1+I)"); check("arccsch(0)", // "ComplexInfinity"); checkNumeric("ArcCsch(1.0)", // "0.8813735870195429"); check("ArcCsch(-Infinity)", // "0"); check("arccsch(-x)", // "-ArcCsch(x)"); check("diff(ArcCsch(x),x)", // "-1/(Sqrt(1+x^2)*Abs(x))"); } @Test public void testArcSec() { check("ArcSec(3.5)", // "1.28104"); check("ArcSec(1.0+3.5*I)", // "1.49778+I*0.261854"); check("ArcSec(1)", // "0"); check("ArcSec(-1)", // "Pi"); check("ArcSec(0)", // "ComplexInfinity"); check("ArcSec(-x)", // "ArcSec(-x)"); check("diff(ArcSec(x),x)", // "1/(Sqrt(1-1/x^2)*x^2)"); } @Test public void testArcSech() { check("ArcSech(0)", // "Infinity"); check("ArcSech(0.0)", // "Indeterminate"); check("ArcSech(1)", // "0"); checkNumeric("ArcSech(0.5)", // "1.3169578969248166"); check("ArcSech(-x)", // "ArcSech(-x)"); check("ArcSech(-2)", // "I*2/3*Pi"); check("D(ArcSech(x),x)", // "-1/(x*Sqrt(1-x^2))"); } @Test public void testArcSin() { check("ArcSin(-1+I)", // "I*ArcSinh(1+I)"); check("ArcSin({x,-3,-1/2})", // "{ArcSin(x),-ArcSin(3),-Pi/6}"); check("ArcSin(Sin(-1/2))", // "-1/2"); check("ArcSin(Sin(-1))", // "-1"); check("ArcSin(Sin(1))", // "1"); check("ArcSin(Sin(-42))", // "42-13*Pi"); check("ArcSin(Sin(42))", // "-42+13*Pi"); check("ArcSin(Sin(Pi/4))", // "Pi/4"); check("ArcSin(Sin(5))", // "5-2*Pi"); check("-3*ArcSin(x)-2*ArcCos(x)", // "-Pi-ArcSin(x)"); check("-ArcSin(x)-2*ArcCos(x)", // "-Pi/2-ArcCos(x)"); check("-5*ArcSin(x)-5*ArcCos(x)", // "-5/2*Pi"); check("ArcSin(x)+ArcCos(x)", // "Pi/2"); check("5*ArcSin(x)+5*ArcCos(x)", // "5/2*Pi"); check("ArcSin(0)", // "0"); check("ArcSin(1)", // "Pi/2"); check("arcsin(-11)", // "-ArcSin(11)"); check("arcsin(-x)", // "-ArcSin(x)"); check("diff(ArcSin(x),x)", // "1/Sqrt(1-x^2)"); } @Test public void testArcSinh() { check("ArcSinh(-1+I)", // "I*ArcSin(1+I)"); check("ArcSinh(0)", // "0"); check("ArcSinh(0.0)", // "0.0"); checkNumeric("ArcSinh(1.0)", // "0.8813735870195429"); // check("ArcSinh(-x)", "-ArcSinh(x)"); check("diff(ArcSinh(x),x)", // "1/Sqrt(1+x^2)"); } @Test public void testArcTan() { // github #110 avoid infinite recursion // check("ArcTan(Re(Sin(3+I*2)),Im(Sin(3+I*2)))", // // "ArcTan(Im(Sin(3+I*2))/Re(Sin(3+I*2)))"); check("ArcTan(-1+I)", // "I*ArcTanh(1+I)"); check("N(ArcTan(2, 1), 50)", // "0.4636476090008061162142562314612144020285370542861"); check("N(ArcTan(2, 4), 50)", // "1.1071487177940905030170654601785370400700476454014"); check("N(ArcTan(2, I*4), 50)", // "1.5707963267948966192313216916397514420985846996875+I*0.5493061443340548456976226184612628523237452789113"); check("N(ArcTan(I*4, 2), 50)", // "I*(-0.54930614433405484569762261846126285232374527891137)"); check("N(ArcTan(2, 1))", // "0.463648"); check("N(ArcTan(2, 4))", // "1.10715"); check("N(ArcTan(I*4, 2))", // "I*(-0.549306)"); check("N(ArcTan(2,I*4 ))", // "1.5708+I*0.549306"); check("ArcTan(y_,x^2)", // "ArcTan(y_,x^2)"); check("ArcTan({}, 2)", // "{}"); check("ArcTan(17, {})", // "{}"); check("ArcTan({}, {})", // "{}"); check("ArcTan(0, Pi)", // "Pi/2"); check("ArcTan(0, -Pi/3)", // "-Pi/2"); check("ArcTan(1, 0)", // "0"); check("ArcTan(1/2, 1/2)", // "Pi/4"); check("ArcTan(0, 1)", // "Pi/2"); check("ArcTan(-1/2, 1/2)", // "3/4*Pi"); check("ArcTan(-1, 0)", // "Pi"); check("ArcTan(-1/2, -1/2)", // "-3/4*Pi"); check("ArcTan(0, -1)", // "-Pi/2"); check("ArcTan(1/2, -1/2)", // "-Pi/4"); check("ArcTan(Tan(-1/2))", // "-1/2"); check("ArcTan(Tan(-1))", // "-1"); check("ArcTan(Tan(1))", // "1"); check("ArcTan(Tan(42))", // "42-13*Pi"); check("ArcTan(Tan(Pi/4))", // "Pi/4"); check("ArcTan(Re(9*Cos(5)+I*9*Sin(5)),Im(9*Cos(5)+I*9*Sin(5)))", // "5-2*Pi"); check("ArcTan(-9*Sqrt(2),0)", // "Pi"); check("ArcTan(0.7071067811865476)", // "0.61548"); check("-ArcTan(x/(2*Sqrt(2)))/(2*Sqrt(2))", // "-ArcTan(x/(2*Sqrt(2)))/(2*Sqrt(2))"); check("7*ArcTan(1/2) + a+ArcTan(1/3)", // "a+Pi/4+6*ArcTan(1/2)"); check("ArcTan(1/3) + ArcTan(1/7)", // "ArcTan(1/2)"); check("ArcTan(a, -a)", // "ArcTan(a,-a)"); check("ArcTan(-a, a)", // "ArcTan(-a,a)"); check("ArcTan(a, a)", // "ArcTan(a,a)"); check("2*ArcTan(x)+4*ArcCot(x)", // "Pi+2*ArcCot(x)"); check("7*ArcTan(x)+3*ArcCot(x)", // "3/2*Pi+4*ArcTan(x)"); check("ArcTan(x)+ArcCot(x)", // "Pi/2"); check("4*ArcTan(x)+4*ArcCot(x)", // "2*Pi"); // issue #180 check("ArcTan(1,Sqrt(3))", // "Pi/3"); check("ArcTan(1)", // "Pi/4"); checkNumeric("ArcTan(1.0)", // "0.7853981633974483"); checkNumeric("ArcTan(-1.0)", // "-0.7853981633974483"); check("ArcTan(0, 0)", // "Indeterminate"); check("ArcTan(1, 1)", // "Pi/4"); check("ArcTan(-1, 1)", // "3/4*Pi"); check("ArcTan(1, -1)", // "-Pi/4"); check("ArcTan(-1, -1)", // "-3/4*Pi"); check("ArcTan(17, 0)", // "0"); check("arctan(Infinity,y)", // "0"); check("arctan(-Infinity,y)", // "Pi*(-1+2*UnitStep(Re(y)))"); check("Abs( ArcTan(ComplexInfinity) )", // "Indeterminate"); check("arctan(infinity)", // "Pi/2"); check("ArcTan(ComplexInfinity)", // "Indeterminate"); check("arctan(1)", // "Pi/4"); check("arctan(-11)", // "-ArcTan(11)"); check("arctan(-x)", // "-ArcTan(x)"); check("arctan(1,1)", // "Pi/4"); check("arctan(-1,-1)", // "-3/4*Pi"); check("arctan(0,0)", // "Indeterminate"); checkNumeric("arctan(1.0,1.0)", // "0.7853981633974483"); checkNumeric("N(1/4*pi)", // "0.7853981633974483"); check("D(ArcTan(x),x)", // "1/(1+x^2)"); } @Test public void testArcTanh() { check("ArcTanh(-1+I)", // "I*ArcTan(1+I)"); check("ArcTanh(0)", // "0"); check("ArcTanh(1)", // "Infinity"); check("ArcTanh(2+I)", // "ArcTanh(2+I)"); checkNumeric("ArcTanh(0.5 + 2*I)", // "0.09641562020299621+I*1.1265564408348223"); check("ArcTanh(I)", // "I*1/4*Pi"); check("ArcTanh(Infinity)", // "-I*1/2*Pi"); check("ArcTanh(-Infinity)", // "I*1/2*Pi"); check("ArcTanh(I*Infinity)", // "I*1/2*Pi"); check("ArcTanh(ComplexInfinity)", // "Pi/2"); check("ArcTanh(-x)", // "-ArcTanh(x)"); check("D(ArcTanh(x),x)", // "1/(1-x^2)"); } @Test public void testArg() { check("FullSimplify(Arg(-I*41*Im(z)-41*Re(z)))", // "Arg(-z)"); check("FullSimplify(Arg(I*2*Im(z)+2*Re(z)))", // "Arg(z)"); check("Arg(42*z)", // "Arg(z)"); check("Arg(-42*z)", // "Arg(-z)"); check("Arg(Interval({1, 3}))", // "Interval({0,0})"); check("Arg(Interval({-7/3, -1/3}))", // "Interval({Pi,Pi})"); // https://github.com/Hipparchus-Math/hipparchus/issues/185 // System.out.println(new Complex(0.0, 0.0).getArgument()); // System.out.println(new Complex(-0.0, 0.0).getArgument()); // System.out.println(new Complex(-0.0, -0.0).getArgument()); // System.out.println(new Complex(0.0, -0.0).getArgument()); System.out.println(ApcomplexNum.valueOf(-0.0).complexArg()); check("Arg(I-Sqrt(3))", // "5/6*Pi"); check("Arg(I-Sqrt(3))", // "5/6*Pi"); check("Arg(E^(-42-5*I))", // "-5+2*Pi"); check("Arg(E^(7+I*3))", // "3"); check("Arg(E^(I*3))", // "3"); check("Arg(E^I)", // "1"); check("Arg(Sqrt(z))", // "Arg(z)/2"); check("Arg(-2*z)", // "Arg(-z)"); check("Arg(1.3)", // "0"); check("Arg(2*z)", // "Arg(z)"); check("Arg(x)", // "Arg(x)"); check("Arg(Infinity)", // "0"); check("Arg(-Infinity)", // "Pi"); check("Arg(2 + I*Pi)", // "ArcTan(Pi/2)"); check("Arg(1+I*Sqrt(3))", // "Pi/3"); check("Arg(I-Sqrt(3))", // "5/6*Pi"); // issue #179 check("N(Arg(1+I*Sqrt(3)))", // "1.0472"); check("Arg(Pi)", // "0"); check("Arg(-Pi*E)", // "Pi"); check("Arg(0)", // "0"); check("Arg(1)", // "0"); check("Arg(-1)", // "Pi"); check("Arg(I)", // "Pi/2"); check("Arg(1+I)", // "Pi/4"); check("Arg(-I)", // "-Pi/2"); check("Arg(-2*Sqrt(Pi))", // "Pi"); check("Arg(Indeterminate)", // "Indeterminate"); check("Arg(0)", // "0"); check("Arg(10/3)", // "0"); check("Arg(-10/3)", // "Pi"); check("Arg(I*Infinity)", // "Pi/2"); check("Arg(-I*Infinity)", // "-Pi/2"); check("Arg(ComplexInfinity)", // "Interval({-Pi,Pi})"); check("Table(Arg(Exp(k*I*3*Pi/8)), {k, 8})", // "{3/8*Pi,3/4*Pi,-7/8*Pi,-Pi/2,-Pi/8,Pi/4,5/8*Pi,Pi}"); } @Test public void testArgMax() { check("ArgMax(x*10-x^2 , x)", // "5"); check("Maximize(-2*x^2 - 3*x + 5, x)", // "{49/8,{x->-3/4}}"); check("ArgMax(-2*x^2 - 3*x + 5, x)", // "-3/4"); } @Test public void testArgMin() { check("ArgMin(x*10+x^2 , x)", // "-5"); check("Minimize(2*x^2 - 3*x + 5, x)", // "{31/8,{x->3/4}}"); check("ArgMin(2*x^2 - 3*x + 5, x)", // "3/4"); } @Test public void testArray() { check("Array(f, 10, {0,1})", // "{f(0),f(1/9),f(2/9),f(1/3),f(4/9),f(5/9),f(2/3),f(7/9),f(8/9),f(1)}"); check("Array(f, 5, {0,Pi/2})", // "{f(0),f(Pi/8),f(Pi/4),f(3/8*Pi),f(Pi/2)}"); check("Array(Sin(2*#) - Cos(3*#) &, 5, {0,Pi/2})", // "{-1,1/Sqrt(2)-Sqrt(2-Sqrt(2))/2,1+1/Sqrt(2),1/Sqrt(2)+Sqrt(2+Sqrt(2))/2,0}"); check("Array(f, -10, {0,1})", // "Array(f,-10,{0,1})"); check("Array(f, 5, a)", // "{f(a),f(1+a),f(2+a),f(3+a),f(4+a)}"); check("Array(f, 5, a, g)", // "g(f(a),f(1+a),f(2+a),f(3+a),f(4+a))"); // TODO return 0 // check("Array(f,0,1,Plus)", // // "0"); check("m=Array(Greater, {4, 4})", // "{{False,False,False,False},{True,False,False,False},{True,True,False,False},{True,True,True,False}}"); check("Boole(m)", // "{{0,0,0,0},{1,0,0,0},{1,1,0,0},{1,1,1,0}}"); check("Array(11,10)", // "{11[1],11[2],11[3],11[4],11[5],11[6],11[7],11[8],11[9],11[10]}"); check("Array(Cos(#1/4)&,12,-1)", // "{Cos(1/4),1,Cos(1/4),Cos(1/2),Cos(3/4),Cos(1),Cos(5/4),Cos(3/2),Cos(7/4),Cos(2),Cos(\n" + "9/4),Cos(5/2)}"); check("Array(Cos(#1/4)&,12)", // "{Cos(1/4),Cos(1/2),Cos(3/4),Cos(1),Cos(5/4),Cos(3/2),Cos(7/4),Cos(2),Cos(9/4),Cos(\n" + "5/2),Cos(11/4),Cos(3)}"); check("Array(Cos(#/4)&, 12, 4)", // "{Cos(1),Cos(5/4),Cos(3/2),Cos(7/4),Cos(2),Cos(9/4),Cos(5/2),Cos(11/4),Cos(3),Cos(\n" + "13/4),Cos(7/2),Cos(15/4)}"); check("Array(Cos(#/4)&, 12, 4, Min)", // "Cos(13/4)"); check("Array(f, {2, 3}, 1, Plus)", // "f(1,1)+f(1,2)+f(1,3)+f(2,1)+f(2,2)+f(2,3)"); check("Array(f, {2, 3}, {1, 2, 3})", // "Array(f,{2,3},{1,2,3})"); check("Array(f, 4)", // "{f(1),f(2),f(3),f(4)}"); check("Array(f, 10, 0)", // "{f(0),f(1),f(2),f(3),f(4),f(5),f(6),f(7),f(8),f(9)}"); check("Array(f, {2, 3})", // "{{f(1,1),f(1,2),f(1,3)},{f(2,1),f(2,2),f(2,3)}}"); check("Array(f, {2, 3}, {4, 6})", // "{{f(4,6),f(4,7),f(4,8)},{f(5,6),f(5,7),f(5,8)}}"); check("Array(f, {2, 3}, {0, 4})", // "{{f(0,4),f(0,5),f(0,6)},{f(1,4),f(1,5),f(1,6)}}"); // TODO implement other non-integer based iterators // check("Array[f, 10, {0, 1}]", ""); } @Test public void testArrayPad() { // display error messages: Maximum AST dimension 4294967296 exceeded check("ArrayPad({{1,0},{0,1}}, 2147483647)", // "ArrayPad(\n" // + "{{1,0},\n" // + " {0,1}},2147483647)"); // display error messages: Maximum AST dimension 4294967296 exceeded check("ArrayPad(E^(I*1/3*Pi),2147483647,2*Pi)", // "ArrayPad(E^(I*1/3*Pi),2147483647,2*Pi)"); check("ArrayPad({a, b, c}, 1, x)", // "{x,a,b,c,x}"); check("ArrayPad({{1, 2}, {3, 4}}, {1,2})", // "{{0,0,0,0,0},{0,1,2,0,0},{0,3,4,0,0},{0,0,0,0,0},{0,0,0,0,0}}"); check("ArrayPad({{1, 2}, {3, 4}}, 2)", // "{{0,0,0,0,0,0},{0,0,0,0,0,0},{0,0,1,2,0,0},{0,0,3,4,0,0},{0,0,0,0,0,0},{0,0,0,0,\n" + "0,0}}"); check("ArrayPad({1, 2, 3}, {2,4})", // "{0,0,1,2,3,0,0,0,0}"); check("ArrayPad({1, 2, 3}, 1)", // "{0,1,2,3,0}"); check("ArrayPad({1, 2, 3}, 2, x)", // "{x,x,1,2,3,x,x}"); } @Test public void testArrayDepth() { check("ArrayDepth(Array(a, {4, 5, 2}))", // "3"); check("ArrayDepth({{a,b},{c,d}})", // "2"); check("ArrayDepth(x)", // "0"); check("ArrayDepth({{1, 2}, {3, 4}})", // "2"); check("ArrayDepth({1, 2, 3, 4})", // "1"); check("ArrayDepth({{a, b}, {c}})", // "1"); check("ArrayDepth(f(f(a, b), f(c, d)))", // "2"); check("ArrayDepth(Array(a, {4, 5, 2}))", // "3"); } @Test public void testArrayFlatten() { check( "s1 = SparseArray({i_, i_} -> i, {2, 2});\ns2 = SparseArray({i_, j_} /; Abs(i-j) == 1 -> i - j, {3, 3});", // ""); check("m = ArrayFlatten({{0, s1}, {-s2, 0}})", // "SparseArray(Number of elements: 6 Dimensions: {5,5} Default value: 0)"); check("m // MatrixForm", // "{{0,0,0,1,0},\n" // + " {0,0,0,0,2},\n" // + " {0,1,0,0,0},\n" // + " {-1,0,1,0,0},\n" // + " {0,-1,0,0,0}}"); check("s = SparseArray({i_, i_, j_, k_} -> i/(j+k-1), {3, 3, 2, 2});", // ""); check("ArrayFlatten(s) // MatrixForm", // "{{1,1/2,0,0,0,0},\n" // + " {1/2,1/3,0,0,0,0},\n" // + " {0,0,2,1,0,0},\n" // + " {0,0,1,2/3,0,0},\n" // + " {0,0,0,0,3,3/2},\n" // + " {0,0,0,0,3/2,1}}"); check("m = {{1,2},{3,4}}", // "{{1,2},{3,4}}"); check("n = {{1,2},{3,4},{5,6}}", // "{{1,2},{3,4},{5,6}}"); check("ArrayFlatten(Array(a, {1,2,3,4}))", // "{{a(1,1,1,1),a(1,1,1,2),a(1,1,1,3),a(1,1,1,4),a(1,2,1,1),a(1,2,1,2),a(1,2,1,3),a(\n" + "1,2,1,4)},{a(1,1,2,1),a(1,1,2,2),a(1,1,2,3),a(1,1,2,4),a(1,2,2,1),a(1,2,2,2),a(1,\n" + "2,2,3),a(1,2,2,4)},{a(1,1,3,1),a(1,1,3,2),a(1,1,3,3),a(1,1,3,4),a(1,2,3,1),a(1,2,\n" + "3,2),a(1,2,3,3),a(1,2,3,4)}}"); check("ArrayFlatten(Array(a, {1,2,3,4})) // Dimensions", // "{3,8}"); // check("ArrayFlatten(Array(a, {1,2,3,4,5}), 3)// Dimensions", // // "{1,2,3,4,5}"); // check("ArrayFlatten(Array(a, {1,2,3,4,5}), 3)", // // ""); // check("ArrayFlatten(Array(a, {1,2,3,4,5,6}), 3) // Dimensions", // // "{4,10,18}"); check("ArrayFlatten(Array(a, {1,2,3,4,5,6})) // Dimensions", // "{3,8,5,6}"); check("ArrayFlatten({{1,1,1}, {m, m,m}})", // "{{1,1,1,1,1,1},{1,2,1,2,1,2},{3,4,3,4,3,4}}"); check("ArrayFlatten({{1,n,3}, {m, m,4}})", // "{{1,1,1,2,3},{1,1,3,4,3},{1,1,5,6,3},{1,2,1,2,4},{3,4,3,4,4}}"); check("ArrayFlatten({{1,1,1}, {m, m,n}})", // "ArrayFlatten({{1,1,1},{{{1,2},{3,4}},{{1,2},{3,4}},{{1,2},{3,4},{5,6}}}})"); check("ArrayFlatten({{0, 0, 0}, {m, m, 0}})", // "{{0,0,0,0,0},{1,2,1,2,0},{3,4,3,4,0}}"); check("ArrayFlatten({{0, 0, m}, {m, m, 0}})", // "{{0,0,0,0,1,2},{0,0,0,0,3,4},{1,2,1,2,0,0},{3,4,3,4,0,0}}"); // message ArrayFlatten: The array depth of the expression at position 1 of // {{{{1,2},{3,4}},{{1,2},{3,4}},{{1,2},{3,4}}},{{{1,2},{3,4}},{{1,2},{3,4}}}} must be at least // equal to the specified rank 2. check("ArrayFlatten({{m, m, m}, {m, m}})", // "ArrayFlatten({{{{1,2},{3,4}},{{1,2},{3,4}},{{1,2},{3,4}}},{{{1,2},{3,4}},{{1,2},{\n" + "3,4}}}})"); check("ArrayFlatten({{m, m, m}, {m, m, m}})", // "{{1,2,1,2,1,2},{3,4,3,4,3,4},{1,2,1,2,1,2},{3,4,3,4,3,4}}"); } @Test public void testArrayQ() { check("ArrayQ({{a, b}, {c, d}}, 2, SymbolQ)", // "True"); check("ArrayQ(SparseArray({{1, 2} -> a, {2, 1} -> b}))", // "True"); check("ArrayQ(SparseArray({{1, 2} -> a, {2, 1} -> b}), 1)", // "False"); check("ArrayQ(SparseArray({{1, 2} -> a, {2, 1} -> b}), 2, SymbolQ)", // "False"); check("ArrayQ(SparseArray({{1, 1} -> a, {1, 2} -> b}), 2, SymbolQ)", // "True"); check("ArrayQ(SparseArray({1, 2}))", // "True"); check("ArrayQ({ })", // "True"); check("ArrayQ({1, 2, 3, 4})", // "True"); check("ArrayQ({1, 2, {3}, 4})", // "False"); check("ArrayQ({{1, 2}, {3}})", // "False"); check("ArrayQ({{1, 2}, {3, 4}})", // "True"); check("ArrayQ({1, 2, 3, 4}, 2)", // "False"); check("ArrayQ({{1, 2}, {3, 4}},2)", // "True"); check("ArrayQ({1, 2, 3, x}, 1, NumericQ)", // "False"); check("ArrayQ({1, 2, 3, 4}, 1, NumericQ)", // "True"); check("ArrayQ({{{E, 1}, {Pi, 2}}, {{Sin(1), Cos(2)}, {Sinh(1), Cosh(1)}}}, _, NumericQ)", // "True"); check("ArrayQ({1, 2., E, Pi + I}, 1)", // "True"); check("ArrayQ({{1,2},{3,4}},2,NumericQ)", // "True"); check("ArrayQ({{a, b}, {c, d}},2,SymbolQ)", // "True"); } @Test public void testArrayReshape() { check("ArrayReshape(SparseArray({1 -> 1, 4 -> 5}, 10), {2, 6}, x)", // "{{1,0,0,5,0,0},{0,0,0,0,x,x}}"); check("ArrayReshape({}, {})", // "0"); check("ArrayReshape({a,b,c}, { })", // "a"); check("ArrayReshape({}, {1,2,3})", // "{{{0,0,0},{0,0,0}}}"); check("ArrayReshape(Range(1000), {3, 2, 2})", // "{{{1,2},{3,4}},{{5,6},{7,8}},{{9,10},{11,12}}}"); check("ArrayReshape({a, b, c, d, e, f}, {2, 3})", // "{{a,b,c},{d,e,f}}"); check("ArrayReshape({a, b, c, d, e, f}, {2, 3, 1})", // "{{{a},{b},{c}},{{d},{e},{f}}}"); check("ArrayReshape(Range(24), {2, 3, 4})", // "{{{1,2,3,4},{5,6,7,8},{9,10,11,12}},{{13,14,15,16},{17,18,19,20},{21,22,23,24}}}"); check("ArrayReshape({a, b, c, d, e, f}, {2, 7})", // "{{a,b,c,d,e,f,0},{0,0,0,0,0,0,0}}"); check("ArrayReshape({a, b, c, d, e, f}, {2, 3, 3,2}, x)", // "{{{{a,b},{c,d},{e,f}},{{x,x},{x,x},{x,x}},{{x,x},{x,x},{x,x}}},{{{x,x},{x,x},{x,x}},{{x,x},{x,x},{x,x}},{{x,x},{x,x},{x,x}}}}"); } @Test public void testAssuming001() { check("Assuming(a < 0 && b > 0, Refine(HeavisideTheta(b, b, a)))", // "0"); check("$Assumptions = { x > 0 }", // "{x>0}"); check("Assuming(y>0, $Assumptions)", // "{x>0,y>0}"); check("Assuming(y>0, ConditionalExpression(y x^2, y>0)//Simplify)", // "x^2*y"); check("Assuming(a > 0, {Refine(Sqrt(a^2)), Integrate(x^a, {x, 0, 1})})", // "{a,1/(1+a)}"); check("Assuming(x>0, Simplify(Sqrt(x^2)))", // "x"); } @Test public void testAssuming002() { check("$Assumptions = Element(m, Matrices({4, 4}, Reals, Symmetric({1, 2})))", // "m∈Matrices({4,4},Reals,Symmetric({1,2}))"); check("TensorRank(m)", // "2"); check("Assuming(y>0, ConditionalExpression(y x^2, y>0)//Simplify)", // "x^2*y"); check("Assuming(a > 0, {Refine(Sqrt(a^2)), Integrate(x^a, {x, 0, 1})})", // "{a,1/(1+a)}"); check("Assuming(x>0, Simplify(Sqrt(x^2)))", // "x"); } @Test public void testAssuming003() { check("$Assumptions = Element(a | b | c, Vectors(3));", // ""); check("{TensorRank(a), TensorDimensions(b), TensorSymmetry(c)}", // "{1,{3},{}}"); } @Test public void testAtomQ() { check("AtomQ(<|\"a\"->1|> // Unevaluated)", // "False"); check("AtomQ(<|\"a\"->1|>)", // "True"); check("AtomQ(Sin(Pi))", // "True"); check("AtomQ(x)", // "True"); check("AtomQ(1.2)", // "True"); check("AtomQ(2 + I)", // "True"); check("AtomQ(2 / 3)", // "True"); check("AtomQ(x + y)", // "False"); } @Test public void testArithmeticGeometricMean() { check("N(ArithmeticGeometricMean(1 - I, 5/2 + I), 30)", // "1.83462883815328396810218573046+I*(-0.19146162519713708344049353505)"); check("N(ArithmeticGeometricMean(1,2), 20)", // "1.4567910310469068691"); check("N(ArithmeticGeometricMean(52,5),30)", // "21.8724836267417540342866215962"); check("ArithmeticGeometricMean(1/2,42.0)", // "11.34094"); check("ArithmeticGeometricMean({1.0, 2.0, 3.0, 4.0}, 42.0)", // "{12.874,14.88314,16.37375,17.62155}"); check("ArithmeticGeometricMean(a, 1/a)", // orderless "ArithmeticGeometricMean(1/a,a)"); check("ArithmeticGeometricMean(a, 0)", // "0"); check("ArithmeticGeometricMean(0, b)", // "0"); check("ArithmeticGeometricMean(d, d)", // "d"); check("ArithmeticGeometricMean({1.0, 2.0, 3.0}, 5)", // "{2.60401,3.329,3.93624}"); check("ArithmeticGeometricMean(1 - I, 2.5 + I)", // "1.83463+I*(-0.191462)"); } @Test public void testAttributes() { check("Attributes(fun) = {ReadProtected, Protected}", // "{ReadProtected,Protected}"); check("Attributes(Plus)", // "{Flat,Listable,NumericFunction,OneIdentity,Orderless,Protected}"); } @Test public void testBeginPackage() { check("BeginPackage(\"test`\")", // ""); check("Context( )", // "test`"); check("$ContextPath", // "{test`,System`}"); check("testit::usage = \"testit(x) gives x^2\"", // "testit(x) gives x^2"); check("testit(x_) := x^2 ", // ""); check("xxx", // "xxx"); check("testit(12)", // "144"); check("Begin(\"`Private`\")", // "test`Private`"); check("End( )", // "test`Private`"); check("EndPackage( )", // ""); check("$ContextPath", // "{test`,System`,Global`}"); check("Context( )", // "Global`"); // print usage message in console check("?testit", // ""); check("testit(12)", // "144"); check("xxx", // "xxx"); // file system disabled => Needs has no effect in this test check("BeginPackage(\"needed`\", {\"needit1`\", \"needit2`\"}) // InputForm", // "{Needs(\"needit1`\"),Needs(\"needit2`\")}"); } @Test public void testBeginPackageNested() { check("BeginPackage(\"test`\")", // ""); check("Context( )", // "test`"); check("$ContextPath", // "{test`,System`}"); check("testit::usage = \"testit(x) gives x^2\"", // "testit(x) gives x^2"); check("testit(x_) := x^2 ", // ""); check("Begin(\"`Private`\")", // "test`Private`"); check("test2(x_) := x^3 ", // ""); check("testit(12)", // "144"); check("Context( )", // "test`Private`"); check("$Context", // "test`Private`"); check("$ContextPath", // "{test`,System`}"); check("End( )", // "test`Private`"); check("$ContextPath", // "{test`,System`}"); check("Context( )", // "test`"); check("EndPackage( )", // ""); check("test`Private`test2(12)", // "1728"); check("$ContextPath", // "{test`,System`,Global`}"); check("Context( )", // "Global`"); // print usage message in console check("?testit", // ""); check("testit(12)", // "144"); } @Test public void testBaseDecode() { check( "ba1 = BaseEncode(StringToByteArray(\"Man is distinguished, not only by his reason, but by this singular passion from other animals, " + "which is a lust of the mind, that by a perseverance of delight in the continued and indefatigable " + "generation of knowledge, exceeds the short vehemence of any carnal pleasure.\")) ", // "TWFuIGlzIGRpc3Rpbmd1aXNoZWQsIG5vdCBvbmx5IGJ5IGhpcyByZWFzb24sIGJ1dCBieSB0aGlzIHNpbmd1bGFyIHBhc3Npb24gZnJvbSBvdGhlciBhbmltYWxzLCB3aGljaCBpcyBhIGx1c3Qgb2YgdGhlIG1pbmQsIHRoYXQgYnkgYSBwZXJzZXZlcmFuY2Ugb2YgZGVsaWdodCBpbiB0aGUgY29udGludWVkIGFuZCBpbmRlZmF0aWdhYmxlIGdlbmVyYXRpb24gb2Yga25vd2xlZGdlLCBleGNlZWRzIHRoZSBzaG9ydCB2ZWhlbWVuY2Ugb2YgYW55IGNhcm5hbCBwbGVhc3VyZS4="); check("ba2 = BaseDecode(ba1)", // "ByteArray[269 Bytes]"); check("ByteArrayToString(ba2)", // "Man is distinguished, not only by his reason, but by this singular passion from other animals, " + "which is a lust of the mind, that by a perseverance of delight in the continued and indefatigable " + "generation of knowledge, exceeds the short vehemence of any carnal pleasure."); } @Test public void testBaseEncode() { check( "BaseEncode(ByteArray({1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20})) ", // "AQIDBAUGBwgJCgsMDQ4PEBESExQ="); } @Test public void testBaseForm() { check("36^^zZz", // "46655"); check("BaseForm(46655, 36)", // "Subscript(zzz,36)"); check("16^^abcdefff", // "2882400255"); check("BaseForm(2882400255, 16)", // "Subscript(abcdefff,16)"); check("37^^abcdefff", // "Syntax error in line: 1 - Base 37^^... is invalid. Only bases between 1 and 36 are allowed\n" + "37^^abcdefff\n" + " ^"); check("16^^6z12xy", // "Syntax error in line: 1 - Number format error: 6z12xy\n" + "16^^6z12xy\n" + " ^"); } @Test public void testBegin() { // Begin: is not a valid context name. check("Begin(\"\")", // "Begin()"); check("Begin(\"mytest`\")", // "mytest`"); check("Context( )", // "mytest`"); check("$ContextPath", // "{System`,Global`}"); check("testit::usage = \"testit(x) gives x^2\"", // "testit(x) gives x^2"); check("testit(x_) := x^2 ", // ""); check("testit(12)", // "144"); check("End( )", // "mytest`"); check("$ContextPath", // "{System`,Global`}"); check("Context( )", // "Global`"); // print usage message in console check("?mytest`testit", // ""); check("mytest`testit(12)", // "144"); check("testit(12)", // "testit(12)"); } @Test public void testBellB() { check("BellB(1009,-9223372036854775807/9223372036854775808)", // "BellB(1009,-9223372036854775807/9223372036854775808)"); check("BellB(10007)", // "BellB(10007)"); check("BellB(1/2,z)", // "BellB(1/2,z)"); check("BellB(10,x)", // "x+511*x^2+9330*x^3+34105*x^4+42525*x^5+22827*x^6+5880*x^7+750*x^8+45*x^9+x^10"); check("BellB(0,z)", // "1"); check("BellB(1,z)", // "z"); check("BellB(42,0)", // "0"); check("BellB(25)", // "4638590332229999353"); check("BellB(n,0)", // "BellB(n,0)"); check("BellB(n,1)", // "BellB(n)"); check("BellB(5,x)", // "x+15*x^2+25*x^3+10*x^4+x^5"); check("BellB(5,x+y^2)", // "x+y^2+15*(x+y^2)^2+25*(x+y^2)^3+10*(x+y^2)^4+(x+y^2)^5"); check("Table(BellB(k), {k, 0, 14})", // "{1,1,2,5,15,52,203,877,4140,21147,115975,678570,4213597,27644437,190899322}"); check("BellB(10)", // "115975"); check("BellB(15)", // "1382958545"); check("BellB(100)", // "4758539127676483365879076884138720782636366968682561146661633463755911449789244\\\n" + "2622672724044217756306953557882560751"); check("BellB({1,2,3,4,5,6})", "{1,2,5,15,52,203}"); } @Test public void testBellY() { // check("x + Sum(x^m/(m!*(m - 1)!) * BellY(Table({(m + k - 2)!, -(k - 1)! * c(k)}, {k, 2, m})), // {m, 2, 4}) ", // // // ""); // display error messages: Polynomial degree 2147483647 exceeded check("BellY(2147483647,3,{x,-3,-1/2})", // "BellY(2147483647,3,{x,-3,-1/2})"); // message Polynomial degree 1009 exceeded check("BellY(1009,19,{-1/2,-2,3})", // "BellY(1009,19,{-1/2,-2,3})"); check("BellY(2,1,{1/2,0})", // "0"); check("BellY(5, 2, {})", // "0"); check("BellY(5, 2, {1})", // "0"); check("BellY(5, 2, {1,2})", // "0"); check("BellY(5, 2, {1,2,3})", // "60"); check("BellY(5, 8, {1,2,3})", // "0"); // https://en.wikipedia.org/wiki/Bell_polynomials check("BellY(6, 2, {x1, x2, x3, x4, x5})", // "10*x3^2+15*x2*x4+6*x1*x5"); check("BellY(6, 3, {x1, x2, x3, x4})", // "15*x2^3+60*x1*x2*x3+15*x1^2*x4"); check("BellY(4, 2, {x1, x2, x3})", // "3*x2^2+4*x1*x3"); check("With({n = 7, k = 2}, BellY(n, k, Array(x, n)))", // "35*x(3)*x(4)+21*x(2)*x(5)+7*x(1)*x(6)"); } @Test public void testBernoulliB() { check("N(BernoulliB(0) )", // "1.0"); checkNumeric("Table(BernoulliB(n, z), {n, 0, 5}, {z, -2, 2,0.25}) // N", // "{{1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0},{-2.5,-2.25,-2.0,-1.75,-1.5,-1.25,-1.0,-0.75,-0.5,-0.25,0.0,0.25,0.5,0.75,1.0,1.25,1.5},{6.166666666666668,4.979166666666667,3.9166666666666674,2.979166666666667,2.1666666666666665,1.4791666666666665,0.9166666666666667,0.47916666666666663,0.16666666666666666,-0.02083333333333333,-0.08333333333333333,-0.02083333333333333,0.16666666666666666,0.47916666666666663,0.9166666666666667,1.4791666666666665,2.1666666666666665},{-15.0,-10.828125,-7.5,-4.921875,-3.0,-1.6406249999999998,-0.75,-0.234375,0.0,0.04687499999999999,0.0,-0.046875,0.0,0.234375,0.75,1.6406249999999998,3.0},{35.96666666666667,23.126822916666665,14.029166666666667,7.876822916666668,3.966666666666667,1.6893229166666666,0.5291666666666667,0.06432291666666666,-0.03333333333333333,0.0018229166666666665,0.02916666666666666,0.0018229166666666665,-0.03333333333333333,0.06432291666666666,0.5291666666666667,1.6893229166666666,3.966666666666667},{-85.0,-48.5009765625,-25.625000000000004,-12.202148437499998,-5.0,-1.6064453124999998,-0.3125,0.0048828125,0.0,-0.02441406249999999,0.0,0.02441406249999999,0.0,-0.0048828125,0.3125,1.6064453124999998,5.0}}"); check("N(BernoulliB(50),50)", // "7500866746076964366855720.0757575757575757575757575"); check("N(BernoulliB(50),50)//IntegerPart", // "7500866746076964366855720"); // slow check("BernoulliB(2009,-1+Sqrt(2))", // "Hold(BernoulliB(2009,-1+Sqrt(2)))"); // message: Non-negative machine-sized integer expected at position 1 in // BernoulliB(-2147483648,1/2). check("BernoulliB(-2147483648,1/2)", // "BernoulliB(-2147483648,1/2)"); // message: Non-negative machine-sized integer expected at position 1 in // BernoulliB(-3). check("BernoulliB(-3)", // "BernoulliB(-3)"); check("BernoulliB(3,-2)", // "-15"); check("BernoulliB(4, 9)", // "155519/30"); check("BernoulliB(4, -9)", // "242999/30"); check("BernoulliB(18, 1/2)", // "-5749691557/104595456"); check("BernoulliB(17, 1/2)", // "0"); check("BernoulliB(n, 0)", // "BernoulliB(n)"); check("BernoulliB(18, 1)", // "43867/798"); check("BernoulliB(51)", // "0"); check("BernoulliB(42)", // "1520097643918070802691/1806"); check("BernoulliB(2)", // "1/6"); check("Table(BernoulliB(k), {k, 0, 10})", // "{1,-1/2,1/6,0,-1/30,0,1/42,0,-1/30,0,5/66}"); // http://fungrim.org/entry/555e10/ check("Table(BernoulliB(k,x), {k, 0, 5})", // "{1,-1/2+x,1/6-x+x^2,x/2-3/2*x^2+x^3,-1/30+x^2-2*x^3+x^4,-x/6+5/3*x^3-5/2*x^4+x^5}"); } @Test public void testBeta() { // https://functions.wolfram.com/GammaBetaErf/Beta4/03/01/03/0003/ check("Beta(z, 1, a, 3)", // "Beta(a,3)-Beta(z,a,3)"); // TODO https://github.com/mtommila/apfloat/issues/31 // checkNumeric("Beta(-0.5,101/(1+Sqrt(5)),1317624576693539401)", // // ""); check("N(Beta(22/10, 33/10), 50)", // "0.056485691373282566807051754004491429369537777015239"); checkNumeric("Beta({-1},7*Sqrt(2),2.718281828459045)", // "{0.291809067060784+I*(-0.09532667408582604)}"); check("N(Beta(13/2, 7/2, 9/2), 50)", // "0.007669903939428206148590437947459723838371995+I*(-35239.47067974661869463578515152264883317438910642)"); check("N(Beta(1/4, 1/3, 1/2, 3/2), 50)", // "0.13027275197090082754239201460417447494316441645475"); check("Beta(z, 1, 12)", // "1/12*(1-(1-z)^12)"); check("Beta( 2.5 + I, 1 - I, 0.5)", // "1.83058+I*3.75044"); check("Beta(0.5, 2.5 + I, 1 - I)", // "0.0506278+I*(-0.0346442)"); check("Beta(0.5, 3.2, 1.5)", // "0.0266833"); check("Beta(2.5 + I, 1 - I)", // "0.0831078+I*0.142164"); check("Beta(1,b) // FunctionExpand", // "1/b"); check("Beta(10,b) // FunctionExpand", // "362880/(b*(1+b)*(2+b)*(3+b)*(4+b)*(5+b)*(6+b)*(7+b)*(8+b)*(9+b))"); check("Beta(2.3, 3.2)", // "0.0540298"); check("Beta(a, a+1)", // "1/(a*(1+a)*CatalanNumber(a))"); check("Beta(b-1, b)", // "1/((-1+b)*b*CatalanNumber(-1+b))"); check("Beta(5,4)", // "1/280"); check("Beta(5/2,7/2)", // "3/256*Pi"); check("Beta(2.3,3.2)", // "0.0540298"); // check("Beta(2.5+I,1-I)", "0.05403"); check("Beta(a, 0)", // "ComplexInfinity"); check("Beta(0,b)", // "ComplexInfinity"); check("Beta(-n-4, n+1)", // "0"); } @Test public void testBetaRegularized() { // 4 args checkNumeric("BetaRegularized({2, 3, 5, 7}, 2, 7/2,1.5)", // "{0.0,I*(-103.37304852766407),I*(-1069.1375512159648),I*(-4377.740983381134)}"); // 3 args check("N(BetaRegularized(15/17, 5, 1), 50)", // "0.53482498589646703858205438998434349374620120195202"); check("BetaRegularized(0.211111111111111111, 5, 1)", // "0.000419329539873664243"); checkNumeric("N(BetaRegularized(23/47, 5 - I, 2))", // "0.0847097829416838+I*0.05452582633879841"); checkNumeric("BetaRegularized({2, 3, 5, 7}, 2.5, 0.5)", // "{1.0000000000000002+I*(-2.661837923372428),1.0000000000000002+I*(-5.407884471224193),1.0000000000000002+I*(-13.256264306821171),1.0000000000000002+I*(-24.415962537061436)}"); check("BetaRegularized(0,0,0)", // "Indeterminate"); check("BetaRegularized(2 , 2 , 3)", // "8"); check("BetaRegularized(2 , 7 , 17)", // "5512320"); check("BetaRegularized(2 , 7 , -17)", // "0"); // see github #203 check("BetaRegularized(1.0000001,1,1)", // "1.0"); check("BetaRegularized(-0.000000001,1,1)", // "-1.*10^-9"); check("BetaRegularized(0.9768451023103443, 337.0, 0.5)", // "0.0000712171"); check("BetaRegularized(2,Quantity(1.2,\"m\"),1009)", // "BetaRegularized(2,1.2[m],1009)"); check("BetaRegularized(0.99,ByteArray(1),1009)", // "BetaRegularized(0.99,ByteArray(1),1009)"); // slow check("BetaRegularized({0.25,0.5,0.75},0.5,2147483647)", // "{BetaRegularized(0.25,0.5,2.14748*10^9),BetaRegularized(0.5,0.5,2.14748*10^9),BetaRegularized(0.75,0.5,2.14748*10^9)}"); checkNumeric("BetaRegularized(-1.5707963267948966,-I,-I)", // "0.8506422193103679+I*(-1.41891817181187441)"); check("BetaRegularized(2,-2147483648,17)", // "1"); check("BetaRegularized(0,1+I,b)", // "0"); check("BetaRegularized(0,-1+I,b)", // "ComplexInfinity"); check("BetaRegularized(z,a,-10)", // "0"); check("BetaRegularized(1,a,42)", // "1"); // TODO get Indeterminate check("BetaRegularized(10^20., 10^30., 10.^20.)", // "BetaRegularized(1.*10^20,1.*10^30,1.*10^20)"); check("BetaRegularized({0.25, 0.5, 0.75}, 2.5, 0.5)", // "{0.0117248,0.0755868,0.25317}"); check("BetaRegularized(0.99 , 255.0 , 2.0)", // "0.273655"); } @Test public void testBlankSequence() { check("Clear(f);f(___,y__?(#>2&)):={y}", // ""); check("{f(2,3),f(1,1,1,2),f(112,1,1,3,4)}", // "{{3},f(1,1,1,2),{3,4}}"); check("Clear(f);f(x__Integer)=2", // "2"); check("{f(2,3),f(a,2),f(2,a),f(2)}", // "{2,f(a,2),f(2,a),2}"); check("Clear(f);f(x__Real) := Plus(x)/Length({x})", // ""); check("{f(1.0,4.0),f(2,2),f(1.0,a)}", // "{2.5,f(2,2),f(1.0,a)}"); check("Clear(f);f(x__,y__,z__):={x,y,z}/;Print({x},{y},{z})", // ""); check("f(a,b,c,d,e)", "f(a,b,c,d,e)"); // print the possible matches // {a}{b}{c,d,e} // {a}{b,c}{d,e} // {a,b}{c}{d,e} // {a}{b,c,d}{e} // {a,b}{c,d}{e} // {a,b,c}{d}{e} System.out.println("-------------"); check("g(x___,y___,z___):={x,y,z}/;Print({x},{y},{z})", // ""); check("g(a,b,c,d,e)", "g(a,b,c,d,e)"); // print the possible matches // {}{}{a,b,c,d,e} // {a}{b}{c,d,e} // {}{a,b,c}{d,e} // {a}{b,c}{d,e} // {a,b}{c}{d,e} // {a,b,c}{}{d,e} // {}{a,b,c,d}{e} // {a}{b,c,d}{e} // {a,b}{c,d}{e} // {a,b,c}{d}{e} // {a,b,c,d}{}{e} // {}{a,b,c,d,e}{} // {a}{b,c,d,e}{} // {a,b}{c,d,e}{} // {a,b,c}{d,e}{} // {a,b,c,d}{e}{} // {a,b,c,d,e}{}{} } @Test public void testBlock() { // Rubi rules use Block variable names in "sub-rules": check("Integrate(E^(E^x + x), x)", // "E^E^x"); // http://oeis.org/A005132 - Recaman's sequence check( "f(s_List) := Block({a = s[[-1]], len = Length@s}, Append(s, If(a > len && !MemberQ(s, a - len), a - len, a + len))); Nest(f, {0}, 70)", // "{0,1,3,6,2,7,13,20,12,21,11,22,10,23,9,24,8,25,43,62,42,63,41,18,42,17,43,16,44,\n" + "15,45,14,46,79,113,78,114,77,39,78,38,79,37,80,36,81,35,82,34,83,33,84,32,85,31,\n" + "86,30,87,29,88,28,89,27,90,26,91,157,224,156,225,155}"); check("blck=Block({i=10}, i=i+1; Return(i))", // "11"); check("xm=10;Block({xm=xm}, xm=xm+1;Print(xm));xm", // "10"); check("Block({testVar}, testVar=2222;testVar)", // "2222"); check("testVar=1111; Block({testVar}, testVar)", // "1111"); check("Block({x=y,y=z,z=3}, Print({Hold(x),Hold(y),Hold(z)});{x,y,z})", // "{3,3,3}"); check("Block({x,f}, f(0)=0;f(x_):=f(x-1)+x;f(3))", // "6"); check("f(3)", // "f(3)"); check("m=i^2;Block({i = a}, i + m)", // "a+a^2"); check("m=i^2;Module({i = a}, i + m)", // "a+i^2"); check("h(x_):=Block({t}, t^2 - 1 /; (t = x - 4) > 1); h(10)", // "35"); check("h(x_):=Block({t}, t^2 - 1 /; (t = x - 4) > 1); h(5)", // "h(5)"); } @Test public void testBinaryDistance() { check("BinaryDistance(SparseArray({1, 2, 3, 4, 5}), SparseArray({1, 2, 3, 4, 5}))", // "1"); check("BinaryDistance({1, 2, 3, 4, 5}, {1, 2, 3, 4, 5})", // "1"); check("BinaryDistance({1, 2, 3, 4, 5}, {1, 2, 3, 4, -5})", // "0"); check("BinaryDistance({1, 2, 3, 4, 5}, {1, 2, 3, 4, 5.0})", // "0"); } @Test public void testBinCounts() { check("BinCounts({{1,0}, {0,1}},-Infinity)", // "BinCounts({{1,0},{0,1}},-Infinity)"); check("BinCounts({1,2,3,4,5},{1,7,2})", // "{2,2,1}"); check("BinCounts({1,2,3,4,5},{1,7,3})", // "{3,2}"); check("BinCounts({1,2,3,4,5,6,7,8,9,10,11,12,13},{1,13,4})", // "{4,4,4}"); check("BinCounts({2,-1,a,b},{-1,3,1})", // "{1,0,0,1}"); check("BinCounts({3/4,-2},{-1,3,1})", // "{0,1,0,0}"); check("BinCounts({3/4},{1,3,1})", // "{0,0}"); check("BinCounts({3/4} )", // "{1}"); check("BinCounts({1,2,3,4,5})", // "{0,1,1,1,1,1}"); check("BinCounts({1,2,3,4,5},3)", // "{2,3}"); check("BinCounts({1,2,3,4,5},4)", // "{3,2}"); check("BinCounts({1,2,3,4,5},5)", // "{4,1}"); check("BinCounts({1,2,3,4,5},10)", // "{5}"); check("BinCounts({0.04, 0.75, 0.3333, 0.03344, 0.9999},0)", // "BinCounts({0.04,0.75,0.3333,0.03344,0.9999},0)"); check("BinCounts({1,2,3,4,5},{3,3,-1})", // "BinCounts({1,2,3,4,5},{3,3,-1})"); check("BinCounts({1,2,3,4,5},{3,3,1})", // "{}"); check("BinCounts({0.04, 0.75, 0.3333, 0.03344, 0.9999},0.1)", // "{2,0,0,1,0,0,0,1,0,1}"); check("BinCounts({0.04, 0.75, 0.3333, 0.03344, 0.9999},-0.1)", // "BinCounts({0.04,0.75,0.3333,0.03344,0.9999},-0.1)"); check("BinCounts({1, 2, 3, 4, 5})", // "{0,1,1,1,1,1}"); check("BinCounts({1.5, 3, a, 2.5, 1, I}, 2)", // "{2,2}"); check("BinCounts({1, 3, 2, 1, 4, 5, 6, 2}, {0, 10, 1})", // "{0,2,2,1,1,1,1,0,0,0}"); check("BinCounts({1, 3, 2, 1, 4, 5, 6, 2}, 2)", // "{2,3,2,1}"); check("BinCounts({1.5, 3, N(3, 20), 2.5, 1, E}, 2)", // "{2,4}"); } @Test public void testBinomial() { // issue #946 // message Binomial: BigInteger bit length `1` exceeded. check("Binomial(12!, 9!)", // "Binomial(12!,9!)"); check("N(Binomial(7/3, 1/5), 20)", // "1.3331254244650286522"); check("Binomial(8.2211111111115000000, 4) ", // "80.344138315176948065"); check("Binomial(8.5, -4.2)", // "0.0000604992"); check("N(Binomial(7/3, 1/5), 20)", // "1.3331254244650286522"); check("Binomial(2. + I, 7 - 3*I)", // "-75.46835+I*106.8153"); check("Binomial(a,b,c)", // "Binomial(a,b,c)"); check("Binomial(a)", // "Binomial(a)"); check("Factorial(10)/Factorial(3)", // "604800"); check("Gamma(11)/Gamma(4)", // "604800"); check("Binomial(4.5, 3.76)", // "3.39253"); check("Binomial(2+k, k)", // "1/2*(1+k)*(2+k)"); check("Binomial(5+k, k)", // "1/120*(1+k)*(2+k)*(3+k)*(4+k)*(5+k)"); check("Binomial(-200,-100)", // "0"); check("Binomial(-100,-200)", // "45274257328051640582702088538742081937252294837706668420660"); check("Binomial(k, -1)", // "0"); check("Binomial(3,3)", // "1"); check("Binomial(0,0)", // "1"); check("Binomial(-3,-5)", // "6"); check("Binomial(Infinity, 0)", // "1"); check("Binomial(-Infinity, {-3,-2,-1,0,1,2,3,4,5,6})", // "{0,0,0,1,-Infinity,Infinity,-Infinity,Infinity,-Infinity,Binomial(-Infinity,6)}"); check("Binomial(-Infinity, -12)", // "0"); check("Binomial(Infinity, {-3,-2,-1,0,1,2,3,4,5,6})", // "{0,0,0,1,Infinity,Infinity,Infinity,Infinity,Infinity,Binomial(Infinity,6)}"); check("Binomial(Infinity, -12)", // "0"); check("Binomial({2, 3, 5, 7, 11}, 3)", // "{0,1,10,35,165}"); check( "With({eps = 10^-6.}, \n" + " Table(Binomial(-3 - p eps, -5 - eps), {p, {-3, -2, -1, \n" + " 1, 2, 3, 4}}))", // "{-2.0,-3.0,-6.0,6.0,3.0,2.0,1.5}"); check("Binomial(k, -1)", // "0"); check("Binomial(k, -1.4)", // "Binomial(k,-1.4)"); check("Binomial(k, 0)", // "1"); check("Binomial(40,1)", // "40"); check("Binomial(40.0,1.0)", // "40.0"); check("Binomial(40.3,1.2)", // "76.37683"); check("Binomial(n, n+1)", // "0"); check("Binomial(n, n+2)", // "0"); check("Binomial(4,2)", // "6"); check("Binomial(5,3)", // "10"); check("Binomial(n0, 2)", // "1/2*(-1+n0)*n0"); check("Binomial(k/3, k)", // "Binomial(k/3,k)"); check("Binomial(0, 0)", // "1"); check("Binomial(1000, 500)", // "2702882409454365695156146936259752754961520084465482870073928751066254287055221\\\n" + "9389861248392450237016536260608502154610480220975005067991754989421969951847542\\\n" + "3665484263751733356162464079737887344364574161119497604571044985756287880514600\\\n" + "994219426752366915856603136862602484428109296905863799821216320"); check("Binomial(n0, n0)", // "1"); check("Binomial(n0, 0)", // "1"); check("Binomial(n0, n0-1)", // "n0"); check("Binomial(n0, 1)", // "n0"); check("Binomial(n0, 2)", // "1/2*(-1+n0)*n0"); check("Binomial(n0, 3)", // "1/6*(-2+n0)*(-1+n0)*n0"); // check("Binomial(-3, -5)", "0"); check("Binomial(k, 2)", // "1/2*(-1+k)*k"); check("Binomial(k, 5)", // "1/120*(-4+k)*(-3+k)*(-2+k)*(-1+k)*k"); check("Binomial(k, 6)", // "Binomial(k,6)"); } @Test public void testBitLength() { check("BitLength(1023)", // "10"); check("BitLength(100) ", // "7"); check("BitLength(-5)", // "3"); check("BitLength(0)", // "0"); check("BitLength(2^123-1)", // "123"); check("BitLength(-(2^123-1))", // "123"); } @Test public void testBrayCurtisDistance() { check("-1*{10.5, 10} ", // "{-10.5,-10}"); check("{-1, -1} - 1 * {10.5, 10} ", // "{-11.5,-11}"); check("{-1, -1} + {10.5, 10} ", // "{9.5,9}"); check("BrayCurtisDistance({-1, -1}, {10.5, 10})", // "1.21622"); check("BrayCurtisDistance({x,-2,3},{x,5,-3})", // "13/(3+2*Abs(x))"); check("BrayCurtisDistance({-1, -1}, {10, 10})", // "11/9"); } @Test public void testBreak() { check("n = 0", // "0"); check("While(True, If(n>10, Break()); n=n+1)", // ""); check("n", // "11"); } @Test public void testByteArray() { // message ByteArray: The argument at position 1 in ByteArray(asy) should be a vector of // unsigned byte values or a Base64 encoded string. check("ba=ByteArray(\"asy\")", // "ByteArray(asy)"); check("ByteArray({})", // "{}"); check("ba=ByteArray(\"AQIDBAUGBwg=\")", // "ByteArray[8 Bytes]"); check("Normal(ba)", // "{1,2,3,4,5,6,7,8}"); } @Test public void testCancel() { check("Simplify(((1 + Sqrt(5))/2)^7 + (-(1 + Sqrt(5))/2)^(-7))", // // TODO 29 "128/(-1-Sqrt(5))^7+(1+Sqrt(5))^7/128"); check("Cancel((1/8-Cos(2/7*Pi)/8) / (8-8*Cos(2/7*Pi)))", // "1/64"); // check("Factor(y*(2*3*x+Pi*x))", // // "(6+Pi)*x*y"); check("Cancel((x*Log(2))/(2*3*x+Pi*x))", // "Log(2)/(6+Pi)"); check("Cancel((x*Log(2))/(2*3*x^2+Pi*x^5))", // "Log(2)/(x*(6+Pi*x^3))"); check("Cancel((x^4*Log(2))/(2*3*x^2+Pi*x^5))", // "(x^2*Log(2))/(6+Pi*x^3)"); check("Cancel((x^7*Log(2))/(2*3*x+Pi*x))", // "(x^6*Log(2))/(6+Pi)"); check("Cancel((c*d+d^2*x)^2/d^3 )", // "(c+d*x)^2/d"); check("Cancel((c*d+d^2*x)^2/d^2 )", // "(c+d*x)^2"); // github #188 check("Cancel(4/n^4)", // "4/n^4"); check("Cancel(n^4/4)", // "n^4/4"); check("Cancel(n^4/4+n^3/2+n^2/4)", // "n^2/4+n^3/2+n^4/4"); check("n^4/4+n^3/2+n^2/4", // "n^2/4+n^3/2+n^4/4"); // check("Cancel(((1+x)*f(x))/x^2)", // // "x/(-1+x)"); // check("Cancel((x*(1+x))/(-1+x^2))", // // "x/(-1+x)"); // see rubi rule 27: check("Cancel(d/(c*d+d^2*x))", // "1/(c+d*x)"); check("Cancel((c*d+d^2*x)/d)", // "c+d*x"); check("Cancel((c*d+d^2*x)^(-1)/(d^2)^(-1) )", // "d/(c+d*x)"); check("Cancel((c*d+d^2*x) /(d^2))", // "(c+d*x)/d"); check("Cancel((c*d+d^2*x)^(-2)/(d^2)^(-1) )", // "1/(c+d*x)^2"); check("Cancel((c*d+d^2*x)^2/d^2 )", // "(c+d*x)^2"); check("Cancel(x / x ^ 2)", // "1/x"); check("Cancel(x / x ^ 2 + y / y ^ 2)", // "1/x+1/y"); check("Cancel(f(x) / x + x * f(x) / x ^ 2)", // "(2*f(x))/x"); check("Cancel((x - a)/(x^2 - a^2) == 0 && (x^2 - 2*x + 1)/(x - 1) >= 0)", // "1/(a+x)==0&&x>=1"); check("9+3*x+x^2", "9+3*x+x^2"); check("(9+3*x+x^2)*(3+x)^(-1)", // "(9+3*x+x^2)/(3+x)"); check("1+(9+3*x+x^2)*(3+x)^(-1)+x+(x+y)^(-1)", // "1+x+(9+3*x+x^2)/(3+x)+1/(x+y)"); check("Cancel(x / x ^ 2)", // "1/x"); check("Cancel(f(x) / x + x * f(x) / x ^ 2)", // "(2*f(x))/x"); check("Cancel(x / x ^ 2 + y / y ^ 2)", // "1/x+1/y"); check("Cancel((x^2 - 1)/(x - 1))", // "1+x"); check("Cancel((x - y)/(x^2 - y^2) + (x^3 - 27)/(x^2 - 9) + (x^3 + 1)/(x^2 - x + 1))", // "1+x+(9+3*x+x^2)/(3+x)-1/(-x-y)"); check("cancel((x - 1)/(x^2 - 1) + (x - 2)/(x^2 - 4))", // "1/(1+x)+1/(2+x)"); check("together((x - 1)/(x^2 - 1) + (x - 2)/(x^2 - 4))", // "(3+2*x)/((1+x)*(2+x))"); check("Cancel(x/(1+x^3))", // "x/(1+x^3)"); check("Together((x - 1)/(x^2 - 1) + (x - 2)/(x^2 - 4))", // "(3+2*x)/((1+x)*(2+x))"); } @Test public void testCarlsonRC() { // TODO apfloat complex numbers // check( // "N(CarlsonRC(Exp(I*Pi/7), Exp(I*Pi/3)),30)", // // "0.918779490030764719521186118777-I*0.414652997036584002880355293518"); check("N( Exp(I*Pi/7) ,30)", // "0.900968867902419126236102319507+I*0.433883739117558120475768332848"); check("N( Exp(I*Pi/3) ,30)", // "0.5+I*0.866025403784438646763723170752"); check("CarlsonRC(4., 5)", // "0.463648"); check("CarlsonRC(3, 1.234567890123456789012345)", // "0.762626353743812501642456"); check("CarlsonRC(3, 1.2345678901234567890123456789012345)", // "0.76262635374381250164245591358368878"); check("CarlsonRC(y,y)", // "Piecewise({{ComplexInfinity,Re(y)<=0&&Im(y)==0}},1/Sqrt(y))"); check("CarlsonRC(42,42)", // "1/Sqrt(42)"); check("CarlsonRC(4., 5)", // "0.463648"); check("CarlsonRC(Exp(I*Pi/7.0), Exp(I*Pi/3.0))", // "0.918779+I*(-0.414653)"); } @Test public void testCarlsonRD() { check("CarlsonRD(2., 3.,5.0)", // "0.133211"); check("CarlsonRD(1.0+I, 1-2*I, 5.0)", // "0.168723+I*0.0201344"); } @Test public void testCarlsonRF() { check("CarlsonRF(x,x,x)", // "1/Sqrt(x)"); check("CarlsonRF(1.,2.,3.)", // "0.726946"); check("CarlsonRF(I, 1-2*I, 3.0+I)", // "0.791737+I*(-0.0471835)"); } @Test public void testCarlsonRG() { check("CarlsonRG(x,x,y)", // "1/2*(Sqrt(y)+x*CarlsonRF(x,x,y))"); check("CarlsonRG(3.,5.,11.0)", // "2.48078"); check("CarlsonRG(I, 1-2*I, 3.0+I)", // "1.18073+I*0.0126244"); } @Test public void testCarlsonRJ() { check("CarlsonRJ(2., 3., 5., 7.2)", // "0.104459"); check("CarlsonRJ(0.7-0.2*I, 4, 2.0+I/3, 0.7*I)", // "0.533311+I*(-0.52701)"); } @Test public void testCarmichaelLambda() { check("CarmichaelLambda(-n)", // "CarmichaelLambda(n)"); check("CarmichaelLambda(0)", // "0"); check("CarmichaelLambda(1)", // "1"); check("CarmichaelLambda(2)", // "1"); check("CarmichaelLambda(10)", // "4"); check("CarmichaelLambda(15)", // "4"); check("CarmichaelLambda(11)", // "10"); check("CarmichaelLambda(35)", // "12"); check("CarmichaelLambda(50)", // "20"); check("Table(CarmichaelLambda(-k), {k, 12})", // "{1,1,2,2,4,2,6,2,6,4,10,2}"); check("Table(CarmichaelLambda(10^k), {k, 0, 10})", // "{1,4,20,100,500,5000,50000,500000,5000000,50000000,500000000}"); } @Test public void testCases() { // check( // " t : {__Integer} :> t^2", // // "(t:{__Integer}):>t^2"); check("Cases({(c*x+d)^(1/3)}, " // + "y:(a_. x + b_.)^n_ /; FreeQ({a,b}, x) && Head(n) == Rational :> {y, a*x + b, Numerator(n), Denominator(n), a, b}, {0, Infinity})", // "{{(d+c*x)^(1/3),d+c*x,1,3,c,d}}"); check("Cases({b, 6, \\[Pi]}, _Symbol, Heads->True)", // "{List,b,Pi}"); check("Cases({b, 6, \\[Pi]}, _Symbol)", // "{b,Pi}"); check("Cases({x,-1,1,1},SparseArray({{1,0},{0,2}}))", // "{}"); check("Cases({{1, 2, 3}, a, {4, 5}}, t : {__Integer} :> t^2)", // "{{1,4,9},{16,25}}"); check("Cases({1,2,3,a}, _?NumberQ)", // "{1,2,3}"); check("Cases({-2,7,-1.2,0,-5-3*I}, _?Negative)", // "{-2,-1.2}"); check("Cases({{a, a}, {b, a}, {a, b, c}, {b, b}, {c, a}, {b, b, b}}, {__, a | b} | {c, __})", // "{{a,a},{b,a},{b,b},{c,a},{b,b,b}}"); check("Cases({{2,1,0},{3,2,0},{2,0,0},{3,3,1}}, {_, 1 | 2, _})", // "{{2,1,0},{3,2,0}}"); check("Cases({{a, a}, {b, a}, {a, b, c}, {b, b}, {c, a}, {b, b, b}}, {a|b, _})", // "{{a,a},{b,a},{b,b}}"); check("Cases({a, 1, 2.5, \"string\"}, _Integer|_Real)", // "{1,2.5}"); check("Cases(_Complex)[{1, 2*I, 3, 4-I, 5}]", // "{I*2,4-I}"); check("Cases(1, 2)", // "{}"); check("Cases(f(1, 2), 2)", // "{2}"); check("Cases(f(f(1, 2), f(2)), 2)", // "{}"); check("Cases(f(f(1, 2), f(2)), 2, 2)", // "{2,2}"); check("Cases(f(f(1, 2), f(2), 2), 2, Infinity)", // "{2,2,2}"); check("Cases({1, f(2), f(3, 3, 3), 4, f(5, 5)}, f(x__) :> Plus(x))", // "{2,9,10}"); check("Cases({1, f(2), f(3, 3, 3), 4, f(5, 5)}, f(x__) -> Plus(x))", // "{2,3,3,3,5,5}"); check("Cases(_Complex)[{1, 2*I, 3, 4-I, 5}]", // "{I*2,4-I}"); check("Cases({x, a, b, x, c}, Except(x))", // "{a,b,c}"); check("Cases({a, 0, b, 1, c, 2, 3}, Except(1, _Integer))", // "{0,2,3}"); check("Cases({1, 1, f(a), 2, 3, y, f(8), 9, f(10)}, _Integer)", // "{1,1,2,3,9}"); check("Cases({1, 1, f(a), 2, 3, y, f(8), 9, f(10)}, _Integer, -1)", // "{1,1,2,3,8,9,10}"); check("Cases({1, 1, f(a), 2, 3, y, f(8), 9, f(10)}, _Integer, -2)", // "{}"); check("Cases({1, 1, f(a), 2, 3, y, f(8), 9, f(10)}, _Integer, {0,4})", // "{1,1,2,3,8,9,10}"); check("Cases({1, 1, f(a), 2, 3, y, g(c,f(8)), 9, f(10)}, f(x_) -> x)", // "{a,10}"); check("Cases({1, 1, f(a), 2, 3, y, g(c,f(8)), 9, f(10)}, f(x_) -> x, -2)", // "{a,8,10}"); check("Cases({3, -4, 5, -2}, x_ /; x < 0)", // "{-4,-2}"); check("Cases({3, 4, x, x^2, x^3}, x^_)", // "{x^2,x^3}"); check("Cases({3, 4, x, x^2, x^3}, x^n_ -> n)", // "{2,3}"); check("Cases({{1, 2}, {2}, {3, 4, 1}, {5, 4}, {3, 3}}, {_, _})", // "{{1,2},{5,4},{3,3}}"); check("Cases({{1, 2}, {2}, {3, 4, 1}, {5, 4}, {3, 3}}, {a_, b_} -> a + b)", // "{3,9,6}"); check("Cases(Sqrt(Range(100)), _Integer, {1}, 3)", // "{1,2,3}"); } @Test public void testCatch() { check("Catch(f(Catch(Throw(a, u), u)), v)", // "f(a)"); check("Catch(f(Catch(Throw(a, u), v)), u)", // "a"); check("Catch(f(Catch(Throw(a, u), u)), v, f)", // "f(a)"); check("Catch(f(Catch(Throw(a, u), v)), u, f)", // "f(a,u)"); check("Catch(Scan(If(IntegerQ(#1),Null,Throw(False))&,{2,3});True)", // "True"); check("Catch(Scan(If(IntegerQ(#1),Null,Throw(False))&,{b+a});True)", // "False"); check("Catch(Scan(If(# > 5, Throw(#)) &, {2, 4, 6, 8}))", // "6"); check("Catch(a; b; Throw(c); d; e)", // "c"); check("$f(x_) := If(x > 10, Throw(overflow), x!);Catch($f(2) + $f(11))", // "Overflow"); check("$f(x_) := If(x > 10, Throw(overflow), x!);Catch($f(2) + $f(3))", // "8"); check("catch(do(If(i0! > 10^10, throw(i0)), {i0, 100}))", // "14"); check("Catch(If(# < 0, Throw(#)) & /@ {1, 2, 0, -1, 5, 6})", // "-1"); check("Catch(a^2 + b^2 + c^2 /. b :> Throw(bbb))", // "bbb"); check("Catch({Catch({a, Throw(b), c}), d, e})", // "{b,d,e}"); check("Catch(Throw /@ {a, b, c})", // "a"); check("$f(x_) := (If(x < 0, Throw(\"negative\")); Sqrt(x));Catch(Sum($f(i0), {i0, 5, -5, -1}))", // "negative"); // check("$lst={0,v1,n1};\n" + // " Catch(\n" + // " {Map(Function($lst=False;\n" + // " If($lst===False,Throw(False),$lst((1)))),\n" + // " u),$lst((2)),$lst((3))})",""); } @Test public void testCatalan() { checkNumeric("N(Catalan)", // "0.915965594177219"); check("N(Catalan,50)", // "0.91596559417721901505460351493238411077414937428167"); } @Test public void testCatalanNumber() { check("N(CatalanNumber(I),20)", // "0.39764993382373624266+I*(-0.0208843416208425557)"); check("N(CatalanNumber(1/4),20)", // "0.86296416190140697066"); check("CatalanNumber(-10)", // "0"); check("CatalanNumber(-1)", // "-1"); check("CatalanNumber(0)", // "1"); check("CatalanNumber(1)", // "1"); check("CatalanNumber(3)", // "5"); check("CatalanNumber(10)", // "16796"); check("CatalanNumber(-5/2)", // "ComplexInfinity"); check("CatalanNumber(5/2)", // "1024/105*1/Pi"); check("CatalanNumber(41/2)", // "2417851639229258349412352/60755857577415*1/Pi"); check("CatalanNumber(1.2 + I)", // "0.730729+I*0.569846"); } @Test public void testCatenate() { check("Catenate({{1, 2, 3}, {4, 5}})", // "{1,2,3,4,5}"); check("Catenate({{1,2,3},{a,b,c},{4,5,6}})", // "{1,2,3,a,b,c,4,5,6}"); check("Catenate({{1, 2}, <|a -> 1, b -> 2|>})", // "{1,2,1,2}"); check("Catenate({<|a -> 1, b -> 2|>, <|c -> 3, a -> 5|>})", // "{1,2,3,5}"); } @Test public void testCeiling() { check("Ceiling(Quantity(8.5, \"Meters\"))", // "9[Meters]"); check("Ceiling(DirectedInfinity(0))", // "ComplexInfinity"); check("Ceiling(DirectedInfinity((1/2-I*1/2)*Sqrt(2)))", // "DirectedInfinity((1/2-I*1/2)*Sqrt(2))"); check("Ceiling(-9/4)", // "-2"); check("Ceiling(1/3)", // "1"); check("Ceiling(-1/3)", // "0"); check("Ceiling(1.2)", // "2"); check("Ceiling(3/2)", // "2"); check("Ceiling(1.3 + 0.7*I)", // "2+I"); check("Ceiling(2.6, 0.5)", // "3.0"); check("Ceiling(10.4, -1) ", // "10"); check("Ceiling(-10.4, -1) ", // "-11"); check("Ceiling(1.5)", // "2"); check("Ceiling(1.5 + 2.7*I)", // "2+I*3"); } @Test public void testCharacterRange() { check("CharacterRange(50, 50)", // "{2}"); check("CharacterRange(\" \", \"~\")", // "{ ,!,\",#,$,%,&,',(,),*,+,,,-,.,/,0,1,2,3,4,5,6,7,8,9,:,;,<,=,>,?,@,A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,[,\\,],^,_,`,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,{,|,},~}"); check("CharacterRange(1000, 1020)", // "{Ϩ,ϩ,Ϫ,ϫ,Ϭ,ϭ,Ϯ,ϯ,ϰ,ϱ,ϲ,ϳ,ϴ,ϵ,϶,Ϸ,ϸ,Ϲ,Ϻ,ϻ,ϼ}"); check("CharacterRange(\"a\", \"z\")", // "{a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}"); check("CharacterRange(\"0\", \"9\")", // "{0,1,2,3,4,5,6,7,8,9}"); } @Test public void testCharacters() { check("Partition(Characters(\"this is a string\"), 3, 1) // InputForm", // "{{\"t\",\"h\",\"i\"},{\"h\",\"i\",\"s\"},{\"i\",\"s\",\" \"},{\"s\",\" \",\"i\"},{\" \",\"i\",\"s\"},{\"i\",\"s\",\" \"},{\"s\",\" \",\"a\"},{\" \",\"a\",\" \"},{\"a\",\" \",\"s\"},{\" \",\"s\",\"t\"},{\"s\",\"t\",\"r\"},{\"t\",\"r\",\"i\"},{\"r\",\"i\",\"n\"},{\"i\",\"n\",\"g\"}}"); } @Test public void testCheck() { check("Check(0^(-42), failure)", // "failure"); check("Check(2^(3), failure)", // "8"); check("Check(0^(-42), failure)", // "failure"); check("Check(0^0, failure)", // "failure"); } @Test public void testCheckAbort() { check("CheckAbort(Abort(); -1, 41) + 1", // "42"); check("CheckAbort(abc; -1, 41) + 1", // "0"); } @Test public void testChessboardDistance() { check("ChessboardDistance({-1, -1.5}, {1, 1})", // "2.5"); check("ChessboardDistance({-1, -1}, {1, 1})", // "2"); } @Test public void testChineseRemainder() { check("mydata = {931074546, 117172357, 482333642, 199386034, 394354985};", // ""); check("mykeys={104881749667,21415628519,50887356077,224339216447,52131541939};", // ""); check("ChineseRemainder(mydata,mykeys)", // "193166521325770200917536987616405491738358926101878755"); check("ChineseRemainder({-1/2,-2,3},{-1/2,-2,3})", // "ChineseRemainder({-1/2,-2,3},{-1/2,-2,3})"); check("ChineseRemainder({1,-15}, {284407855036305,47})", // "8532235651089151"); check("ChineseRemainder({-2,-17}, {284407855036305,47})", // "9669867071234368"); check("ChineseRemainder({2,17}, {284407855036305,47})", // "3697302115471967"); check("ChineseRemainder({2123, 7213},{11,13})", // "11"); // wikipedia example check("ChineseRemainder({0,3,4},{3,4,5})", // "39"); check("ChineseRemainder({23},{17})", // "6"); check("ChineseRemainder({91},{25})", // "16"); check("ChineseRemainder({913},{25})", // "13"); check("ChineseRemainder({3,4},{4,5})", // "19"); check("ChineseRemainder({1, 2}, {6, 10})", // "ChineseRemainder({1,2},{6,10})"); } @Test public void testChop() { check("-4.898587196589413*^-16*I ", // "I*(-0.0000000000000004898587196589413)"); check("Chop( 1. - 4.898587196589413*^-16*I)", // "1"); check( "Chop(f( {-1. + 1.2246467991473532*^-16*I, 1. - 2.4492935982947064*^-16*I, -1. + 3.6739403974420594*^-16*I, 1. - 4.898587196589413*^-16*I} ))", // "f({-1,1,-1,1})"); check("Chop(abc)", // "abc"); check("Chop(Sin(3/7))", // "Sin(3/7)"); check("Chop(Sin(1/1000000000000000))", // "Sin(1/1000000000000000)"); check("{{2.02.77556*10^-16, -3.88578*10^-16, -5.55112*10^-16}}=={{0,0,0}}", // "True"); check("Chop(x)", // "x"); check("Chop(0.00000000001)", // "0"); check("Chop(18.35051+I*1.32213*10^-11)", // "18.35051"); check("Exp(N(Range(4)*Pi*I))", // "{-1.0,1.0+I*(-2.44929*10^-16),-1.0+I*3.67394*10^-16,1.0+I*(-4.89859*10^-16)}"); check("Chop(Exp(N(Range(4)*Pi*I)))", // "{-1.0,1.0,-1.0,1.0}"); check("x=N(Pi);r=Rationalize(x,10^-12)", // "4272943/1360120"); check("Chop(x-r)==0", // "True"); check("Chop(x-r,10^-14)==0", // "False"); check("Chop(10.^-12+2*I)", // "I*2.0"); check("Chop(2. + 10.^-12*I)", // "2.0"); } @Test public void testClear() { check("x=100;y=42", // "42"); check("x", // "100"); check("y", // "42"); check("Clear(x,y)", // ""); check("x", // "x"); check("y", // "y"); } @Test public void testClearAll() { check("x=100;y=42", // "42"); check("x", // "100"); check("y", // "42"); check("ClearAll(x,y)", // ""); check("x", // "x"); check("y", // "y"); } @Test public void testClearAttributes() { // print error message "SetAttributes: test is not a known attribute." check("SetAttributes(f, {Orderless, Test})", // ""); // print error message "ClearAttributes: test is not a known attribute." check("ClearAttributes(f, {Orderless, Test})", // "ClearAttributes(f,{Orderless,test})"); check("SetAttributes(f, {Orderless, Flat})", // ""); check("Attributes(f)", // "{Flat,Orderless}"); check("ClearAttributes(f, Flat)", // ""); check("Attributes(f)", // "{Orderless}"); check("ClearAttributes(f, Flat)", // ""); check("Attributes(f)", // "{Orderless}"); } @Test public void testClebschGordan() { // https://en.wikipedia.org/wiki/Table_of_Clebsch%E2%80%93Gordan_coefficients check("ClebschGordan({3/2, -3/2}, {3/2, 3/2}, {1, 0})", // "3/2*1/Sqrt(5)"); // print message "is not physical check("ClebschGordan({2, 1}, {2, 4}, {4, 2})", // "0"); check("ClebschGordan({5, 0}, {4, 0}, {1, 0})", // "Sqrt(5/33)"); check("ClebschGordan({1/2, -1/2}, {1/2, -1/2}, {1, -1})", // "1"); check("ClebschGordan({1/2, -1/2}, {1, 0}, {1/2, -1/2})", // "-1/Sqrt(3)"); check("With({j1 = 3, j2 = 2},\n" // + " Table(Sum(\n" // + " If(Abs(m1 + m2) > j || Abs(m1 + m2) > ji, 0, \n" // + " ClebschGordan({j1, m1}, {j2, m2}, {j, \n" // + " m1 + m2}) ClebschGordan({j1, m1}, {j2, m2}, {ji, \n" // + " m1 + m2})), {m1, -j1, j1}, {m2, -j2, j2}), {j, Abs(j1 - j2), \n" // + " j1 + j2}, {ji, Abs(j1 - j2), j1 + j2})) // MatrixForm", // "{{3,0,0,0,0},\n" // + " {0,5,0,0,0},\n" // + " {0,0,7,0,0},\n" // + " {0,0,0,9,0},\n" // + " {0,0,0,0,11}}"); } @Test public void testClip() { check("Clip(7.5,{-7.0,7.0})", // "7.0"); check("Table(Clip(n,{-2,2}),{n,{-E,-1/17,1/7,2/3,5/2,Pi}})", // "{-2,-1/17,1/7,2/3,2,2}"); check("Table(Clip(n,{-1/2,1/2}),{n,{-Infinity,-E,-1/17,1/7,2/3,5/2,Pi,Infinity}})", // "{-1/2,-1/2,-1/17,1/7,1/2,1/2,1/2,1/2}"); check("Clip({-Infinity,1,2,{7},2.00001})", // "{-1,1,1,{1},1}"); check("Clip(Infinity)", // "1"); check("Clip(0)", // "0"); check("Clip({1,2,{7},a})", // "Clip({1,2,{7},a})"); check("Clip(Tan(E),{-1/2,1/2})", // "Tan(E)"); check("Clip(Tan(2*E),{-1/2,1/2})", // "-1/2"); check("Clip(Tan(-2*E),{-1/2,1/2})", // "1/2"); check("Clip(Tan(E), {-1/2,1/2}, {a,b})", // "Tan(E)"); check("Clip(Tan(2*E), {-1/2,1/2}, {a,b})", // "a"); check("Clip(Tan(-2*E), {-1/2,1/2}, {a,b})", // "b"); check("Clip(x)", // "Clip(x)"); check("Clip(1)", // "1"); check("Clip(-1)", // "-1"); check("Clip(Sin(Pi/7))", // "Sin(Pi/7)"); check("Clip(Tan(E))", // "Tan(E)"); check("Clip(Tan(2*E))", // "-1"); check("Clip(Tan(-2*E))", // "1"); check("Clip({-2, 0, 2})", // "{-1,0,1}"); } @Test public void testCoefficient() { check("Coefficient(x+y+z, x+y)", // "1"); // https://oeis.org/A236191 check("Coefficient(Series((x + x^2 + 2*x^3 + x^4 - x^5)/(1 + 4*x^3 - x^6), {x, 0, 38}), x^10)", // "-55"); check("Coefficient(ComplexInfinity,{x,y,z})", // "{0,0,0}"); check("Coefficient(ComplexInfinity,x)", // "0"); check("Coefficient(7*y^w, y, w)", // "7"); check("Coefficient(7*y^(3*w), y, 3*w)", // "7"); check("Coefficient(c*x^(-2)+a+b*x,x,-2)", // "c"); // TODO // check("Coefficient(2*x*y+5*x^3,x^3,0)", // // "0"); check("Coefficient(x*y,z,0)", // "x*y"); check("Coefficient(2*x*y+5*x^3,2*x)", // "y"); check("Coefficient((2*x)^7*y+5*x^3,x^3)", // "5"); check("Coefficient(2*x *y+5*x^3,x^3)", // "5"); check("Coefficient(Cos(x*y), Cos(x*y))", // "1"); check("Coefficient(2*x^2,x^2)", // "2"); check("Coefficient(2*x^4,x^2)", // "0"); check("Coefficient(2*x^2,x^3)", // "0"); check("Coefficient((1+2*x)/Sqrt(3),x,1)", // "2/Sqrt(3)"); check("g = (x + 3)^5;Coefficient(g, x, #) & /@ Range(0, Exponent(g, x))", // "{243,405,270,90,15,1}"); // http://oeis.org/A133314 check("b(0) = 1; " // + "b(n_) := b(n)=-Sum(Binomial(n, j)*a(j)*b(n-j), {j, 1, n}); crow(0) = {1}; " // + "crow(n_) := Coefficient(b(n), #)& /@ (Times @@ (a /@ #)&) /@ IntegerPartitions(n); " // + "Table(crow(n), {n, 0, 8}) // Flatten", // "{1,-1,-1,2,-1,6,-6,-1,8,6,-36,24,-1,10,20,-60,-90,240,-120,-1,12,30,-90,20,-360,\n" + "480,-90,1080,-1800,720,-1,14,42,-126,70,-630,840,-420,-630,5040,-4200,2520,-\n" + "12600,15120,-5040,-1,16,56,-168,112,-1008,1344,70,-1680,-1260,10080,-8400,-1680,\n" + "6720,20160,-67200,40320,2520,-50400,151200,-141120,40320}"); check("Coefficient(a+b*x,x,0)", // "a"); check("Coefficient(a+b*x,x,1)", // "b"); check("Coefficient(a*b*x,x,1)", // "a*b"); check("Coefficient(x*y,y,Exponent(x*y,y))", // "x"); check("Coefficient(-3*a(1)*(2*a(1)^2-a(2))+3*a(1)*a(2)-a(3),a(1)*a(2))", // "6"); check("Coefficient(SeriesData(x, 0, {1, 1, 0, 1, 1, 0, 1, 1}, 0, 9, 1), x, 4)", // "1"); check("Coefficient(x^2*y^2 + 3*x + 4*y+y^w, y, 0)", // "3*x"); check("Coefficient(x^2*y^2 + 3*x + 4*y+3/(y^4), x, 0)", // "3/y^4+4*y"); check("Coefficient(x^2*y^2 + 3*x + 4*y+Sin(y), x, 0)", // "4*y+Sin(y)"); check("Coefficient(x^2*y^2 + 3*x + 4*y+Sin(y), y, 0)", // "3*x+Sin(y)"); check("Coefficient(x^2*y^2 + 3*x + 4*y+Sin(y)^3, x, 0)", // "4*y+Sin(y)^3"); check("Coefficient(x^2*y^2 + 3*x + 4*y+Sin(y)^3, y, 0)", // "3*x+Sin(y)^3"); check("poly=(c*x-2*y+z)^7", // "(c*x-2*y+z)^7"); check("Coefficient(poly, x^2*y*z^4)", // "-210*c^2"); check("coeff=CoefficientList(poly,{x,y,z})", // "{{{0,0,0,0,0,0,0,1},{0,0,0,0,0,0,-14,0},{0,0,0,0,0,84,0,0},{0,0,0,0,-280,0,0,0},{\n" + "0,0,0,560,0,0,0,0},{0,0,-672,0,0,0,0,0},{0,448,0,0,0,0,0,0},{-128,0,0,0,0,0,0,0}},{{\n" + "0,0,0,0,0,0,7*c,0},{0,0,0,0,0,-84*c,0,0},{0,0,0,0,420*c,0,0,0},{0,0,0,-1120*c,0,\n" + "0,0,0},{0,0,1680*c,0,0,0,0,0},{0,-1344*c,0,0,0,0,0,0},{448*c,0,0,0,0,0,0,0},{0,0,\n" + "0,0,0,0,0,0}},{{0,0,0,0,0,21*c^2,0,0},{0,0,0,0,-210*c^2,0,0,0},{0,0,0,840*c^2,0,\n" + "0,0,0},{0,0,-1680*c^2,0,0,0,0,0},{0,1680*c^2,0,0,0,0,0,0},{-672*c^2,0,0,0,0,0,0,\n" + "0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}},{{0,0,0,0,35*c^3,0,0,0},{0,0,0,-280*c^3,\n" + "0,0,0,0},{0,0,840*c^3,0,0,0,0,0},{0,-1120*c^3,0,0,0,0,0,0},{560*c^3,0,0,0,0,0,0,\n" + "0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}},{{0,0,0,35*c^4,0,0,0,0},{\n" + "0,0,-210*c^4,0,0,0,0,0},{0,420*c^4,0,0,0,0,0,0},{-280*c^4,0,0,0,0,0,0,0},{0,0,0,\n" + "0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}},{{0,0,21*c^5,0,\n" + "0,0,0,0},{0,-84*c^5,0,0,0,0,0,0},{84*c^5,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,\n" + "0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}},{{0,7*c^6,0,0,\n" + "0,0,0,0},{-14*c^6,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,\n" + "0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}},{{c^7,0,0,0,0,0,0,\n" + "0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,\n" + "0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}}"); check("Part(coeff, 3,2,5)", // "-210*c^2"); check("Coefficient(poly, x^5)", // "84*c^5*y^2-84*c^5*y*z+21*c^5*z^2"); check("Coefficient(poly, x, 5)", // "84*c^5*y^2-84*c^5*y*z+21*c^5*z^2"); check("coeff[[6]]", // "{{0,0,21*c^5,0,0,0,0,0},{0,-84*c^5,0,0,0,0,0,0},{84*c^5,0,0,0,0,0,0,0},{0,0,0,0,\n" + "0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0}}"); check("Part(coeff, 6,1,3)", // "21*c^5"); check("Part(coeff, 6,2,2)", // "-84*c^5"); check("Part(coeff, 6,3,1)", // "84*c^5"); // check("Apply(Plus,((Coefficient(x*(b+a),x,#1)*x^#1)&))", ""); check("Coefficient(x*y,y,1)", // "x"); check("Coefficient(Sin(x*y),y,1)", // "0"); check("Coefficient(x*y,y,Exponent(x*y,y))", // "x"); check("Coefficient(Sin(a)^3*#1 + b*y + c, #1)", // "Sin(a)^3"); check("Coefficient((#1 + 2)^2 + (#1 + 3)^3, #1, 0)", // "31"); check("Coefficient(42*#1^2+y^3*#1^2+(#1 + 2)^2*(#1 + 2)^2,#1,2)", // "66+y^3"); check("Coefficient(#1,#1,1)", // "1"); check("Coefficient(#1^2,#1,2)", // "1"); check("Coefficient(Null,x,0)", // ""); check("Coefficient(Null,x)", // "0"); check("Coefficient(Sin(x^2),x^2)", // "0"); check("Coefficient(Sin(x^2)^2,Sin(x^2),2)", // "1"); check("Coefficient(2*Sin(x^2)^3,Sin(x^2),3)", // "2"); check("Coefficient(f(x)+2*Sin(x^2)^3,Sin(x^2),3)", // "2"); check("Coefficient(f(x^2)+2*f(x^2)^3,f(x^2),3)", // "2"); check("ExpandAll((x + y)*(x + 2*y)*(3*x + 4*y + 5))", // "5*x^2+3*x^3+15*x*y+13*x^2*y+10*y^2+18*x*y^2+8*y^3"); check("Coefficient(Sin(x^2),Sin(x^2))", // "1"); check("Coefficient(x*(b+a),x,1)*x^1", // "(a+b)*x"); check("Coefficient((x + 1)^3, x, 2)", // "3"); check("Coefficient(a*x + b*y + c, x)", // "a"); check("Coefficient(Sin(a)^3*x + b*y + c, x)", // "Sin(a)^3"); check("Coefficient(Sin(a*x)^3*x + b*y + c, x)", // "Sin(a*x)^3"); check("Coefficient((x + 2)^2 + (x + 3)^3, x, 0)", // "31"); check("Coefficient(v,x,1)", // "0"); check("Coefficient(42,x,0)", // "42"); check("Coefficient(42*a,x,0)", // "42*a"); check("Coefficient(x,x,1)", // "1"); check("Coefficient(x^2,x,2)", // "1"); check("Coefficient(42*x^2+y^3*x^2+(x + 2)^2*(x + 2)^2,x,2)", // "66+y^3"); check("Coefficient(2*x*a,x,1)", // "2*a"); check("Coefficient(2*x*a,x,2)", // "0"); check("Coefficient(2*x*a,x,3)", // "0"); check("Coefficient(2*x*a,x,4)", // "0"); check("Coefficient(2*x^2*a+x,x,1)", // "1"); check("Coefficient(2*x^2*a,x,2)", // "2*a"); check("Coefficient(2*x^3*a,x,3)", // "2*a"); check("Coefficient(2*x^4*a,x,4)", // "2*a"); check("Coefficient(0,x,0)", // "0"); // allow multinomials check("ExpandAll((x + y)^4)", // "x^4+4*x^3*y+6*x^2*y^2+4*x*y^3+y^4"); check("Coefficient((x + y)^4, x*y^3)", // "4"); check("Coefficient((x + y)^4, y^4)", // "1"); check("Coefficient((x + y)^4, y,4)", // "1"); check("Expand((x + y)*(x + 2*y)*(3*x + 4*y + 5))", // "5*x^2+3*x^3+15*x*y+13*x^2*y+10*y^2+18*x*y^2+8*y^3"); check("ExpandAll((x + y)*(x + 2*y)*(3*x + 4*y + 5))", // "5*x^2+3*x^3+15*x*y+13*x^2*y+10*y^2+18*x*y^2+8*y^3"); check("Coefficient((x + y)*(x + 2*y)*(3*x + 4*y + 5), x^2*y)", // "13"); check("Coefficient((x + y)*(x + 2*y)*(3*x + 4*y + 5), x*y^2)", // "18"); check("Coefficient((x + y)*(x + 2*y)*(3*x + 4*y + 5), x*y)", // "15"); check("Coefficient((x + y)*(x + 2*y)*(3*x + 4*y + 5), y^3)", // "8"); } @Test public void testCoefficientList() { // check("1.0 * 10.0* x^9", // // "10.0*x^9"); check("Expand((1.0 + x)^10)", // "1.0+10.0*x+45.0*x^2+120.0*x^3+210.0*x^4+252.0*x^5+210.0*x^6+120.0*x^7+45.0*x^8+10.0*x^\n"// + "9+x^10"); check("CoefficientList((1.0 + x)^10 , x)", // "{1.0,10.0,45.0,120.0,210.0,252.0,210.0,120.0,45.0,10.0,1}"); check("CoefficientList(Series(-(x/(-1 + x + x^2)), {x, 0, 20}), x)", // "{0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765}"); // https://oeis.org/A236191 check("CoefficientList(Series((x + x^2 + 2*x^3 + x^4 - x^5)/(1 + 4*x^3 - x^6), {x, 0, 38}), x)", // "{0,1,1,2,-3,-5,-8,13,21,34,-55,-89,-144,233,377,610,-987,-1597,-2584,4181,6765,\n" // + "10946,-17711,-28657,-46368,75025,121393,196418,-317811,-514229,-832040,1346269,\n" // + "2178309,3524578,-5702887,-9227465,-14930352,24157817,39088169}"); check("CoefficientList(ComplexInfinity,x)", // "{ComplexInfinity}"); check("CoefficientList(ComplexInfinity, {x,y,z} )", // "{{{ComplexInfinity}}}"); check("CoefficientList(7*y^w, y )", // "{7*y^w}"); check("CoefficientList(2*x*y+5*x^3,2*x)", // "{5*x^3+2*x*y}"); check("CoefficientList((2*x)^7*y+5*x^3,x^3)", // "{128*x^7*y,5}"); check("CoefficientList(2*x *y+5*x^3,x^3)", // "{2*x*y,5}"); check("CoefficientList(Cos(x*y), Cos(x*y))", // "{0,1}"); // http://oeis.org/A000045 - Fibonacci numbers check("CoefficientList(Series(-(x/(-1 + x + x^2)), {x, 0, 20}), x)", // "{0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765}"); check("CoefficientList(x^2*y^2 + 3*x + 4*y+y^w, {x, y})", // "{{y^w,4,0},{3,0,0},{0,0,1}}"); check("CoefficientList(x^2*y^2 + 3*x + 4*y+3/(y^4), {x, y})", // "{{3/y^4,4,0},{3,0,0},{0,0,1}}"); check("CoefficientList(x^2*y^2 + 3*x + 4*y+Sin(y), {x, y})", // "{{Sin(y),4,0},{3,0,0},{0,0,1}}"); check("CoefficientList(x^2*y^2 + 3*x + 4*y+Sin(y)^3, {x, y})", // "{{Sin(y)^3,4,0},{3,0,0},{0,0,1}}"); check("CoefficientList(0, {x})", // "{}"); check("CoefficientList(0, {x, y})", // "{}"); check("CoefficientList(x^2*y^2 + 3*x + 4*y + 7*y^5, {x, y})", // "{{0,4,0,0,0,7},{3,0,0,0,0,0},{0,0,1,0,0,0}}"); check("CoefficientList(x^2*y^2 + 3*x + 4*y + 7*y^5, {x, y, z})", // "{{{0},{4},{0},{0},{0},{7}},{{3},{0},{0},{0},{0},{0}},{{0},{0},{1},{0},{0},{0}}}"); check("CoefficientList(x^2*y^2 + 3*x + 4*y + 7*y^5+z, {x, y, z})", // "{{{0,1},{4,0},{0,0},{0,0},{0,0},{7,0}},{{3,0},{0,0},{0,0},{0,0},{0,0},{0,0}},{{0,\n" + "0},{0,0},{1,0},{0,0},{0,0},{0,0}}}"); check("CoefficientList(x^2*y^2 + 3*x + 4*y, {x, y})", // "{{0,4,0},{3,0,0},{0,0,1}}"); check("CoefficientList(x^2*y^2 + 3*x + 4*y, {x, y, z})", // "{{{0},{4},{0}},{{3},{0},{0}},{{0},{0},{1}}}"); check("CoefficientList(a+b*x, x)", // "{a,b}"); check("CoefficientList(a+b*x+c*x^2, x)", // "{a,b,c}"); check("CoefficientList(a+c*x^2, x)", // "{a,0,c}"); check("CoefficientList(0, x)", // "{}"); check("CoefficientList((x+3)^5, x)", // "{243,405,270,90,15,1}"); check("CoefficientList(1 + 6*x - x^4, x)", // "{1,6,0,0,-1}"); check("CoefficientList((1 + x)^10 , x)", // "{1,10,45,120,210,252,210,120,45,10,1}"); check("CoefficientList(a*42*x^3+12*b*x+c*4, x)", // "{4*c,12*b,0,42*a}"); } @Test public void testCoefficientRules() { check("CoefficientRules(x^3+3*x^2*y+3*x*y^2+y^3, {x,y})", // "{{3,0}->1,{2,1}->3,{1,2}->3,{0,3}->1}"); check("CoefficientRules(x^3+3*x^2*y+3*x*y^2+y^3)", // "{{3,0}->1,{2,1}->3,{1,2}->3,{0,3}->1}"); check("CoefficientRules(7*y^w, {y,z})", // "{{0,0}->7*y^w}"); check("CoefficientRules(7*y^(3*w), y )", // "{{0}->7*y^(3*w)}"); check("CoefficientRules(c*x^2+a+b*x,x)", // "{{2}->c,{1}->b,{0}->a}"); check("CoefficientRules(c*x^(-2)+a+b*x,x)", // "{{0}->a+c/x^2+b*x}"); check("CoefficientRules(SeriesData(x, 0, {1, 1, 0, 1, 1, 0, 1, 1}, 0, 9, 1))", // "{{0}->1+x+x^3+x^4+x^6+x^7+O(x)^9}"); check("CoefficientRules((x + y)^3)", // "{{3,0}->1,{2,1}->3,{1,2}->3,{0,3}->1}"); check("CoefficientRules( a*x*y^2 + b*x^2*z, {x, y, z}, DegreeReverseLexicographic)", // "{{1,2,0}->a,{2,0,1}->b}"); check("CoefficientRules((x + y)^3)", "{{3,0}->1,{2,1}->3,{1,2}->3,{0,3}->1}"); // check("CoefficientRules(x^2 y^2 + x^3, {x, y})", "{x^3,x^2*y^2}"); // check("CoefficientRules(x^2 y^2 + x^3, {x, // y},\"DegreeLexicographic\")", "{x^2*y^2,x^3}"); check("CoefficientRules((x + 1)^5, x, Modulus -> 2)", // "{{5}->1,{4}->1,{1}->1,{0}->1}"); check( "CoefficientRules(-10*x^5*y^4*z^2 + 7*x^2*y^5*z^3 - 10*x^2*y*z^5 - 7*x*y^5*z^4 + 6*x*y^4*z^3 + 6*x*y^3*z^3 + 3*x*y^2*z + y^4*z - 7*y^2*z + 2*z^5, {x, y, z})", // "{{5,4,2}->-10,{2,5,3}->7,{2,1,5}->-10,{1,5,4}->-7,{1,4,3}->6,{1,3,3}->6,{1,2,1}->\n" + "3,{0,4,1}->1,{0,2,1}->-7,{0,0,5}->2}"); check( "CoefficientRules(-10*x^5*y^4*z^2 + 7*x^2*y^5*z^3 - 10*x^2*y*z^5 - 7*x*y^5*z^4 + 6*x*y^4*z^3 + 6*x*y^3*z^3 + 3*x*y^2*z + y^4*z - 7*y^2*z + 2*z^5, {x, y, z}, NegativeLexicographic)", // "{{0,0,5}->2,{0,2,1}->-7,{0,4,1}->1,{1,2,1}->3,{1,3,3}->6,{1,4,3}->6,{1,5,4}->-7,{\n" + "2,1,5}->-10,{2,5,3}->7,{5,4,2}->-10}"); check( "CoefficientRules(-10*x^5*y^4*z^2 + 7*x^2*y^5*z^3 - 10*x^2*y*z^5 - 7*x*y^5*z^4 + 6*x*y^4*z^3 + 6*x*y^3*z^3 + 3*x*y^2*z + y^4*z - 7*y^2*z + 2*z^5, {x, y, z}, DegreeLexicographic)", // "{{5,4,2}->-10,{2,5,3}->7,{1,5,4}->-7,{2,1,5}->-10,{1,4,3}->6,{1,3,3}->6,{0,4,1}->\n" + "1,{0,0,5}->2,{1,2,1}->3,{0,2,1}->-7}"); check( "CoefficientRules(-10*x^5*y^4*z^2 + 7*x^2*y^5*z^3 - 10*x^2*y*z^5 - 7*x*y^5*z^4 + 6*x*y^4*z^3 + 6*x*y^3*z^3 + 3*x*y^2*z + y^4*z - 7*y^2*z + 2*z^5, {x, y, z}, NegativeDegreeReverseLexicographic)", // "{{0,2,1}->-7,{1,2,1}->3,{0,4,1}->1,{0,0,5}->2,{1,3,3}->6,{1,4,3}->6,{2,1,5}->-10,{\n" + "2,5,3}->7,{1,5,4}->-7,{5,4,2}->-10}"); check( "CoefficientRules(-10*x^5*y^4*z^2 + 7*x^2*y^5*z^3 - 10*x^2*y*z^5 - 7*x*y^5*z^4 + 6*x*y^4*z^3 + 6*x*y^3*z^3 + 3*x*y^2*z + y^4*z - 7*y^2*z + 2*z^5, {x, y, z}, DegreeReverseLexicographic)", // "{{5,4,2}->-10,{2,5,3}->7,{1,5,4}->-7,{1,4,3}->6,{2,1,5}->-10,{1,3,3}->6,{0,4,1}->\n" + "1,{0,0,5}->2,{1,2,1}->3,{0,2,1}->-7}"); check( "CoefficientRules(-10*x^5*y^4*z^2 + 7*x^2*y^5*z^3 - 10*x^2*y*z^5 - 7*x*y^5*z^4 + 6*x*y^4*z^3 + 6*x*y^3*z^3 + 3*x*y^2*z + y^4*z - 7*y^2*z + 2*z^5, {x, y, z}, NegativeDegreeLexicographic)", // "{{0,2,1}->-7,{1,2,1}->3,{0,4,1}->1,{0,0,5}->2,{1,3,3}->6,{2,1,5}->-10,{1,4,3}->6,{\n" + "2,5,3}->7,{1,5,4}->-7,{5,4,2}->-10}"); } @Test public void testCollect() { check("Collect((1 + a + x)^4, x)", // "1+4*a+6*a^2+4*a^3+a^4+(4+12*a+12*a^2+4*a^3)*x+(6+12*a+6*a^2)*x^2+(4+4*a)*x^3+x^4"); check("Collect((1 + a + x)^4, x, Factor)", // "(1+a)^4+4*(1+a)^3*x+6*(1+a)^2*x^2+4*(1+a)*x^3+x^4"); check("Collect(a*x*Log(x)+ b*(x*Log(x)), x*Log(x))", // "(a+b)*x*Log(x)"); check("Collect(e+f*x, {})", // "e+f*x"); check("Collect(e+f*x, {x})", // "e+f*x"); check("Collect(e+f*x, x)", // "e+f*x"); check("Collect((1 + a + x)^4, x)", // "1+4*a+6*a^2+4*a^3+a^4+(4+12*a+12*a^2+4*a^3)*x+(6+12*a+6*a^2)*x^2+(4+4*a)*x^3+x^4"); check("Collect((1 + a + x)^4, x, Simplify)", // "(1+a)^4+4*(1+a)^3*x+6*(1+a)^2*x^2+4*(1+a)*x^3+x^4"); check("Collect(x^2 + y*x^2 + x*y + y + a*y, {x, y})", // "(1+a)*y+x*y+x^2*(1+y)"); check("Collect(a*x^2 + b*x^2 + a*x - b*x + c, x)", // "c+(a-b)*x+(a+b)*x^2"); check("Collect(a*Exp(2*x) + b*Exp(2*x), Exp(2*x))", // "(a+b)*E^(2*x)"); check("a*Exp(2*x) + b*Exp(2*x)", // "a*E^(2*x)+b*E^(2*x)"); // check("Collect(D(f(Sqrt(x^2 + 1)), {x, 3}), Derivative(_)[f][_], // Together)", ""); check("x*(4*a^3+12*a^2+12*a+4)+x^4+(4*a+4)*x^3+(6*a^2+12*a+6)*x^2+a^4+4*a^3+6*a^2+4*a+1", // "1+4*a+6*a^2+4*a^3+a^4+(4+12*a+12*a^2+4*a^3)*x+(6+12*a+6*a^2)*x^2+(4+4*a)*x^3+x^4"); check("x+x^4", // "x+x^4"); check("Collect(a, x)", // "a"); check("Collect(a*y, {x,y})", // "a*y"); check("Collect(42*a, {x,y})", // "42*a"); check("Collect(a*Sqrt(x) + Sqrt(x) + x^(2/3) - c*x + 3*x - 2*b*x^(2/3) + 5, x)", // "5+(1+a)*Sqrt(x)+(1-2*b)*x^(2/3)+(3-c)*x"); check("Collect(3*b*x + x, x)", // "(1+3*b)*x"); check("Collect(a*x^4 + b*x^4 + 2*a^2*x - 3*b*x + x - 7, x)", "-7+(1+2*a^2-3*b)*x+(a+b)*x^4"); check("Collect((1 + a + x)^4, x)", "1+4*a+6*a^2+4*a^3+a^4+(4+12*a+12*a^2+4*a^3)*x+(6+12*a+6*a^2)*x^2+(4+4*a)*x^3+x^4"); check("Collect((1 + a + x)^4, x, Simplify)", // "(1+a)^4+4*(1+a)^3*x+6*(1+a)^2*x^2+4*(1+a)*x^3+x^4"); check("Collect(a*x + b*y + c*x, x)", // "(a+c)*x+b*y"); check("Collect((x + y + z + 1)^4, {x, y})", // "1+x^4+y^4+4*z+y^3*(4+4*z)+x^3*(4+4*y+4*z)+6*z^2+y^2*(6+12*z+6*z^2)+x^2*(6+6*y^2+\n" + "12*z+y*(12+12*z)+6*z^2)+4*z^3+y*(4+12*z+12*z^2+4*z^3)+x*(4+4*y^3+12*z+y^2*(12+12*z)+\n" + "12*z^2+y*(12+24*z+12*z^2)+4*z^3)+z^4"); } @Test public void testCommonest() { // https://en.wikipedia.org/wiki/Mode_(statistics) check("Commonest({1, 3, 6, 6, 6, 6, 7, 7, 12, 12, 17})", // "{6}"); // bimodal check("Commonest({1, 1, 2, 4, 4})", // "{1,4}"); check("Commonest({b, a, c, 2, a, b, 1, 2}, 4)", // "{b,a,2,c}"); check("Commonest({b, a, c, 2, a, b, 1, 2})", // "{b,a,2}"); check("Commonest({1, 2, 2, 3, 3, 3, 4})", // "{3}"); // print warning: Commonest: The requested number of elements 6 is greater than the number of // distinct elements 5. Only 5 elements will be returned. check("Commonest({b, a, c, 2, a, b, 1, 2}, 6)", // "{b,a,2,c,1}"); } @Test public void testComplement() { check("Complement({2, -2, 1, 3}, {2, 1, -2, -1},SameTest->(Abs(#1)==Abs(#2) &))", // "{3}"); check( "Complement({1.1, 3.4, .5, 7.6, 7.1, 1.9}, {1.2, 3.3, 1.3},SameTest->(Floor(#1)==Floor(#2)&))", // "{0.5,7.1}"); check( "Complement({{1, 2}, {3}, {4, 5, 6}, {9, 5}}, {{2, 1}, {8, 4, 3}},SameTest->(Total(#1)==Total(#2) &))", // "{{9,5}}"); check("Complement(#,#)", // "Slot()"); check("Complement(#,#1*#2)", // "Complement(#1,#1*#2)"); check("Complement(#2,#1)", // "#2"); check("Complement({},{})", "{}"); check("Complement({1,2,3},{2,3,4})", "{1}"); check("Complement({2,3,4},{1,2,3})", "{4}"); check("Complement({1},{2})", "{1}"); check("Complement({1,2,2,4,6},{2,3,4,5})", "{1,6}"); check("Complement({3, 2, 7, 5, 2, 2, 3, 4, 5, 6, 1}, {2, 3}, {4, 6, 27, 23})", // "{1,5,7}"); check("Complement({1,2,3},{2,3,4})", // "{1}"); check("Complement({2,3,4},{1,2,3})", // "{4}"); } @Test public void testComplex() { // github #267 check("1/(I*2*Pi*5000*25*10^-6)+10", // "10+(-I*4)/Pi"); check("2.0000000000072014`*^-144+I*2.1 // FullForm", // "Complex(2.0000000000072015`*^-144,2.1`)"); check("Complex(0,1)*2", // "I*2"); // see Outputform conversions check("Complex(a, I)", // "a+I*I"); check("a*((- 1/3 )*I)", // "-I*1/3*a"); check("Head(2 + 3*I)", // "Complex"); check("Complex(1, 2/3)", // "1+I*2/3"); check("Abs(Complex(3, 4))", // "5"); check("-2 / 3 - I", // "-2/3-I"); check("Complex(10, 0)", // "10"); check("0. + I", // "I*1.0"); check("1 + 0*I", // "1"); check("Head(1 + 0*I)", // "Integer"); check("Complex(0.0, 0.0)", // "0.0"); check("0.*I", // "0.0"); check("0. + 0.*I", // "0.0"); check("1. + 0.*I", // "1.0"); check("0. + 1.*I", // "I*1.0"); check("Complex(1, Complex(0, 1))", // "0"); check("Complex(1, Complex(1, 0))", // "1+I"); check("Complex(1, Complex(1, 1))", // "I"); check("3/4+6/7", // "45/28"); check("Complex(3/4,-(6/7)*I)", // "45/28"); } @Test public void testComplexInfinity() { check("1 / ComplexInfinity", // "0"); check("ComplexInfinity + ComplexInfinity", // "Indeterminate"); check("ComplexInfinity * Infinity", // "ComplexInfinity"); check("FullForm(ComplexInfinity)", // "DirectedInfinity()"); } @Test public void testComposeList() { check("ComposeList({f,g,h}, x)", // "{x,f(x),g(f(x)),h(g(f(x)))}"); check("ComposeList({1 - # &, 1/# &}[[{2, 2, 1, 2, 2, 1}]], x)", // "{x,1/x,x,1-x,1/(1-x),1-x,x}"); check("ComposeList({f, g}[[{1, 2, 1, 1, 2}]], x)", // "{x,f(x),g(f(x)),f(g(f(x))),f(f(g(f(x)))),g(f(f(g(f(x)))))}"); check("ComposeList({a, b, c, d}, x)", // "{x,a(x),b(a(x)),c(b(a(x))),d(c(b(a(x))))}"); } @Test public void testComposition() { check("Composition(u, v, w)[x, y]", // "u(v(w(x,y)))"); check("Composition(1 + #^# &, a*# &, #/(# + 1) &)[x]", // "1+((a*x)/(1+x))^((a*x)/(1+x))"); check("Composition(f, g, h) @@ {x, y, z}", // "f(g(h(x,y,z)))"); } @Test public void testCompositeQ() { check("CompositeQ({0,-1,-2,-4,-5,-6,-7,-8,-9,-10,-11,-12,-13,-14})", // "{False,False,False,True,False,True,False,True,True,True,False,True,False,True}"); check("Select(Range(100), CompositeQ)", // "{4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,35,36,38,39,40,42,\n" // + "44,45,46,48,49,50,51,52,54,55,56,57,58,60,62,63,64,65,66,68,69,70,72,74,75,76,77,\n" // + "78,80,81,82,84,85,86,87,88,90,91,92,93,94,95,96,98,99,100}"); // check("CompositeQ(Range(20))", // "{False,False,False,True,False,True,False,True,True,True,False,True,False,True,True,True,False,True,False,True}"); check("CompositeQ(10^300+1)", // "True"); } @Test public void testCompoundExpression() { check("1; 2; 3;", // ""); check("1; 2; 3", // "3"); check("a=100", // "100"); check("a=100;", // ""); check("a", // "100"); check("Catch($a = 2; Throw($a); $a = 5)", // "2"); } @Test public void testCondition() { check("Cases({z(1, 1), z(-1, 1), z(-2, 2)}, z(x_ /; x < 0, y_))", // "{z(-1,1),z(-2,2)}"); check("q(i_,j_):=q(i,j)=q(i-1,j)+q(i,j-1);q(i_,j_)/;i<0||j<0=0;q(0,0)=1", // "1"); check("Definition(q)", // "q(0,0)=1\n" // + "\n" // + "q(i_,j_)/;i<0||j<0=0\n" // + "\n" // + "q(i_,j_):=q(i,j)=q(-1 + i,j) + q(i,-1 + j)"); check("q(5,5)", // "252"); check("Condition(Condition(cond(x_),x>1),x<2):=Denominator(x)", // ""); check("cond(3/2)", // "2"); check("cond(0)", // "cond(0)"); check("x /; x > 0", // "x/;x>0"); check("x /; (10==10)", // "x/;10==10"); check("fac(n_ /; n > 0) := n!", // ""); check("fac(3)+fac(-4)", // "6+fac(-4)"); check("Cases({3, -4, 5, -2}, x_ /; x < 0)", // "{-4,-2}"); check("Cases({z(1, 1), z(-1, 1), z(-2, 2)}, z(x_ /; x < 0, y_))", // "{z(-1,1),z(-2,2)}"); check("{1 + a, 2 + a, -3 + a} /. (x_ /; x < 0) + a -> p(x)", // "{1+a,2+a,p(-3)}"); check("{6, -7, 3, 2, -1, -2} /. x_ /; x < 0 -> w", // "{6,w,3,2,w,w}"); check("f(3) /. f(x_) /; x>0 -> t", // "t"); check("f(-3) /. f(x_) /; x>0 -> t", // "f(-3)"); check("f(x_) := p(x) /; x>0", // ""); check("f(3)", // "p(3)"); check("f(-3)", // "f(-3)"); check("f(x_) := Module({u}, u^2 /; ((u = x - 1) > 0))", // ""); check("f(0)", // "f(0)"); check("g(x_) := Module({a}, a = Prime(10^x); (FactorInteger(a + 1)) /; a < 10^6)", // ""); check("g(4)", // "{{2,1},{3,1},{5,1},{3491,1}}"); check("g(5)", // "g(5)"); } @Test public void testConditionNested() { // nested(x_,y_)/; x>0 /; x0 /; x ConditionalExpression(2*Pi*C(1), Element(C(1), Integers))}, \n" + " {x -> ConditionalExpression(Pi + 2*Pi*C(1), Element(C(1), Integers))}} ", // "{ConditionalExpression(Sin(2*Pi*C(1)),C(1)∈Integers),ConditionalExpression(-Sin(\n" // + "2*Pi*C(1)),C(1)∈Integers)}"); check("ref=Refine(cd)", // "{ConditionalExpression(0,C(1)∈Integers),ConditionalExpression(0,C(1)∈Integers)}"); check("PossibleZeroQ(ref)", // "{True,True}"); check("ConditionalExpression(x, x > 0)^2 == 1 && ConditionalExpression(y, y < 0) > -1", // "ConditionalExpression(x^2==1&&y>-1,x>0&&y<0)"); check("{ConditionalExpression(x^2, x > 0) == 1, ConditionalExpression(x^a, a > 0) < 2}", // "{ConditionalExpression(x^2==1,x>0),ConditionalExpression(x^a<2,a>0)}"); check("Sin(ConditionalExpression(x,x>0))", // "ConditionalExpression(Sin(x),x>0)"); check("Sin(ConditionalExpression(x, x > 0)) + 3*ConditionalExpression(Cos(x), x < 1)^2", // "ConditionalExpression(3*Cos(x)^2+Sin(x),x<1&&x>0)"); check("ConditionalExpression(a,True)", // "a"); check("ConditionalExpression(a,False)", // "Undefined"); } @Test public void testConjugate() { check("Conjugate(Cosh(Im(x)))", // "Cosh(Im(x))"); check("Conjugate(Quantity(2,\"m\"))", // "2[m]"); check("Conjugate(Quantity(a,\"m\"))", // "Conjugate(a)[m]"); check("Conjugate(3*E^(4*I))", // "3/E^(I*4)"); check("Conjugate(Sin(Pi+I))", // "I*Sinh(1)"); check("Conjugate(3 + 4*I)", // "3-I*4"); check("Conjugate(3)", // "3"); check("Conjugate(a + b * I)", // "Conjugate(a)-I*Conjugate(b)"); check("Conjugate(a * b * I)", // "-I*Conjugate(a*b)"); check("Conjugate({{1, 2 + I*4, a + I*b}, {I}})", // "{{1,2-I*4,Conjugate(a)-I*Conjugate(b)},{-I}}"); check("{Conjugate(Pi), Conjugate(E)}", // "{Pi,E}"); check("Conjugate(1.5 + 2.5*I)", // "1.5+I*(-2.5)"); check("Conjugate(1-I)", // "1+I"); check("Conjugate(1+I)", // "1-I"); check("Conjugate(Conjugate(x))", // "x"); check("Conjugate(3*a*z)", // "3*Conjugate(a*z)"); check("Conjugate(E^z)", // "E^Conjugate(z)"); check("Conjugate(Pi)", // "Pi"); check("Conjugate(0)", // "0"); check("Conjugate(I)", // "-I"); check("Conjugate(Indeterminate)", // "Indeterminate"); check("Conjugate(Infinity)", // "Infinity"); check("Conjugate(-Infinity)", // "-Infinity"); check("Conjugate(ComplexInfinity)", // "ComplexInfinity"); check("Conjugate(Transpose({{1,2+I,3},{4,5-I,6},{7,8,9}}))", // "{{1,4,7},{2-I,5+I,8},{3,6,9}}"); check("Conjugate(Zeta(x))", // "Zeta(Conjugate(x))"); check("Conjugate(Zeta(11,7))", // "Zeta(11,7)"); check("Conjugate(Erf(x))", // "Erf(Conjugate(x))"); } @Test public void testConstant() { check("Attributes(E)", // "{Constant,Protected}"); check("Solve(x + E == 0, E) ", // "Solve(E+x==0,E)"); } @Test public void testConstantArray() { // message Maximum AST dimension 2147483647 exceeded check("ConstantArray(2,2147483647)", // "ConstantArray(2,2147483647)"); check("ConstantArray({},{})", // "{}"); check("ConstantArray(a, 3)", // "{a,a,a}"); check("ConstantArray(a, {2, 3})", // "{{a,a,a},{a,a,a}}"); check("ConstantArray(c, 10)", // "{c,c,c,c,c,c,c,c,c,c}"); check("ConstantArray(c, {3, 4})", // "{{c,c,c,c},{c,c,c,c},{c,c,c,c}}"); } @Test public void testContainsAny() { check("ContainsAny({b, a, b}, {a, b, c})", // "True"); check("ContainsAny({d,f,e}, {a, b, c})", // "False"); check("ContainsAny({ }, {a, b, c})", // "False"); check("ContainsAny(1, {1,2,3})", // "ContainsAny(1,{1,2,3})"); check("ContainsAny({1,2,3}, 4)", // "ContainsAny({1,2,3},4)"); check("ContainsAny({1.0,2.0}, {1,2,3})", // "False"); check("ContainsAny({1.0,2.0}, {1,2,3}, SameTest->Equal)", // "True"); } @Test public void testContainsAll() { check("ContainsAll({b,a,b,c}, {a, b})", // "True"); check("ContainsAll({b,a,b,c}, {a, b, d})", // "False"); check("ContainsAll({b, a, d}, {a, b, c})", // "False"); check("ContainsAll({ }, {a, b, c})", // "False"); check("ContainsAll({a, b, c},{ })", // "True"); check("ContainsAll(1, {1,2,3})", // "ContainsAll(1,{1,2,3})"); check("ContainsAll({1,2,3}, 4)", // "ContainsAll({1,2,3},4)"); check("ContainsAll({1.0,2.0}, {1,2,3})", // "False"); check("ContainsAll({1.0,2.0}, {1,2,3}, SameTest->Equal)", // "False"); check("ContainsAll({1,2,3}, {1.0,2.0})", // "False"); check("ContainsAll({1,2,3}, {1.0,2.0}, SameTest->Equal)", // "True"); } @Test public void testContainsOnly() { check("ContainsOnly(<|a -> x, b -> y|>, {x, y, z})", // "True"); check("ContainsOnly(<|a -> x, b -> y|>, <|1 -> x, 2 -> y, 3 -> z|>)", // "True"); check("ContainsOnly({b, a, a}, {a, b, c})", // "True"); check("ContainsOnly({b, a, d}, {a, b, c})", // "False"); check("ContainsOnly({ }, {a, b, c})", // "True"); check("ContainsOnly(1, {1,2,3})", // "ContainsOnly(1,{1,2,3})"); check("ContainsOnly({1,2,3}, 4)", // "ContainsOnly({1,2,3},4)"); check("ContainsOnly({1.0,2.0}, {1,2,3})", // "False"); check("ContainsOnly({1.0,2.0}, {1,2,3}, SameTest->Equal)", // "True"); } @Test public void testContainsExactly() { check("ContainsExactly({a, b, c},{ })", // "False"); check("ContainsExactly({b,a,b,c}, {a, b,c})", // "True"); check("ContainsExactly({b,a,d,d}, {a, b,c})", // "False"); check("ContainsExactly({b, a, d}, {a, b, c})", // "False"); check("ContainsExactly({ }, {a, b, c})", // "False"); check("ContainsExactly({a, b, c},{ })", // "False"); check("ContainsExactly(1, {1,2,3})", // "ContainsExactly(1,{1,2,3})"); check("ContainsExactly({1,2,3}, 4)", // "ContainsExactly({1,2,3},4)"); check("ContainsExactly({1.0,2.0}, {1,2,3})", // "False"); check("ContainsExactly({1.0,2.0}, {1,2,3}, SameTest->Equal)", // "False"); check("ContainsExactly({1,2,3}, {1.0,2.0})", // "False"); check("ContainsExactly({1,2,1,2}, {1.0,2.0}, SameTest->Equal)", // "True"); } @Test public void testContainsNone() { check("ContainsNone({d,f,e}, {a, b, c})", // "True"); check("ContainsNone({b, a, b}, {a, b, c})", // "False"); check("ContainsNone({ }, {a, b, c})", // "True"); check("ContainsNone(1, {1,2,3})", // "ContainsNone(1,{1,2,3})"); check("ContainsNone({1,2,3}, 4)", // "ContainsNone({1,2,3},4)"); check("ContainsNone({1.0,2.0}, {1,2,3})", // "True"); check("ContainsNone({1.0,2.0}, {1,2,3}, SameTest->Equal)", // "False"); } @Test public void testContext() { check("Context(a)", // "Global`"); check("Context()", // "Global`"); check("Context(Context)", // "System`"); check("{x, Global`x}", // "{x,x}"); check("a`b`x", // "a`b`x"); } @Test public void test$Context() { check("$Context", // "Global`"); } @Test public void test$ContextPath() { check("$ContextPath", // "{System`,Global`}"); } @Test public void test$MachineEpsilon() { // use the non-formatted output engine check("$MachineEpsilon", // "2.22045*10^-16"); check("a1=(1.0+$MachineEpsilon)", // "1.0"); check("a2=(1.0+$MachineEpsilon/2)", // "1.0"); check("{a1-1.0, a2-1.0}", // "{2.22045*10^-16,0.0}"); // use the non-formatted engine checkNumeric("$MachineEpsilon", // "2.220446049250313E-16"); checkNumeric("a1=(1.0+$MachineEpsilon)", // "1.0000000000000002"); checkNumeric("a2=(1.0+$MachineEpsilon/2)", // "1.0"); checkNumeric("{a1-1.0, a2-1.0}", // "{2.220446049250313E-16,0.0}"); } @Test public void test$MachinePrecision() { check("$MachinePrecision", // "16"); check("N(Sqrt(2), $MachinePrecision)", // "1.414213562373095"); // compare shorter string result to work under unix and windows: String evalStr = evalString("N(Sqrt(2), $MachinePrecision+1)"); String resultStr = "1.414213562373095"; assertEquals(evalStr.substring(0, evalStr.length()), resultStr); } @Test public void test$MaxMachineNumber() { check("$MaxMachineNumber// FullForm", // "1.7976931348623157`*^308"); } @Test public void test$MinMachineNumber() { check("2.2250738585072014`*^-308 // FullForm", // "2.2250738585072014`*^-308"); check("$MinMachineNumber// FullForm", // "2.2250738585072014`*^-308"); } @Test public void test$Version() { check("$Version", // Config.getVersion()); } @Test public void testContinue() { check("For(i=1, i<=8, i=i+1, If(Mod(i,2) == 0, Continue()); Print(i))", // ""); } @Test public void testContinuedFraction() { // print message: ContinuedFraction: Positive integer (less than 2147483647) expected at // position 2 in // ContinuedFraction(Pi,-20). check("ContinuedFraction(9/22)", // "{0,2,2,4}"); check("ContinuedFraction(9.0/22)", // "{0,2,2,3,1}"); check("ContinuedFraction(-19/10)", // "{-1,-1,-9}"); check("ContinuedFraction(7283752929681393 / 4096)", // "{1778259992597,1,272,15}"); check("ContinuedFraction(30000000000000/53*Pi,10)", // "{1778259992597,1,272,15}"); check("ContinuedFraction(-7283752929681393 / 4096)", // "{-1778259992597,-1,-272,-15}"); check("ContinuedFraction(-30000000000000/53*Pi,10)", // "{-1778259992597,-1,-272,-15}"); check("ContinuedFraction(2476979795053773 / 4503599627370496)", // "{0,1,1,4,2,56294995342130,1,3}"); check("N(30000000000000/53*Pi)", // "1.77826*10^12"); check("ContinuedFraction((2-2*Sqrt(3))/11,20)", // "{0,-7,-1,-1,-18,-1,-1,-9,-76,-9,-1,-1,-18,-1,-1,-9,-76,-9,-1,-1}"); check("ContinuedFraction((2-2*Sqrt(3))/11 )", // "{0,-7,{-1,-1,-18,-1,-1,-9,-76,-9}}"); check("ContinuedFraction(-5*Sqrt(11))", // "{-16,{-1,-1,-2,-1,-1,-32}}"); check("ContinuedFraction(-Sqrt(70))", // < "{-8,{-2,-1,-2,-1,-2,-16}}"); check("ContinuedFraction(4*Sqrt(48))", // "{27,{1,2,2,13,2,2,1,54}}"); check("ContinuedFraction(Sqrt(70))", // "{8,{2,1,2,1,2,16}}"); check("ContinuedFraction(5*Sqrt(11))", // "{16,{1,1,2,1,1,32}}"); check("ContinuedFraction((3+Sqrt(2))/7)", // "{0,1,1,1,{2}}"); check("ContinuedFraction(Sqrt(13))", // "{3,{1,1,1,1,6}}"); check("ContinuedFraction((1 + 2*Sqrt(3))/5)", // "{0,1,{8,3,34,3}}"); check("ContinuedFraction(Sqrt(70))", // "{8,{2,1,2,1,2,16}}"); // START ContinuedFraction -> FromContinuedFraction check("ContinuedFraction((7*Sqrt(2) + 1)/11)", // "{0,1,{108,2,4,4,4,2}}"); check("period=FromContinuedFraction({108,2,4,4,4,2,t})", // "108+1/(2+1/(4+1/(4+1/(4+1/(2+1/t)))))"); check("period // Together", // "(17460+39041*t)/(161+360*t)"); check("y=Solve(period-t==0,t) [[2,1,2]]", // "1/720*(38880+27720*Sqrt(2))"); // TODO check("FromContinuedFraction({0,1,x}) /. x->y // Simplify", // "1/11*(1+7*Sqrt(2))"); // END ContinuedFraction -> FromContinuedFraction check("ContinuedFraction(Pi, 10)", // "{3,7,15,1,292,1,1,1,2,1}"); check("ContinuedFraction(-Pi, 10)", // "{-3,-7,-15,-1,-292,-1,-1,-1,-2,-1}"); check("ContinuedFraction(Sqrt(-1))", // "ContinuedFraction(I)"); check("ContinuedFraction(Sqrt(1))", // "{1}"); check("ContinuedFraction(Pi,-20)", // "ContinuedFraction(Pi,-20)"); check("ContinuedFraction(Pi,a)", // "ContinuedFraction(Pi,a)"); // github #127 check("ContinuedFraction( (10+(2*Sqrt(10)))/(Sqrt(5)+Sqrt(2))+8/(1-Sqrt(5)))", // "{-2}"); check("(10+(2*Sqrt(10)))/(Sqrt(5)+Sqrt(2))+8/(1-Sqrt(5)) // N", // "-2.0"); check("ContinuedFraction(E,100)", // "{2,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,1,11,1,1,1,11,5,1,1,2,1,4,2,1,1,9,17,3}"); // print message: ContinuedFraction: calculations of double number values require a iteration // limit less equal 100. check("ContinuedFraction(E,101)", // "{2,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,1,11,1,1,1,11,5,1,1,2,1,4,2,1,1,9,17,3}"); check("ContinuedFraction(Sqrt(0))", // "{0}"); check("ContinuedFraction(Sqrt(2))", // "{1,{2}}"); check("ContinuedFraction(Sqrt(3))", // "{1,{1,2}}"); check("ContinuedFraction(Sqrt(4729494))", // "{2174,{1,2,1,5,2,25,3,1,1,1,1,1,1,15,1,2,16,1,2,1,1,8,6,1,21,1,1,3,1,1,1,2,2,6,1,\n" // + "1,5,1,17,1,1,47,3,1,1,6,1,1,3,47,1,1,17,1,5,1,1,6,2,2,1,1,1,3,1,1,21,1,6,8,1,1,2,\n" // + "1,16,2,1,15,1,1,1,1,1,1,3,25,2,5,1,2,1,4348}}"); check("ContinuedFraction(Sqrt(919))", // "{30,{3,5,1,2,1,2,1,1,1,2,3,1,19,2,3,1,1,4,9,1,7,1,3,6,2,11,1,1,1,29,1,1,1,11,2,6,\n" // + "3,1,7,1,9,4,1,1,3,2,19,1,3,2,1,1,1,2,1,2,1,5,3,60}}"); check("ContinuedFraction(Sqrt(13))", "{3,{1,1,1,1,6}}"); check("ContinuedFraction(0.753)", // "{0,1,3,20,1,1,2,1,1}"); check("ContinuedFraction(0.55)", // "{0,1,1,4,2}"); check("ContinuedFraction(-0.753)", // "{0,-1,-3,-20,-1,-1,-2,-1,-1}"); check("ContinuedFraction(-0.55)", // "{0,-1,-1,-4,-2}"); check("ContinuedFraction(Pi,30)", // "{3,7,15,1,292,1,1,1,2,1,3,1,14,3,3,2,1,3,3,7,2,1,1,3,2,42,2}"); check("ContinuedFraction(47/17)", // "{2,1,3,4}"); check("ContinuedFraction(Sqrt(13))", // "{3,{1,1,1,1,6}}"); check("ContinuedFraction(Sqrt(13),20)", // "{3,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1}"); check("ContinuedFraction(Sqrt(13),1)", // "{3}"); check("ContinuedFraction(Sqrt(13),4)", // "{3,1,1,1}"); } @Test public void testConvergents() { // TODO // check( // "Convergents({1,Quantity(1.2,\"m\")})", // // ""); // check( // "Convergents({1,Quantity(1.2,\"m\"),3,a})", // // ""); check("Convergents({1,2,3,a})", // "{1,3/2,10/7,(3+10*a)/(2+7*a)}"); check("Convergents({{1,0},{0,1},0})", // "Convergents({{1,0},{0,1},0})"); check("Convergents({2,3,4,5})", // "{2,7/3,30/13,157/68}"); check("Convergents({1,1,1,1,1})", // "{1,2,3/2,5/3,8/5}"); check("Convergents({a,b,c,d})", // "{a,(1+a*b)/b,(a+c+a*b*c)/(1+b*c),(1+a*b+a*d+c*d+a*b*c*d)/(b+d+b*c*d)}"); } @Test public void testConvexHullMesh() { check( "ConvexHullMesh({{0.0, 0.0, 0.0}, {1.0, 0.5, 0.0}, {2.0, 0.0, 0.0}, " + "{0.5, 0.5, 0.5}, {0.0, 0.0, 2.0}, {0.1, 0.2, 0.3}, {0.0, 2.0, 0.0}})", // "{{0.0,0.0,0.0},{2.0,0.0,0.0},{0.0,0.0,2.0},{0.0,2.0,0.0}}"); check("ConvexHullMesh({{0., 0.}, {1., 0.}, {0.5, 0.1}, {4.5,1.1}, {2., 3.}})", // "{{0.0,0.0},{1.0,0.0},{4.5,1.1},{2.0,3.0}}"); } @Test public void testCoprimeQ() { check("CoprimeQ(7,3)", // "True"); check("CoprimeQ(7)", // "False"); check("CoprimeQ( )", // "False"); check("CoprimeQ(8,9,11)", // "True"); check("CoprimeQ({1, 2, 3, 4, 5}, 6)", // "{True,False,False,False,True}"); check("CoprimeQ(2, 3, 5)", // "True"); } @Test public void testCos() { // {-(1/2), (1/4)*(1 - Sqrt(5)), -Sin(Pi/30), Sin(Pi/30), (1/4)*(-1 + Sqrt(5)), // 1/2, Sin((7*Pi)/30), (1/4)*(1 + Sqrt(5)), Cos((2*Pi)/15), Cos(Pi/15), 1, // Cos(Pi/15), Cos((2*Pi)/15), (1/4)*(1 + Sqrt(5)), Sin((7*Pi)/30), 1/2, // (1/4)*(-1 + Sqrt(5)), Sin(Pi/30), -Sin(Pi/30), (1/4)*(1 - Sqrt(5)), -(1/2)} check("Table(Cos(i/15*Pi),{i,-10,10})", // "{-1/2,1/4*(1-Sqrt(5)),-Cos(7/15*Pi),Cos(7/15*Pi),1/4*(-1+Sqrt(5)),1/2,Cos(4/15*Pi),\n" + "1/4*(1+Sqrt(5)),Cos(2/15*Pi),Cos(Pi/15),1,Cos(Pi/15),Cos(2/15*Pi),1/4*(1+Sqrt(5)),Cos(\n" + "4/15*Pi),1/2,1/4*(-1+Sqrt(5)),Cos(7/15*Pi),-Cos(7/15*Pi),1/4*(1-Sqrt(5)),-1/2}"); // {Sin(a - Pi/6), Sin(a - Pi/10), Sin(a - Pi/30), Sin(a + Pi/30), // Sin(a + Pi/10), Sin(a + Pi/6), Sin(a + (7*Pi)/30), Cos(a - Pi/5), // Cos(a - (2*Pi)/15), Cos(a - Pi/15), Cos(a), Cos(a + Pi/15), // Cos(a + (2*Pi)/15), Cos(a + Pi/5), -Sin(a - (7*Pi)/30), -Sin(a - Pi/6), // -Sin(a - Pi/10), -Sin(a - Pi/30), -Sin(a + Pi/30), -Sin(a + Pi/10), // -Sin(a + Pi/6)} check("Table(Cos(a+i/15*Pi),{i,-10,10})", // "{-Cos(a+Pi/3),-Cos(a+2/5*Pi),-Cos(a+7/15*Pi),Sin(a+Pi/30),Sin(a+Pi/10),Sin(a+Pi/\n" + "6),Sin(a+7/30*Pi),Sin(a+3/10*Pi),Sin(a+11/30*Pi),Sin(a+13/30*Pi),Cos(a),Cos(a+Pi/\n" + "15),Cos(a+2/15*Pi),Cos(a+Pi/5),Cos(a+4/15*Pi),Cos(a+Pi/3),Cos(a+2/5*Pi),Cos(a+7/\n" + "15*Pi),-Sin(a+Pi/30),-Sin(a+Pi/10),-Sin(a+Pi/6)}"); check("Cos(1.20000000000000000000000)", // "0.362357754476673577638373"); // print argx message check("Cos( )", // "Cos()"); check("Cos(a,b)", // "Cos(a,b)"); check("Cos(I*a+I*b*x)/b", // "Cosh(a+b*x)/b"); // TODO return Cosh((1 + 2*I)*a - 3*I*b*x) check("Cos((-2+I)*a+3*b*x)", // "Cosh((1+I*2)*a-I*3*b*x)"); check("Cos(-2*a+3*b*x)", // "Cos(2*a-3*b*x)"); check("Cos(-2*a-3*b*x)", // "Cos(2*a+3*b*x)"); check("Refine(Cos(x+k*Pi), Element(k, Integers))", // "(-1)^k*Cos(x)"); check("Cos(5/8*Pi+2*x)", // "-Sin(Pi/8+2*x)"); check("Cos(3/4*Pi+2*x)", // "-Sin(Pi/4+2*x)"); check("Cos(Pi/4 - r/2 - s + x)", // "Sin(Pi/4+r/2+s-x)"); check("Cos(I*x)-I*Sin(I*x)", // "Cosh(x)+Sinh(x)"); check("Cos(3/4*Pi+x)", // "-Sin(Pi/4+x)"); // -Cos(Pi/4-x) check("Cos(-3/4*Pi+x)", // "-Cos(Pi/4+x)"); check("Cos(e - Pi/2 + f*x)", // "Sin(e+f*x)"); check("Cos(-1/2*E+z)", // "Cos(E/2-z)"); check("Cos(-Pi/2+z)", // "Sin(z)"); check("Cos(e-Pi/2+f*x)", // "Sin(e+f*x)"); check("Cos(e-3/2*Pi+f*x)", // "-Sin(e+f*x)"); check("Cos(e-1+f*x)", // "Cos(1-e-f*x)"); check("Cos(I*a+I*b*x)/b", // "Cosh(a+b*x)/b"); check("Cos(ArcSin(x))", // "Sqrt(1-x^2)"); check("Cos(ArcCos(x))", // "x"); check("Cos(ArcTan(x))", // "1/Sqrt(1+x^2)"); check("Cos(ArcCot(x))", // "1/Sqrt(1+1/x^2)"); check("Cos(ArcCsc(x))", // "Sqrt(1-1/x^2)"); check("Cos(ArcSec(x))", // "1/x"); check("Cos(0)", // "1"); check("Cos(3*Pi)", // "-1"); check("Cos(1.5*Pi)", // "-1.83697*10^-16"); check("Cos(z+1/2*Pi)", // "-Sin(z)"); check("Cos(Pi)", // "-1"); check("Cos(z+Pi)", // "-Cos(z)"); check("Cos(z+42*Pi)", // "Cos(z)"); check("Cos(x+y+z+43*Pi)", // "-Cos(x+y+z)"); check("Cos(z+42*a*Pi)", // "Cos(42*a*Pi+z)"); // this rule was moved to FunctionExpand check("Cos(Sqrt(x^2))", // "Cos(Sqrt(x^2))"); } @Test public void testCosh() { check("Cosh(10*Pi*I)", // "1"); check("Cosh(43*Pi*I)", // "-1"); check("Cosh(17/2*Pi*I)", // "0"); check("Refine(Cosh(x+I*k*Pi), Element(k, Integers))", // "(-1)^k*Cosh(x)"); check("Refine(Cosh(x-I*k*Pi), Element(k, Integers))", // "(-1)^k*Cosh(x)"); check("Refine(Cosh(x+4*I*k*Pi), Element(k, Integers))", // "Cosh(x)"); check("Cosh(Pi*I+x)", // "-Cosh(x)"); check("Cosh(10*Pi*I+x)", // "Cosh(x)"); check("Cosh(43*Pi*I+x)", // "-Cosh(x)"); check("Cosh(0)", // "1"); check("Cosh(1/6*Pi*I)", // "Sqrt(3)/2"); check("Cosh(Infinity)", // "Infinity"); check("Cosh(ComplexInfinity)", // "Indeterminate"); } @Test public void testCreateDirectory() { // Config.FILESYSTEM_ENABLED = true; // check("CreateDirectory()", // // "C:\\Users\\dev\\AppData\\Local\\Temp\\1539799359607-0"); } @Test public void testCanberraDistance() { check("CanberraDistance({0,0},{0,0})", // "0"); check("CanberraDistance(SparseArray({11,1,19,2}),SparseArray({5,7,1,23}))", // "573/200"); check("CanberraDistance( {11,1,19,2} , {5,7,1,23} )", // "573/200"); check("CanberraDistance({-1, -1.0}, {1, 1})", // "2.0"); check("CanberraDistance({-1, -1}, {1, 1})", // "2"); } @Test public void testCorrelation() { check("Correlation({a,b},{c,d})", // "((a-b)*(Conjugate(c)-Conjugate(d)))/(Sqrt((a-b)*(Conjugate(a)-Conjugate(b)))*Sqrt((c-d)*(Conjugate(c)-Conjugate(d))))"); check("Correlation({1.5, 3, 5, 10}, {2, 1.25, 15, 8})", // "0.475976"); check("N(Correlation({5.0, 3/4, 1}, {2, 1/2, 1}))", // "0.960769"); check("Correlation({a,b},{c,d})", // "((a-b)*(Conjugate(c)-Conjugate(d)))/(Sqrt((a-b)*(Conjugate(a)-Conjugate(b)))*Sqrt((c-d)*(Conjugate(c)-Conjugate(d))))"); check( "Correlation({10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5}, {8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26,10.84, 4.82, 5.68})", // "0.816421"); check("Correlation({5, 3/4, 1}, {2, 1/2, 1})", // "2*Sqrt(3/13)"); check("Correlation({\n" + // "{60323,83.0,234289,2356,1590,107608,1947},\n" + // "{61122,88.5,259426,2325,1456,108632,1948},\n" + // "{60171,88.2,258054,3682,1616,109773,1949},\n" + // "{61187,89.5,284599,3351,1650,110929,1950},\n" + // "{63221,96.2,328975,2099,3099,112075,1951},\n" + // "{63639,98.1,346999,1932,3594,113270,1952},\n" + // "{64989,99.0,365385,1870,3547,115094,1953},\n" + // "{63761,100.0,363112,3578,3350,116219,1954},\n" + // "{66019,101.2,397469,2904,3048,117388,1955},\n" + // "{67857,104.6,419180,2822,2857,118734,1956},\n" + // "{68169,108.4,442769,2936,2798,120445,1957},\n" + // "{66513,110.8,444546,4681,2637,121950,1958},\n" + // "{68655,112.6,482704,3813,2552,123366,1959},\n" + // "{69564,114.2,502601,3931,2514,125368,1960},\n" + // "{69331,115.7,518173,4806,2572,127852,1961},\n" + // "{70551,116.9,554894,4007,2827,130081,1962}})", // "{{1.0,0.970899,0.983552,0.502498,0.457307,0.960391,0.971329},\n" + // " {0.970899,1.0,0.991589,0.620633,0.464744,0.979163,0.991149},\n" + // " {0.983552,0.991589,1.0,0.604261,0.446437,0.99109,0.995273},\n" + // " {0.502498,0.620633,0.604261,1.0,-0.177421,0.686552,0.668257},\n" + // " {0.457307,0.464744,0.446437,-0.177421,1.0,0.364416,0.417245},\n" + // " {0.960391,0.979163,0.99109,0.686552,0.364416,1.0,0.993953},\n" + // " {0.971329,0.991149,0.995273,0.668257,0.417245,0.993953,1.0}}"); // check("Correlation(RandomReal(1, 10^4), RandomReal(1, 10^4))", // // "0.000430087"); } @Test public void testCorrelationDistance() { check("CorrelationDistance({2,2},{5,10})", // "0"); check("N(CorrelationDistance({2,2},{5,10}))", // "0.0"); check("N(CorrelationDistance({4,5},{4,5}))", // "0.0"); check("CorrelationDistance({4,5},{4,5})", // "0"); check("CorrelationDistance({1, 2, 3}, {3,5,10})", // "1-7/2*1/Sqrt(13)"); check("N(CorrelationDistance({1, 2, 3}, {3,5,10}))", // "0.0292747"); check("CorrelationDistance({a,b}, {x,y})", // "1-((a+1/2*(-a-b))*(Conjugate(x)+1/2*(-Conjugate(x)-Conjugate(y)))+(1/2*(-a-b)+b)*(\n"// + "1/2*(-Conjugate(x)-Conjugate(y))+Conjugate(y)))/Sqrt((Abs(a+1/2*(-a-b))^2+Abs(1/\n"// + "2*(-a-b)+b)^2)*(Abs(x+1/2*(-x-y))^2+Abs(1/2*(-x-y)+y)^2))");// check("CorrelationDistance({a,b,c}, {x,y,z})", // "1-((a+1/3*(-a-b-c))*(Conjugate(x)+1/3*(-Conjugate(x)-Conjugate(y)-Conjugate(z)))+(b+\n"// + "1/3*(-a-b-c))*(Conjugate(y)+1/3*(-Conjugate(x)-Conjugate(y)-Conjugate(z)))+(1/3*(-a-b-c)+c)*(\n"// + "1/3*(-Conjugate(x)-Conjugate(y)-Conjugate(z))+Conjugate(z)))/Sqrt((Abs(a+1/3*(-a-b-c))^\n"// + "2+Abs(b+1/3*(-a-b-c))^2+Abs(1/3*(-a-b-c)+c)^2)*(Abs(x+1/3*(-x-y-z))^2+Abs(y+1/3*(-x-y-z))^\n"// + "2+Abs(1/3*(-x-y-z)+z)^2))");// check("CorrelationDistance(N({1, 5, 2, 3, 10}, 50), N({4, 15, 20, 5, 5}, 50))", // "1.2106635188398813533035274347761676650148587810028"); // check("CorrelationDistance(RandomReal(5, 100), RandomReal(5, 100))", // // "1.0697"); } @Test public void testCosineDistance() { check("CosineDistance({7.0, 9}, {71, 89})", // "0.0000759646"); check("N(CosineDistance({7, 9}, {71, 89}))", // "0.0000759646"); check("CosineDistance({a, b}, {c, d})", // "1-(a*Conjugate(c)+b*Conjugate(d))/Sqrt((Abs(a)^2+Abs(b)^2)*(Abs(c)^2+Abs(d)^2))");// check("CosineDistance({a, b, c}, {x, y, z})", // "1-(a*Conjugate(x)+b*Conjugate(y)+c*Conjugate(z))/Sqrt((Abs(a)^2+Abs(b)^2+Abs(c)^\n" // + "2)*(Abs(x)^2+Abs(y)^2+Abs(z)^2))"); } @Test public void testCosIntegral() { checkNumeric("CosIntegral(2.8)", // "0.18648838964317577"); check("Table(CosIntegral(x), {x,-4.0, 4.0, 1/4})", // "{-0.140982+I*3.14159,-0.093103+I*3.14159,-0.0321285+I*3.14159,0.0398086+I*3.14159,0.11963+I*3.14159," // + "0.203307+I*3.14159,0.285871+I*3.14159,0.361402+I*3.14159,0.422981+I*3.14159,0.46252+I*3.14159," // + "0.470356+I*3.14159,0.434301+I*3.14159,0.337404+I*3.14159,0.152164+I*3.14159,-0.177784+I*3.14159," // + "-0.824663+I*3.14159,-Infinity,-0.824663,-0.177784,0.152164,0.337404,0.434301,0.470356,0.46252," // + "0.422981,0.361402,0.285871,0.203307,0.11963,0.0398086,-0.0321285,-0.093103,-0.140982}"); check("Table(CosIntegral(x+I), {x,-4.0, 4.0, 1/4})", // "{-0.265563+I*3.31255,-0.208538+I*3.37786,-0.130716+I*3.43686,-0.0341048+I*3.48549,0.0781342+I*3.51974," // + "0.201739+I*3.53574,0.331465+I*3.52983,0.461254+I*3.49865,0.584476+I*3.43909,0.694251+I*3.34816," // + "0.783918+I*3.22281,0.847756+I*3.05959,0.882172+I*2.85434,0.887634+I*2.60237,0.871301+I*2.30022," // + "0.848481+I*1.95082,0.837867+I*1.5708,0.848481+I*1.19077,0.871301+I*0.841369,0.887634+I*0.539222," // + "0.882172+I*0.287249,0.847756+I*0.0820006,0.783918+I*(-0.0812194),0.694251+I*(-0.206567)," // + "0.584476+I*(-0.297495),0.461254+I*(-0.35706),0.331465+I*(-0.388237),0.201739+I*(-0.394143)," // + "0.0781342+I*(-0.378147),-0.0341048+I*(-0.343896),-0.130716+I*(-0.295264),-0.208538+I*(-0.236271)," // + "-0.265563+I*(-0.170956)}"); } @Test public void testCoshIntegral() { // TODO https://github.com/paulmasson/math/issues/15 check("CoshIntegral(-4.0)", // "9.81355+I*3.14159"); check("CoshIntegral(2.8)", // "4.33122"); check("Table(CoshIntegral(x), {x,-4.0, 4.0, 1/4})", // "{9.81355+I*3.14159,8.2561+I*3.14159,6.95919+I*3.14159,5.87389+I*3.14159,4.96039+I*3.14159," // + "4.18616+I*3.14159,3.52443+I*3.14159,2.9529+I*3.14159,2.45267+I*3.14159,2.00708+I*3.14159," // + "1.60063+I*3.14159,1.21732+I*3.14159,0.837867+I*3.14159,0.433496+I*3.14159,-0.0527768+I*3.14159," // + "-0.793413+I*3.14159,-Infinity,-0.793413,-0.0527768,0.433496,0.837867,1.21732,1.60063,2.00708," // + "2.45267,2.9529,3.52443,4.18616,4.96039,5.87389,6.95919,8.2561,9.81355}"); } @Test public void testCot() { // check("Cot(4/15*Pi)", // // "Tan((7*Pi)/30)"); check("Cot(0.0)", // "ComplexInfinity"); check("Cot(0)", // "ComplexInfinity"); // check("Cot(z-Pi/3)", // // "-Tan(Pi/6+z)"); check("Cot(e-Pi/2+f*x)", // "-Tan(e+f*x)"); check("Cot(e+Pi/2+f*x)", // "-Tan(e+f*x)"); check("Cot(ComplexInfinity)", // "Indeterminate"); check("Cot(Indeterminate)", // "Indeterminate"); check("Sin(x)*Cot(x)", // "Cos(x)"); // check("Sin(x)^2*Cot(x)^2", "Cos(x)^2"); // check("Sin(x)^2*Cot(x)^4", "Cos(x)^2*Cot(x)^2"); // check("Sin(x)^4*Cot(x)^2", "Cos(x)^2*Sin(x)^2"); check("Cot(ArcSin(x))", // "Sqrt(1-x^2)/x"); check("Cot(ArcCos(x))", // "x/Sqrt(1-x^2)"); check("Cot(ArcTan(x))", // "1/x"); check("Cot(ArcCot(x))", // "x"); check("Cot(ArcCsc(x))", // "Sqrt(1-1/x^2)*x"); check("Cot(ArcSec(x))", // "1/(Sqrt(1-1/x^2)*x)"); check("Cot(Pi/4)", // "1"); check("Cot(0)", // "ComplexInfinity"); check("Cot(1.)", // "0.642093"); check("Cot(z+1/2*Pi)", // "-Tan(z)"); check("Cot(Pi)", // "ComplexInfinity"); check("Cot(z+Pi)", // "Cot(z)"); check("Cot(z+42*Pi)", // "Cot(z)"); check("Cot(x+y+z+43*Pi)", // "Cot(x+y+z)"); check("Cot(z+42*a*Pi)", // "Cot(42*a*Pi+z)"); } @Test public void testCoth() { check("Coth(0)", // "ComplexInfinity"); check("Coth(0.)", // "ComplexInfinity"); } @Test public void testCount() { check("Count(2,2)", // "0"); check("SeedRandom(12345);Count(RandomReal(1, {100}), u_ /; u > 0.5)", // "46"); check("Count(Sin(x) + Cos(x) + Sin(x)^2, Sin, -1 )", // "0"); check("Count(Sin(x) + Cos(x) + Sin(x)^2, Sin, -1, Heads -> True)", // "2"); check("Count(a)[{{a, a}, {a, a, a}, a}]", // "1"); check("Count(a)[{{a, a}, {a, a, a}, a}, {2}]", // "Count(a)[{{a,a},{a,a,a},a},{2}]"); check("Count({1,List},List)", // "1"); check("Count({1,List},Last({1,List}))", // "1"); check("Count(<|a -> 1, b -> 2, c -> 2|>, 2)", // "2"); check("Count({3, 7, 10, 7, 5, 3, 7, 10}, 3)", // "2"); check("Count({{a, a}, {a, a, a}, a}, a, {2})", // "5"); check("count({a, b, a, a, b, c, b}, b)", // "3"); check("count({a, b, f(g(b,a)), a, b, c, b}, b)", // "3"); check("count({a, b, f(g(b,a)), a, b, c, b}, b, infinity)", // "4"); check("count({a, b, f(g(b,a)), a, b, c, b}, b, {1,2})", // "3"); check("count({a, b, f(g(b,a)), a, b, c, b}, b, {1,3})", // "4"); check("count({a, b, f(g(b,a)), a, b, c, b}, b, 3)", // "4"); check("count({a, b, f(g(b,a)), a, b, c, b}, b, {3})", // "1"); check("count({a, b, f(g(b,a)), a, b, c, b}, b, {-1})", // "4"); check("count({3, 4, x, x^2, x^3}, x^_)", // "2"); } @Test public void testCounts() { check("Counts({a, a, b, c, a, a, b, c, c, a, a})", // "<|a->6,b->2,c->3|>"); } @Test public void testCountDistinct() { check("CountDistinct({3, 7, 10, 7, 5, 3, 7, 10})", // "4"); check("CountDistinct({{a, a}, {a, a, a}, a, a})", // "3"); check("CountDistinct({a, b, b, c, a})", // "3"); check("CountDistinct(<|a -> 1, b -> 2, c -> 2|>)", // "2"); } @Test public void testCovariance() { check("Covariance({{0.25,0.33,0.45}})", // "Covariance(\n" // + "{{0.25,0.33,0.45}})"); check("Covariance({{0.25,0.13,0.45,0.02},{0.25,0.36,0.45,0.02}})", // "{{0.0,0.0,0.0,0.0},\n" // + " {0.0,0.02645,0.0,0.0},\n" // + " {0.0,0.0,0.0,0.0},\n" // + " {0.0,0.0,0.0,0.0}}"); check("Covariance({{0.25,0.33,0.45},{0.25,0.33,0.45}})", // "{{0.0,0.0,0.0},\n" // + " {0.0,0.0,0.0},\n" // + " {0.0,0.0,0.0}}"); check("Covariance(I,x^2)", // "Covariance(I,x^2)"); check( "Covariance({10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5}, {8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68})", // "5.501"); check("Covariance({0.2, 0.3, 0.1}, {0.3, 0.3, -0.2})", // "0.025"); check("Covariance({a, b, c,d,e}, {x, y, z,v,w})", // "1/20*(-(a+b+c-4*d+e)*Conjugate(v)-(a+b+c+d-4*e)*Conjugate(w)-(-4*a+b+c+d+e)*Conjugate(x)-(a-\n" + "4*b+c+d+e)*Conjugate(y)-(a+b-4*c+d+e)*Conjugate(z))"); check("Covariance({a, b, c}, {x, y, z})", // "1/6*(-(-2*a+b+c)*Conjugate(x)-(a-2*b+c)*Conjugate(y)-(a+b-2*c)*Conjugate(z))"); check("Covariance({a, b}, {x, y})", // "1/2*(a-b)*(Conjugate(x)-Conjugate(y))"); checkNumeric("Covariance({1.5, 3, 5, 10}, {2, 1.25, 15, 8})", // "11.260416666666666"); } @Test public void testCsc() { // check("Csc(8/15*Pi)", // // "Sec(Pi/30)"); check("Csc(z+Pi)", // "-Csc(z)"); check("Csc(-3/4*Pi+x)", // "-Csc(Pi/4+x)"); check("Csc(5/7*Pi+x)", // "Sec(3/14*Pi+x)"); check("Csc(3/4*Pi+x)", // "Sec(Pi/4+x)"); check("Csc(e - Pi/2 + f*x)", // "-Sec(e+f*x)"); check("Csc(x)^m*Cot(x)", // "Cos(x)*Csc(x)^(1+m)"); check("Csc(x)^m*Cot(x)^3", // "Cos(x)^3*Csc(x)^(3+m)"); check("Csc(3.5)", // "-2.85076"); check("Csc(1.0+3.5*I)", // "0.0508282+I*(-0.0325769)"); check("Csc(0)", // "ComplexInfinity"); check("Csc(1)", // "Csc(1)"); check("Csc(1.)", // "1.1884"); check("Csc(2/5*Pi)", // "Sqrt(2-2/Sqrt(5))"); check("Csc(23/12*Pi)", // "-2*Sqrt(2+Sqrt(3))"); check("Csc(z+1/2*Pi)", // "Sec(z)"); check("Csc(Pi)", // "ComplexInfinity"); check("Csc(z+Pi)", // "-Csc(z)"); check("Csc(z+42*Pi)", // "Csc(z)"); check("Csc(x+y+z+43*Pi)", // "-Csc(x+y+z)"); check("Csc(z+42*a*Pi)", // "Csc(42*a*Pi+z)"); check("Csc(ArcSin(x))", // "1/x"); check("Csc(ArcCos(x))", // "1/Sqrt(1-x^2)"); check("Csc(ArcTan(x))", // "Sqrt(1+x^2)/x"); check("Csc(ArcCot(x))", // "Sqrt(1+x^2)"); check("Csc(ArcCsc(x))", // "x"); check("Csc(ArcSec(x))", // "1/Sqrt(1-1/x^2)"); } @Test public void testCsch() { // gitbub #173 check("Csch(Log(5/3))", // "15/8"); check("Refine(Csch(x+I*k*Pi), Element(k, Integers))", // "(-1)^k*Csch(x)"); check("Refine(Csch(x-I*k*Pi), Element(k, Integers))", // "(-1)^k*Csch(x)"); check("Refine(Csch(x-42*I*k*Pi), Element(k, Integers))", // "Csch(x)"); check("Csch(x)^m*Coth(x)^2", // "Cosh(x)^2*Csch(x)^(2+m)"); check("Csch(0)", // "ComplexInfinity"); check("Csch(-x)", // "-Csch(x)"); checkNumeric("Csch(1.8)", // "0.3398846914154937"); check("D(Csch(x),x)", // "-Coth(x)*Csch(x)"); } @Test public void testCubeRoot() { check("N(CubeRoot(18), 100)", // "2.620741394208896607141661280441996270239427645723631725102773805728699819196042108828455825989073597"); check("CubeRoot(-64)", // "-4"); check("(-8)^(-4/3)", // "(-1)^(2/3)/16"); check("CubeRoot(((-8)^(-4)))", // "1/16"); // github #158 check("(-1)^(1/3) //N", // "0.5+I*0.866025"); check("CubeRoot(-1) //N", // "-1.0"); // message - CubeRoot: The parameter 3+I*4 should be real-valued. check("CubeRoot(3 + 4*I)", // "CubeRoot(3+I*4)"); check("CubeRoot(16)", // "2*2^(1/3)"); check("CubeRoot(-5)", // "-5^(1/3)"); check("CubeRoot(-510000)", // "-10*510^(1/3)"); check("CubeRoot(-5.1)", // "-1.7213"); check("CubeRoot(b)", // "Surd(b,3)"); check("CubeRoot(-0.5)", // "-0.793701"); check("CubeRoot({-3, -2, -1, 0, 1, 2, 3})", // "{-3^(1/3),-2^(1/3),-1,0,1,2^(1/3),3^(1/3)}"); check("CubeRoot(-2.)", // "-1.25992"); } @Test public void testCurl() { check("Curl({y, -x}, {x, y})", // "-2"); check("Curl({y, -x, 2 z}, {x, y, z})", // "{0,0,-2}"); check("Curl(SparseArray({{1}->y,{2}->-x,{3}->-z},Automatic,0),{x,y,z})", // "{0,0,-2}"); check("Curl({f(x, y, z), g(x, y, z), h(x, y, z)}, {x, y, z})", // "{-Derivative(0,0,1)[g][x,y,z]+Derivative(0,1,0)[h][x,y,z],Derivative(0,0,1)[f][x,y,z]-Derivative(\n" + "1,0,0)[h][x,y,z],-Derivative(0,1,0)[f][x,y,z]+Derivative(1,0,0)[g][x,y,z]}"); } @Test public void testCyclotomic() { // check( // "Cyclotomic(10009,-9223372036854775808/9223372036854775807)", // // ""); check("Cyclotomic(101,-3/4)", // "918250311005358176390006343336822827639729834135611094824501/\n" + "1606938044258990275541962092341162602522202993782792835301376"); check("Cyclotomic(10, z)", // "1-z+z^2-z^3+z^4"); check("Cyclotomic(101,-Infinity)", // "Indeterminate"); // message Cyclotomic: Polynomial degree 2147483647 exceeded check("Cyclotomic(2147483647,3/4)", // "Cyclotomic(2147483647,3/4)"); // https://en.wikipedia.org/wiki/Cyclotomic_polynomial check("Cyclotomic(0,x)", // "1"); check("Cyclotomic(1,x)", // "-1+x"); check("Cyclotomic(5,x)", // "1+x+x^2+x^3+x^4"); check("Cyclotomic(10,x)", // "1-x+x^2-x^3+x^4"); check("Cyclotomic(25,x)", // "1+x^5+x^10+x^15+x^20"); check("Cyclotomic(32,x)", // "1+x^16"); if (Config.EXPENSIVE_JUNIT_TESTS) { check("Cyclotomic(94,x)", // "1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8-x^9+x^10-x^11+x^12-x^13+x^14-x^15+x^16-x^17+x^18-x^\n" + "19+x^20-x^21+x^22-x^23+x^24-x^25+x^26-x^27+x^28-x^29+x^30-x^31+x^32-x^33+x^34-x^\n" + "35+x^36-x^37+x^38-x^39+x^40-x^41+x^42-x^43+x^44-x^45+x^46"); // The case of the 105-th cyclotomic polynomial is interesting because 105 is the lowest // integer that is the // product of three distinct odd prime numbers and this polynomial is the first one that has a // coefficient other than 1, 0, or −1: check("Cyclotomic(105, x)", // "1+x+x^2-x^5-x^6-2*x^7-x^8-x^9+x^12+x^13+x^14+x^15+x^16+x^17-x^20-x^22-x^24-x^26-x^\n" + "28+x^31+x^32+x^33+x^34+x^35+x^36-x^39-x^40-2*x^41-x^42-x^43+x^46+x^47+x^48"); } } @Test public void testD() { check("D(z^n*E^(z),{z,n})", // "E^z*n!*Hypergeometric1F1(-n,1,-z)"); check("D(z^n*E^(-z),{z,n})", // "(n!*Hypergeometric1F1(-n,1,z))/E^z"); check("D(Hypergeometric0F1(a,x), x)", // "Hypergeometric0F1(1+a,x)/a"); check("D(Hypergeometric1F1(a,b,x), x)", // "(a*Hypergeometric1F1(1+a,1+b,x))/b"); check("D(Hypergeometric2F1(a,b,c,f(x)), x)", // "(a*b*Hypergeometric2F1(1+a,1+b,1+c,f(x))*f'(x))/c"); check("D(Hypergeometric2F1Regularized(a,b,c,f(x)), x)", // "a*b*Hypergeometric2F1Regularized(1+a,1+b,1+c,f(x))*f'(x)"); check("D(HypergeometricPFQ({}, {}, x), x)", // "E^x"); check("D(HypergeometricPFQ({a}, {}, x), x)", // "a/(1-x)^(1+a)"); check("D(HypergeometricPFQ({a,b}, {u,v,w}, x), x)", // "(a*b*HypergeometricPFQ({1+a,1+b},{1+u,1+v,1+w},x))/(u*v*w)"); check("D(HypergeometricPFQ({a, b,c,d,e,f}, {u,v,w,y,z}, x), x)", // "(a*b*c*d*e*f*HypergeometricPFQ({1+a,1+b,1+c,1+d,1+e,1+f},{1+u,1+v,1+w,1+y,1+z},x))/(u*v*w*y*z)"); check("D(HarmonicNumber(Sin(Cos(x)), y), x)", // "y*Cos(Cos(x))*Sin(x)*(HarmonicNumber(Sin(Cos(x)),1+y)-Zeta(1+y))"); check("D(Sin(f(x)),{x,3})", // "-Cos(f(x))*f'(x)^3-3*Sin(f(x))*f'(x)*f''(x)+Cos(f(x))*Derivative(3)[f][x]"); check("D(Sin(#), {#,-1+n})", // "D(Sin(#1),{#1,-1+n})"); check("D(f(x), {x, n})", // "D(f(x),{x,n})"); check("D(PolyLog(n,z),z)", // "PolyLog(-1+n,z)/z"); check("D(PolyLog(n,p,z),z)", // "PolyLog(-1+n,p,z)/z"); check("D(Polygamma(x),{x,n})", // "PolyGamma(n,x)"); check("D(Sin(x)==x^2==y*x^4,x )", // "Cos(x)==2*x==4*x^3*y"); // message - D: D called with 0 arguments; 1 or more arguments are expected. check("D( )", // "D()"); // github #302 - special case - only 1 argument check("D(f)", // "f"); // github #302 test case check("Integrate(D(x),x)", // "x^2/2"); // github #302 test case check("Integrate(D(y)*D(x),x,y)", // "1/4*x^2*y^2"); // github #302 test case check("Integrate(D(x),x)*Integrate(D(y),y)", // "1/4*x^2*y^2"); check("D(StruveH(n,x),x)", // "1/2*(x^n/(2^n*Sqrt(Pi)*Gamma(3/2+n))+StruveH(-1+n,x)-StruveH(1+n,x))"); check("D(Surd(x,3),x)", // "1/(3*Surd(x,3)^2)"); check("D(Surd(x,-3),x)", // "-1/(3*x*Surd(x,3))"); check("D(Surd(x,4),x)", // "1/(4*Surd(x,4)^3)"); check("D(Surd(x,-4),x)", // "-1/(4*Surd(x,4)^5)"); check("D(Surd(x,5),x)", // "1/(5*Surd(x,5)^4)"); check("D(Surd(x,-5),x)", // "-1/(5*x*Surd(x,5))"); check("D(Sin(#), {#,-1+n})", // "D(Sin(#1),{#1,-1+n})"); check("D(f(x)+ g(x)+h(x), {x, n})", // "D(f(x),{x,n})+D(g(x),{x,n})+D(h(x),{x,n})"); check("D(Sin(x)+ Cos(y), {x, n})", // "Piecewise({{Cos(y),n==0}},0)+Sin(1/2*n*Pi+x)"); check("D(Sin(x),{x,0.5})", // "D(Sin(x),{x,0.5})"); check("D(Sin(x),{x,f(a)})", // "D(Sin(x),{x,f(a)})"); check("D(Sin(x),{x,f(a)+I})", // "D(Sin(x),{x,I+f(a)})"); check("D(x^a, {x,n})", // "x^(a-n)*FactorialPower(a,n)"); check("D(x^a, {x,3})", // "((-2+a)*(-1+a)*a)/x^(3-a)"); check("D(a^x, {x,2})", // "a^x*Log(a)^2"); check("D(Sin(x),{x,n})", // "Sin(1/2*n*Pi+x)"); check("D(InverseFunction(f)[x],x)", // "1/f'(InverseFunction(f)[x])"); // message - D: 2*x is not a valid variable. check("D(2*x, 2*x)", // "D(2*x,2*x)"); check("D(E^f(x),x)", // "E^f(x)*f'(x)"); check("D(AiryAi(Sqrt(x)),x)", // "AiryAiPrime(Sqrt(x))/(2*Sqrt(x))"); check("D(AiryAiPrime(Sqrt(x)),x)", // "AiryAi(Sqrt(x))/2"); check("D(Piecewise({{x^2, x < 0}, {x, x > 0}}),x)", // "Piecewise({{2*x,x<0},{1,x>0}},0)"); check("D(Piecewise({{(x^2 - 1)/(x - 1), x != 1}},2),x)", // "Piecewise({{(2*x)/(-1+x)+(1-x^2)/(1-x)^2,x!=1}},0)"); // TODO simplify result to 1 check("D(Piecewise({{(x^2 - 1)/(x - 1), x < 1 || x > 1}},2),x)", // "Piecewise({{(2*x)/(-1+x)+(1-x^2)/(1-x)^2,x<1||x>1}},0)"); check("D(Factorial(b*x),x)", // "b*Gamma(1+b*x)*PolyGamma(0,1+b*x)"); check("D(E^(E^x + x),x)", // "(1+E^x)*E^(E^x+x)"); check("D((2*x*(Sqrt(d)*Sqrt(-e)+e*x))/(d+e*x^2),x)", // "(-4*e*(Sqrt(d)*Sqrt(-e)+e*x)*x^2)/(d+e*x^2)^2+(2*e*x)/(d+e*x^2)+(2*(Sqrt(d)*Sqrt(-e)+e*x))/(d+e*x^\n" + "2)"); check("D(ArcTan(x,y),x)", // "-y/(x^2+y^2)"); check("D(ArcTan(x,y),y)", // "x/(x^2+y^2)"); check("D(ArcTan(x,x),x)", // "0"); check("D(Cosh(b*x),x)", // "b*Sinh(b*x)"); check("D(Sinh(x),x)", // "Cosh(x)"); check("D(Sinc(x),x)", // "Cos(x)/x-Sin(x)/x^2"); check("D(SinIntegral(x),x)", // "Sinc(x)"); check("D(SinhIntegral(x),x)", // "Sinh(x)/x"); check("D(CoshIntegral(x),x)", // "Cosh(x)/x"); check("D(Cosh(b*x)*CoshIntegral(b*x),x)", // "Cosh(b*x)^2/x+b*CoshIntegral(b*x)*Sinh(b*x)"); // gradient check("D(f(x, y), {{x, y}})", // "{Derivative(1,0)[f][x,y],Derivative(0,1)[f][x,y]}"); // hessian matrix check("D(f(x, y), {{x, y}}, {{x, y}})", // "{{Derivative(2,0)[f][x,y],Derivative(1,1)[f][x,y]},{Derivative(1,1)[f][x,y],Derivative(\n" + "0,2)[f][x,y]}}"); // generalization of Hessian matrix for n > 2 check("D(f(x, y, z), {{x, y, z}, 3})", // "{{{Derivative(3,0,0)[f][x,y,z],Derivative(2,1,0)[f][x,y,z],Derivative(2,0,1)[f][x,y,z]},{Derivative(\n" + "2,1,0)[f][x,y,z],Derivative(1,2,0)[f][x,y,z],Derivative(1,1,1)[f][x,y,z]},{Derivative(\n" + "2,0,1)[f][x,y,z],Derivative(1,1,1)[f][x,y,z],Derivative(1,0,2)[f][x,y,z]}},{{Derivative(\n" + "2,1,0)[f][x,y,z],Derivative(1,2,0)[f][x,y,z],Derivative(1,1,1)[f][x,y,z]},{Derivative(\n" + "1,2,0)[f][x,y,z],Derivative(0,3,0)[f][x,y,z],Derivative(0,2,1)[f][x,y,z]},{Derivative(\n" + "1,1,1)[f][x,y,z],Derivative(0,2,1)[f][x,y,z],Derivative(0,1,2)[f][x,y,z]}},{{Derivative(\n" + "2,0,1)[f][x,y,z],Derivative(1,1,1)[f][x,y,z],Derivative(1,0,2)[f][x,y,z]},{Derivative(\n" + "1,1,1)[f][x,y,z],Derivative(0,2,1)[f][x,y,z],Derivative(0,1,2)[f][x,y,z]},{Derivative(\n" + "1,0,2)[f][x,y,z],Derivative(0,1,2)[f][x,y,z],Derivative(0,0,3)[f][x,y,z]}}}"); check("Refine(D(Abs(x),x), Element(x, Reals))", // "x/Abs(x)"); check("D(HarmonicNumber(x), x)", // "Pi^2/6-HarmonicNumber(x,2)"); check("D(ArcCsc(x),{x,2})", // "(-1+2*x^2)/(Sqrt(1-1/x^2)*x^3*(-1+x^2))"); check("D(ArcSec(x),{x,2})", // "(1-2*x^2)/(Sqrt(1-1/x^2)*x^3*(-1+x^2))"); check("D(x*f(x)*f'(x), x)", // "f(x)*f'(x)+x*f'(x)^2+x*f(x)*f''(x)"); check("D(f(x), x)", // "f'(x)"); check("Sin'(2)", // "Cos(2)"); check("D(Sin(x) + Cos(2*x), {x, 2}) /. x -> 0", // "-4"); check("D(Sin(t), {t, 1})", // "Cos(t)"); check("D(Derivative(0,1,0)[f][x,x*y,z+x^2],x)", // "2*x*Derivative(0,1,1)[f][x,x*y,x^2+z]+y*Derivative(0,2,0)[f][x,x*y,x^2+z]+Derivative(\n" + "1,1,0)[f][x,x*y,x^2+z]"); check("D(x^3 + x^2, x)", // "2*x+3*x^2"); check("D(x^3 + x^2, {x, 2})", // "2+6*x"); check("D(Sin(Cos(x)), x)", // "-Cos(Cos(x))*Sin(x)"); check("D(Sin(x), {x, 2})", // "-Sin(x)"); check("D(Cos(t), {t, 2})", // "-Cos(t)"); check("D(y, x)", // "0"); check("D(x, x)", // "1"); check("D(f(x), x)", // "f'(x)"); check("D(f(x, x), x)", // "Derivative(0,1)[f][x,x]+Derivative(1,0)[f][x,x]"); // chain rule check("D(f(2*x+1, 2*y, x+y), x)", // "Derivative(0,0,1)[f][1+2*x,2*y,x+y]+2*Derivative(1,0,0)[f][1+2*x,2*y,x+y]"); check("D(f(x^2, x, 2*y), {x,2}, y) // Expand", // "2*Derivative(0,2,1)[f][x^2,x,2*y]+4*Derivative(1,0,1)[f][x^2,x,2*y]+8*x*Derivative(\n" + "1,1,1)[f][x^2,x,2*y]+8*x^2*Derivative(2,0,1)[f][x^2,x,2*y]"); check("D(x ^ 3 * Cos(y), {{x, y}})", // "{3*x^2*Cos(y),-x^3*Sin(y)}"); check("D(Sin(x) * Cos(y), {{x,y}, 2})", // "{{-Cos(y)*Sin(x),-Cos(x)*Sin(y)},{-Cos(x)*Sin(y),-Cos(y)*Sin(x)}}"); check("D(2/3*Cos(x) - 1/3*x*Cos(x)*Sin(x) ^ 2,x)//Expand ", // "-2/3*Sin(x)-2/3*x*Cos(x)^2*Sin(x)-1/3*Cos(x)*Sin(x)^2+1/3*x*Sin(x)^3"); check("D(f(#1), {#1,2})", // "f''(#1)"); check("D((#1&)*(t),{t,4})", // "0"); // TODO allow Attributes(f) = {HoldAll} check("Attributes(f) = {HoldAll}; Apart(f''(x + x))", // "f''(2*x)"); check("Attributes(f) = {}; Apart(f''(x + x)) ", // "f''(2*x)"); check("D({#^2}, #)", // "{2*#1}"); // Koepf Seite 40-43 check("D(Sum(k*x^k, {k,0,10}),x)", // "1+4*x+9*x^2+16*x^3+25*x^4+36*x^5+49*x^6+64*x^7+81*x^8+100*x^9"); check("D((x^2+3)*(3*x+2),x)", // "2*x*(2+3*x)+3*(3+x^2)"); check("D(Sin(x^2),x)", // "2*x*Cos(x^2)"); check("D((1+x^2)^Sin(x),x)", // "(1+x^2)^Sin(x)*(Cos(x)*Log(1+x^2)+(2*x*Sin(x))/(1+x^2))"); check("D(Exp(x),x)", // "E^x"); check("D((x^2+3)/(3*x+2),x)", // "(-3*(3+x^2))/(2+3*x)^2+(2*x)/(2+3*x)"); // others ----- check("D(InverseErf(x),x)", // "1/2*E^InverseErf(x)^2*Sqrt(Pi)"); check("D(f(Sqrt(x^2 + 1)), {x, 3})", // "(3*x^3*f'(Sqrt(1+x^2)))/(1+x^2)^(5/2)+(-3*x*f'(Sqrt(1+x^2)))/(1+x^2)^(3/2)+(-3*x^\n" + "3*f''(Sqrt(1+x^2)))/(1+x^2)^2+(3*x*f''(Sqrt(1+x^2)))/(1+x^2)+(x^3*Derivative(3)[f][Sqrt(\n" + "1+x^2)])/(1+x^2)^(3/2)"); check("f(x_) := x^5 + 6*x^3", // ""); check("D(f(x), x)", // "18*x^2+5*x^4"); check("f'(x)", // "18*x^2+5*x^4"); check("D(f(x), x) /. x->5", // "3575"); check("D(f(x), {x, 3}) /. x -> -1", // "96"); check("D(x^2 * E^(5*y), x)", // "2*E^(5*y)*x"); check("D(x^2 * E^(5*y), y)", // "5*E^(5*y)*x^2"); check("D(x^2 * E^(5*y), {x,2}, {y,3})", // "250*E^(5*y)"); check("D(Sin(g(x)) + g''(x), x)", // "Cos(g(x))*g'(x)+Derivative(3)[g][x]"); check("D(Subscript(x, 1)^2 + Sin(Subscript(x, 1)*Subscript(x, 2)), Subscript(x, 1))", // "2*Subscript(x,1)+Cos(Subscript(x,1)*Subscript(x,2))*Subscript(x,2)"); check("D({3*t^2, 4*t, Sin(t)}, t)", // "{6*t,4,Cos(t)}"); check("D({x^n, {Exp(x), Log(x)}, {Sin(x), Cos(x), Tan(x)}}, x)", // "{n/x^(1-n),{E^x,1/x},{Cos(x),-Sin(x),Sec(x)^2}}"); check("D(x^2 + 5*y^3, {{x, y}})", // "{2*x,15*y^2}"); check("D(x^2 + 5*y^3, {{x, y}, 2})", // "{{2,0},{0,30*y}}"); check("D((x^2+5*y^3+z^4)/E^w,{{x,y}})", // "{(2*x)/E^w,(15*y^2)/E^w}"); check("D(E^(-w)*(x^2 + 5*y^3 + z^4), {{{x, y}, {z, w}}})", // "{{(2*x)/E^w,(15*y^2)/E^w},{(4*z^3)/E^w,-(x^2+5*y^3+z^4)/E^w}}"); check("D(ExpIntegralEi(b*x),x)", // "E^(b*x)/x"); check("D(StruveH(n,x),x)", // "1/2*(x^n/(2^n*Sqrt(Pi)*Gamma(3/2+n))+StruveH(-1+n,x)-StruveH(1+n,x))"); check("D(StruveH(x,y),x)", // "Derivative(1,0)[StruveH][x,y]"); check("D(StruveL(n,x),x)", // "1/2*(x^n/(2^n*Sqrt(Pi)*Gamma(3/2+n))+StruveL(-1+n,x)+StruveL(1+n,x))"); check("D(StruveL(x,y),x)", // "Derivative(1,0)[StruveL][x,y]"); check("D(JacobiAmplitude(x,y),x)", // "JacobiDN(x,y)"); check("D(JacobiAmplitude(x,y),y)", // "((x*(-1+y)+EllipticE(JacobiAmplitude(x,y),y))*JacobiDN(x,y)-y*JacobiCN(x,y)*JacobiSN(x,y))/(\n" + // "2*(-1+y)*y)"); check("D(CatalanNumber(x),x)", // "CatalanNumber(x)*(Log(4)+PolyGamma(0,1/2+x)-PolyGamma(0,2+x))"); check("D(Sin(x^5)/x^10,x)", // "(5*Cos(x^5))/x^6+(-10*Sin(x^5))/x^11"); check("D(AppellF1(a,b1,b2,c,f1(x),f2(x)),x)", // "(a*b1*AppellF1(1+a,1+b1,b2,1+c,f1(x),f2(x))*f1'(x))/c+(a*b2*AppellF1(1+a,b1,1+b2,\n" // + "1+c,f1(x),f2(x))*f2'(x))/c"); } @Test public void testDefault() { check("Default(test) := 1", // "1"); check("Default(test) = 1", // "1"); check("test(x_., y_.) = {x, y}", // "{x,y}"); check("test(a)", // "{a,1}"); check("test( )", // "{1,1}"); check("Default(Plus)", // "0"); check("Default(Power)", // "Default(Power)"); check("Default(Power, 2)", // "1"); check("Default(Times)", // "1"); } @Test public void testDefer() { // check("Defer(3*2)", "3*2"); check("Defer(6/8)==6/8", // "6/8==3/4"); } @Test public void testDefinition() { check("Definition(ArcSinh)", // "Attributes(ArcSinh)={Listable,NumericFunction,Protected}\n" // + "\n" // + "ArcSinh(I/Sqrt(2))=I*1/4*Pi\n" // + "\n" // + "ArcSinh(Undefined)=Undefined\n" // + "\n" // + "ArcSinh(Infinity)=Infinity\n" // + "\n" // + "ArcSinh(I*Infinity)=Infinity\n" // + "\n" // + "ArcSinh(I)=I*1/2*Pi\n" // + "\n" // + "ArcSinh(0)=0\n" // + "\n" // + "ArcSinh(I*1/2)=I*1/6*Pi\n" // + "\n" // + "ArcSinh(I*1/2*Sqrt(3))=I*1/3*Pi\n" // + "\n" // + "ArcSinh(ComplexInfinity)=ComplexInfinity"); check("a := 42", // ""); check("Definition(a)", // "a:=42"); check("a", // "42"); check("a = 24", // "24"); check("Definition(a)", // "a=24"); check("a", // "24"); check("g(abc_):={abc}", // ""); check("g(abc_):={abc}", // ""); check("Definition(g)", // "g(abc_):={abc}"); check("SetAttributes(f,Listable)", // ""); check("f(x_):={x}", // ""); check("Definition(f)", // "Attributes(f)={Listable}\n"// + "\n"// + "f(x_):={x}"); } @Test public void testDegree() { check("\\[Pi]", // "Pi"); check("\\[Degree]", // "Pi/180"); check("\u00B0", // "Pi/180"); check("Sin(30*\\[Pi])", // "0"); check("Sin(30*\\[Degree])", // "1/2"); check("Sin(30\\[Degree])", // "1/2"); check("Sin(30*Degree)", // "1/2"); check("Degree == Pi / 180", // "True"); check("Cos(Degree(x))", // "Cos(Degree(x))"); checkNumeric("N(Degree)", // "0.017453292519943295"); check("Round(Pi/Degree^2)", // "10313"); check("Pi/4 < 60*Degree < Pi", // "True"); check("FullSimplify(Pi/Degree)", // "180"); } @Test public void testDelete() { // TODO // check("Delete({{1,2},{3,4}},{{1,2},{2,1},{2,1}})", // // "{{1},{4}}"); check("Delete(a+b+c,0)", // "Identity(a,b,c)"); check("Delete({ }, 0)", // "Identity()"); // print Cannot delete position 5 in {a,b,c,d} check("Delete({a, b, c, d}, 5)", // "Delete({a,b,c,d},5)"); check("Delete({a, b, c, d}, 3)", // "{a,b,d}"); check("Delete({a, b, c, d}, -2)", // "{a,b,d}"); check("Delete({{1,2},{3,4}},{1,2})", // "{{1},{3,4}}"); check("Delete({{1,2},{3,4}},{1,0})", // "{1,2,{3,4}}"); // check("Delete({{1,2},{3,4}},{{1,2},{2,1}})", // // "{{1},{4}}"); // check("Delete({{1,2},{3,4}},{{1,2},{2,1},{2,1}})", // // "{{1},{4}}"); // test operator form check("Delete(pos)", // "Delete(pos)"); check("Delete(pos)[x]", // "Delete(pos)[x]"); check("Delete(2)[{1,2,3,4}]", // "{1,3,4}"); } @Test public void testDeleteCases() { check("DeleteCases(Sqrt(Range(10)),_Integer,{1},Infinity)", // "{Sqrt(2),Sqrt(3),Sqrt(5),Sqrt(6),Sqrt(7),2*Sqrt(2),Sqrt(10)}"); check("DeleteCases(Sqrt(Range(10)),_Integer,{1},-1)", // "DeleteCases(Sqrt(Range(10)),_Integer,{1},-1)"); check("DeleteCases({a, 1, 2.5, \"string\"}, _Integer|_Real)", // "{a,string}"); check("DeleteCases({a, b, 1, c, 2, 3}, _Symbol)", // "{1,2,3}"); check("Sqrt(Range(10))", // "{1,Sqrt(2),Sqrt(3),2,Sqrt(5),Sqrt(6),Sqrt(7),2*Sqrt(2),3,Sqrt(10)}"); check("DeleteCases(Sqrt(Range(10)), _Integer, {1}, 3)", // "{Sqrt(2),Sqrt(3),Sqrt(5),Sqrt(6),Sqrt(7),2*Sqrt(2),Sqrt(10)}"); check("DeleteCases({1, 1, f(a), 2, 3, y, f(8), 9, f(10)}, _Integer)", // "{f(a),y,f(8),f(10)}"); check("DeleteCases({1, 1, f(a), 2, 3, y, f(8), 9, f(10)}, _Integer, -1)", // "{f(a),y,f(),f()}"); check("DeleteCases({1, 1, f(a), 2, 3, y, f(8), 9, f(10)}, _Integer, -2)", // "{1,1,f(a),2,3,y,f(8),9,f(10)}"); check("DeleteCases({1, 1, f(a), 2, 3, y, f(8), 9, f(10)}, _Integer, {0,4})", // "{f(a),y,f(),f()}"); check("DeleteCases({1, 1, f(a), 2, 3, y, g(c,f(8)), 9, f(10)}, f(x_) -> x)", // "{1,1,f(a),2,3,y,g(c,f(8)),9,f(10)}"); check("DeleteCases({1, 1, f(a), 2, 3, y, g(c,f(8)), 9, f(10)}, f(x_) -> x, -2)", // "{1,1,f(a),2,3,y,g(c,f(8)),9,f(10)}"); check("DeleteCases({1, 1, x, 2, 3, y, 9, y}, _Integer)", // "{x,y,y}"); // // check("Cases({3, -4, 5, -2}, x_ /; x < 0)", "{-4,-2}"); // check("Cases({3, 4, x, x^2, x^3}, x^_)", "{x^2,x^3}"); // check("Cases({3, 4, x, x^2, x^3}, x^n_ -> n)", "{2,3}"); // check("Cases({{1, 2}, {2}, {3, 4, 1}, {5, 4}, {3, 3}}, {_, _})", // "{{1,2},{5,4},{3,3}}"); // check("Cases({{1, 2}, {2}, {3, 4, 1}, {5, 4}, {3, 3}}, {a_, b_} -> a // + b)", "{3,9,6}"); } @Test public void testDeleteDuplicates() { check("DeleteDuplicates({1, 7, 8, 4, 3, 4, 1, 9, 9, 2, 1})", // "{1,7,8,4,3,9,2}"); check("DeleteDuplicates({3,2,1,2,3,4}, Less)", // "{3,2,1}"); check("DeleteDuplicates({3,2,1,2,3,4}, Greater)", // "{3,3,4}"); check("DeleteDuplicates({})", // "{}"); check( "l = {{0, 0, 0, 1, 0}, {1, 0, 1, 0, 1}, {1, 1, 1, 0, 0}, {0, 0, 0, 0, 1}, {1, 1, 1, 0, 1}};", // ""); check("DeleteDuplicates(l, Total(#1) == Total(#2) &)", // "{{0,0,0,1,0},{1,0,1,0,1},{1,1,1,0,1}}"); } @Test public void testDeleteDuplicatesBy() { check("DeleteDuplicatesBy(<|a -> 1, b -> -1, c -> 2, d -> -2|>, Abs)", // "<|a->1,c->2|>"); check("DeleteDuplicatesBy({{a, y}, {b, y}, {c, z}, {d, y}}, Last)", // "{{a,y},{c,z}}"); check("DeleteDuplicatesBy(Last) @ {{a, y}, {b, y}, {c, z}, {d, y}}", // "{{a,y},{c,z}}"); } @Test public void testDeleteMissing() { check("DeleteMissing({a, b, Missing(), c, d, Missing()})", // "{a,b,c,d}"); check("DeleteMissing(<| a -> x, b -> y, c -> Missing() |>)", // "<|a->x,b->y|>"); } @Test public void testDateObject() { // Current date // check("DateObject()", // // "2020-02-01T00:00"); check("DateObject({2016,8,1})", // "2016-08-01T00:00"); check("d=DateObject({2018,8,8});t=TimeObject({13,15});DateObject(d,t)", // "2018-08-08T13:15"); } @Test public void testDateString() { check("DateString(3155673600)", // "Sat 01 Jan 2000 00:00:00"); // check( // "DateString( )", // // "Thu 26 Aug 2021 22:15:13"); } @Test public void testDateValue() { check("DateValue(DateObject({2016,8,1}), {\"Year\",\"Month\",\"Day\"})", // "{2016,8,1}"); check("DateValue(DateObject({2016,8,1}), {\"Year\",\"MonthName\",\"DayName\"})", // "{2016,August,Monday}"); check("DateValue(DateObject({2016,8,1}), {\"Year\",\"MonthNameShort\",\"DayNameShort\"})", // "{2016,Aug,Mon}"); // Current values // check("DateValue(\"Second\")", // // "20"); // check("DateValue(\"Minute\")", // // "36"); // check("DateValue(\"Hour\")", // // "19"); // check("DateValue(\"MonthNameInitial\")", // // "A"); // check("DateValue(\"MonthNameShort\")", // // "Apr"); // check("DateValue(\"MonthName\")", // // "April"); // check("DateValue({\"Year\",\"Month\",\"Day\"})", // // "{2020,4,18}"); } @Test public void testDecrement() { check("a = 5", // "5"); check("a--", // "5"); check("a", // "4"); check("index = {1,2,3,4,5,6}", // "{1,2,3,4,5,6}"); check("index[[2]]--", // "2"); check("index", // "{1,1,3,4,5,6}"); } @Test public void testDedekindNumber() { check("Table(DedekindNumber(i), {i,0,11})", "{2,3,6,20,168,7581,7828354,2414682040998,56130437228687557907788,\n" // + "286386577668298411128469151667598498812366,DedekindNumber(10),DedekindNumber(11)}"); } @Test public void testRamseyNumber() { check("Table(RamseyNumber(1,j), {j,1,20})", // "{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}"); check("Table(RamseyNumber(2,j), {j,1,20})", // "{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}"); check("Table(RamseyNumber(i,j), {i,1,4},{j,i,10})", // "{{1,1,1,1,1,1,1,1,1,1},{2,3,4,5,6,7,8,9,10},{6,9,14,18,23,28,36,RamseyNumber(3,\n" // + "10)},{18,25,RamseyNumber(4,6),RamseyNumber(4,7),RamseyNumber(4,8),RamseyNumber(4,\n" // + "9),RamseyNumber(4,10)}}"); } @Test public void testDenominator() { check("Denominator(ConditionalExpression(a/13,Element(C1,Integers)))", // "1"); check("Denominator(-1/p^(1-n))", // "p"); check("Numerator(-1/p^(1-n))", // "-p^n"); check("Denominator( a*x^n*y^- m*Exp(a - b - 2 c + 3 d) )", // "E^(b+2*c)*y^m"); check("Denominator(a^-b/x)", // "a^b*x"); // github #151 check("N(Denominator(Pi/E))", // "2.71828"); // test undefined option message in stderr: check("Denominator(x, y)", // "Denominator(x,y)"); check("Denominator(a/(b*c))", // "b*c"); check("Denominator(a^2*b)", // "1"); check("Denominator(a^2*b^-2*c^-3)", // "b^2*c^3"); check("Denominator(a^2*b^-a*c^-d)", // "b^a*c^d"); check("Denominator(Csc(x))", // "1"); check("Denominator(Csc(x), Trig->True)", // "Sin(x)"); check("Denominator(Csc(x)^4)", // "1"); check("Denominator(Csc(x)^4, Trig->True)", // "Sin(x)^4"); check("Denominator(42*Csc(x))", // "1"); check("Denominator(42*Csc(x), Trig->True)", // "Sin(x)"); check("Denominator(42*Csc(x)^3)", // "1"); check("Denominator(42*Csc(x)^3, Trig->True)", // "Sin(x)^3"); check("Denominator(E^(-x)*x^(1/2))", // "E^x"); check("Denominator(Sec(x))", // "1"); check("Denominator(Tan(x))", // "1"); check("Denominator(Tan(x), Trig->True)", // "Cos(x)"); check("Denominator(a / b)", // "b"); check("Denominator(2 / 3)", // "3"); check("Denominator(a + b)", // "1"); } @Test public void testDepth() { check("Depth(f(a, b)[c])", // "2"); check("Depth(f(a, b)[c], Heads->True)", // "3"); check("Depth(x)", // "1"); check("Depth(g(a))", // "2"); check("Depth({{{a}, b}})", // "4"); check("Depth(x + y)", // "2"); check("Depth({{{{x}}}})", // "5"); check("Depth(1 + 2*I)", // "1"); check("Depth(f(a, b)[c])", // "2"); } @Test public void testCapitalDifferentialD() { check("\"start \\[CapitalDifferentialD] 123 end\"", // "startⅅ 123 end"); } @Test public void testDerivative() { check("Derivative(0,0,0,n)[Hypergeometric2F1Regularized]", // "Hypergeometric2F1Regularized(n+#1,n+#2,n+#3,#4)*Pochhammer(#1,n)*Pochhammer(#2,n)&"); check("Derivative(0,0,0,Sin(7))[Hypergeometric2F1Regularized]", // "Derivative(0,0,0,Sin(7))[Hypergeometric2F1Regularized]"); check("Derivative(0,0,0,3)[Hypergeometric2F1Regularized]", // "Hypergeometric2F1Regularized(3+#1,3+#2,3+#3,#4)*Pochhammer(#1,3)*Pochhammer(#2,3)&"); check("Derivative(0,0,0)[Sequence()]", // "Derivative(0,0,0)[]"); check("Derivative(1)[Abs]", // "Derivative(1)[Abs]"); check("Derivative(1,0)[StruveH][#1,#2]", // "Derivative(1,0)[StruveH][#1,#2]"); check("f1(x_) := Sin(x)", // ""); check("Derivative(n)[f1][x]", // "Sin(1/2*n*Pi+x)"); check("f2(x_, y_) := Cos(x)*Sin(y)", // ""); check("Derivative(1,0)[f2][x, y]", // "-Sin(x)*Sin(y)"); check("D(f(x), x)", // "f'(x)"); check("D(f(x, x), x)", // "Derivative(0,1)[f][x,x]+Derivative(1,0)[f][x,x]"); check("Derivative(2147483647)[x[[-1,1,1]]]", // "Derivative(2147483647)[x[[-1,1,1]]]"); check("Derivative(10)[Sin]", // "-Sin(#1)&"); check("Derivative(10)[Sin][x]", // "-Sin(x)"); check("Derivative(n)[Sin]", // "Sin(1/2*n*Pi+#1)&"); check("Derivative(I+a)[Sin]", // "Derivative(I+a)[Sin]"); check("f''(k^(1/3) x) - f(k^(1/3) x) == 0 /. x -> (x k^(-1/3))", // "-f(x)+f''(x)==0"); check("h(x_):= 4 x / (x ^ 2 + 3*x + 5)", // ""); check("extremes=Solve(h'(x)==0,x)", // "{{x->-Sqrt(5)},{x->Sqrt(5)}}"); check("h''(x) /.extremes // N", // "{1.65086,-0.064079}"); check("h(x_):=Sin(x)+x^2", // ""); check("h'(x)", // "2*x+Cos(x)"); check("h'(0.5)", // "1.87758"); check("h''(x)", // "2-Sin(x)"); check("h(x_):=x*Cos(x)", // ""); check("h'", // "Cos(#1)-Sin(#1)*#1&"); check("h''", // "-2*Sin(#1)-Cos(#1)*#1&"); check("y''", // "Derivative(2)[y]"); check("Derivative(1)[Sin]", // "Cos(#1)&"); check("Derivative(1)[Haversine]", // "Sin(#1)/2&"); check("Derivative(1)[InverseHaversine]", // "1/Sqrt((1-#1)*#1)&"); check("Derivative(0)[#1^2&]", // "#1^2&"); check("Derivative(1)[#1^2&]", // "2*#1&"); check("Derivative(1)[3*# ^ 2+5*# ^ 3&] ", // "6*#1+15*#1^2&"); check("Derivative(1)[# ^ 3&] ", // "3*#1^2&"); check("Derivative(2)[# ^ 3&] ", // "6*#1&"); check("Derivative(1)[E ^ #&] ", // "E^#1&"); check("Derivative(1)[Sin]", // "Cos(#1)&"); check("Derivative(3)[Sin]", // "-Cos(#1)&"); check("Sin'(x)", // "Cos(x)"); check("(# ^ 4&)''", // "12*#1^2&"); // check("f'(x) // FullForm", "Derivative(1)[f][x]"); // TODO // check("Derivative(1)[#2 Sin(#1)+Cos(#2)&]", "Cos(#1)*#2&"); // check("Derivative(1,2)[#2^3 Sin(#1)+Cos(#2)&]", "6*Cos(#1)*#2&"); // TODO Deriving with respect to an unknown parameter yields 0 // check("Derivative(1,2,1)[#2^3*Sin(#1)+Cos(#2)&]", ""); check("Derivative(0,0,0)[a+b+c]", // "a+b+c"); // TODO You can calculate the derivative of custom functions // check("f(x_) := x ^ 2", ""); // check("f'(x)", ""); check("Derivative(2, 1)[h]", // "Derivative(2,1)[h]"); check("Derivative(2, 0, 1, 0)[k(g)]", // "Derivative(2,0,1,0)[k(g)]"); // parser tests check("Hold(f'') // FullForm ", // "Hold(Derivative(2)[f])"); check("Hold(f ' ') // FullForm ", // "Hold(Derivative(2)[f])"); check("Hold(f '' '') // FullForm ", // "Hold(Derivative(4)[f])"); check("Hold(Derivative(x)[4] ') // FullForm ", // "Hold(Derivative(1)[Derivative(x)[4]])"); check("D(f(a,b),b)", // "Derivative(0,1)[f][a,b]"); check("D(f(a,b),x)", // "0"); check("g(u0_,u1_):=D(f(u0,u1),u1);g(a,b)", // "Derivative(0,1)[f][a,b]"); check("Derivative(1)[ArcCoth]", // "1/(1-#1^2)&"); check("y''", // "Derivative(2)[y]"); check("y''(x)", // "y''(x)"); check("y''''(x)", // "Derivative(4)[y][x]"); check("x*x^a", // "x^(1+a)"); check("x/x^(1-x)", // "x^x"); check("Derivative(0,1)[BesselJ][a, x]", // "1/2*(BesselJ(-1+a,x)-BesselJ(1+a,x))"); check("Derivative(1,0)[Power][x, 4]", // "4*x^3"); check("Derivative(1,0)[Power][x, y]", // "y/x^(1-y)"); check("Derivative(1,1)[Power][x, 4]", // "x^3+4*x^3*Log(x)"); check("Derivative(1,1)[Power][x, y]", // "x^(-1+y)+(y*Log(x))/x^(1-y)"); check("Derivative(0,1)[Power][a, x]", // "a^x*Log(a)"); check("Derivative(1,1)[Power][a, x]", // "a^(-1+x)+(x*Log(a))/a^(1-x)"); check("Derivative(1,1)[Power][x, x]", // "x^(-1+x)+x^x*Log(x)"); check("Hold((-1)*Sin(#)&[x])", // "Hold(-Sin(#1)&[x])"); check("Hold(Derivative(1)[Cos][x])", // "Hold(Cos'(x))"); check("Derivative(1)[Cos][x]", // "-Sin(x)"); check("Derivative(1)[Sin][x]", // "Cos(x)"); check("Derivative(4)[Cos][x]", // "Cos(x)"); check("Derivative(1)[Tan]", // "Sec(#1)^2&"); check("Derivative(2)[Tan]", // "2*Sec(#1)^2*Tan(#1)&"); check("Derivative(4)[Log][x]", // "-6/x^4"); check("Derivative(2)[ArcSin][x]", // "x/(1-x^2)^(3/2)"); check("Derivative(1)[2]", // "0&"); check("Derivative(1)[2][x,y,z]", // "0"); check("Derivative(10)[2][x,y,z]", // "0"); check("Derivative(10,9,8)[2][a,b,c]", // "0"); check("Derivative(1)[Cos[3]][z]", // "Cos(3)'[z]"); check("y = x^2 + 1; x = 1", // "1"); check("y'", // "0&"); check("Derivative(1)[CatalanNumber]", // "CatalanNumber(#1)*(Log(4)+PolyGamma(1/2+#1)-PolyGamma(2+#1))&"); } @Test public void testDiceDissimilarity() { check("DiceDissimilarity({1, 0, 1, 1, 0}, {1, 1, 0, 1, 1})", // "3/7"); check("DiceDissimilarity({True, False, True}, {True, True, False})", // "1/2"); check("DiceDissimilarity({1, 1, 1, 1}, {1, 1, 1, 1})", // "0"); check("DiceDissimilarity({0, 0, 0, 0}, {1, 1, 1, 1})", // "1"); } @Test public void testDifferenceDelta() { check("DifferenceDelta(Cosh(a*i+b),{i,2,h})", // "Cosh(b+a*i)-2*Cosh(b+a*(h+i))+Cosh(b+a*(2*h+i))"); check("DifferenceDelta(Sin(a*i+b),{i,5})", // "-Sin(b+a*i)+5*Sin(b+a*(1+i))-10*Sin(b+a*(2+i))+10*Sin(b+a*(3+i))-5*Sin(b+a*(4+i))+Sin(b+a*(\n" + "5+i))"); check("DifferenceDelta(b(a),{a,2,c})", // "b(a)-2*b(a+c)+b(a+2*c)"); check("DifferenceDelta(b(a),{a,3,c})", // "-b(a)+3*b(a+c)-3*b(a+2*c)+b(a+3*c)"); check("DifferenceDelta(b(a),{a,5,c})", // "-b(a)+5*b(a+c)-10*b(a+2*c)+10*b(a+3*c)-5*b(a+4*c)+b(a+5*c)"); check("DifferenceDelta(b(a),{a,1,c})", // "-b(a)+b(a+c)"); check("DifferenceDelta(b(a),a)", // "-b(a)+b(1+a)"); } @Test public void testDifferences() { // TODO: two args function // check( // "Differences({a, b, c, d},3)", // // "{-a+3*b-3*c+d}"); check("Differences({ })", // "{}"); check("Differences({a})", // "{}"); check("Differences({a,b})", // "{-a+b}"); check("Differences({a, b, c, d} )", // "{-a+b,-b+c,-c+d}"); check("Differences({a,b,c})", // "{-a+b,-b+c}"); check("Differences(SparseArray(10 -> 1, 21))", // "{0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0}"); check("t=Table(n^5 + 2*n - 1, {n, 8})", // "{2,35,248,1031,3134,7787,16820,32783}"); check("FixedPointList(Differences, %)", // "{{2,35,248,1031,3134,7787,16820,32783},{33,213,783,2103,4653,9033,15963},{180,\n" + "570,1320,2550,4380,6930},{390,750,1230,1830,2550},{360,480,600,720},{120,120,120},{\n" + "0,0},{0},{},{}}"); check("NestList(Differences, Normal(SparseArray(10 -> 1, 21)), 11)", // "{{0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,\n" + "0,0,0},{0,0,0,0,0,0,0,1,-2,1,0,0,0,0,0,0,0,0,0},{0,0,0,0,0,0,1,-3,3,-1,0,0,0,0,0,\n" + "0,0,0},{0,0,0,0,0,1,-4,6,-4,1,0,0,0,0,0,0,0},{0,0,0,0,1,-5,10,-10,5,-1,0,0,0,0,0,\n" + "0},{0,0,0,1,-6,15,-20,15,-6,1,0,0,0,0,0},{0,0,1,-7,21,-35,35,-21,7,-1,0,0,0,0},{\n" + "0,1,-8,28,-56,70,-56,28,-8,1,0,0,0},{1,-9,36,-84,126,-126,84,-36,9,-1,0,0},{-10,\n" + "45,-120,210,-252,210,-120,45,-10,1,0},{55,-165,330,-462,462,-330,165,-55,11,-1}}"); } @Test public void testDigitCount() { // message Maximum AST dimension 2147483647 exceeded check("DigitCount({2,5,3},2147483647)", // "DigitCount({2,5,3},2147483647)"); check("DigitCount(1, 17)", // "{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}"); check("DigitCount(4, 3)", // "{2,0,0}"); check("DigitCount(6, 5)", // "{2,0,0,0,0}"); check("DigitCount(7, 5)", // "{1,1,0,0,0}"); check("DigitCount(10, 5)", // "{0,1,0,0,1}"); check("DigitCount(-4, 3)", // "{2,0,0}"); check("DigitCount(-6, 5)", // "{2,0,0,0,0}"); check("DigitCount(-7, 5)", // "{1,1,0,0,0}"); check("DigitCount(-10, 5)", // "{0,1,0,0,1}"); check("DigitCount(0, 2)", // "{0,1}"); check("DigitCount(0)", // "{0,0,0,0,0,0,0,0,0,1}"); check("DigitCount(0, 12)", // "{0,0,0,0,0,0,0,0,0,0,0,1}"); check("DigitCount(145, 12)", // "{2,0,0,0,0,0,0,0,0,0,0,1}"); // https://oeis.org/A098949 check("Select(Range(1000), " // + "DigitCount( # )[[1]] == 0 && DigitCount( # )[[3]] == 0 && DigitCount( # )[[5]] == 0 && DigitCount( # )[[7]] == 0 && DigitCount( # )[[9]] >0 &)", // "{9,29,49,69,89,90,92,94,96,98,99,209,229,249,269,289,290,292,294,296,298,299,409,\n" + // "429,449,469,489,490,492,494,496,498,499,609,629,649,669,689,690,692,694,696,698,\n" + // "699,809,829,849,869,889,890,892,894,896,898,899,900,902,904,906,908,909,920,922,\n" + // "924,926,928,929,940,942,944,946,948,949,960,962,964,966,968,969,980,982,984,986,\n" + // "988,989,990,992,994,996,998,999}"); check("DigitCount(2147)", // "{1,1,0,1,0,0,1,0,0,0}"); check("DigitCount(2147, 2, 1)", // "5"); check("DigitCount(2147, 16)", // "{0,0,1,0,0,1,0,1,0,0,0,0,0,0,0,0}"); check("DigitCount(100!)", // "{15,19,10,10,14,19,7,14,20,30}"); check("DigitCount(-100!)", // "{15,19,10,10,14,19,7,14,20,30}"); check("DigitCount(242442422, 3, {1, 2})", // "{6,7}"); check("DigitCount(-242442422, 3, {1, 2})", // "{6,7}"); check("Table(1 - Mod(DigitCount(n - 1, 2, 1), 2), {n, 25})", // "{1,0,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1}"); check("Table(2^DigitCount(t, 2, 1), {t, 0, 10})", // "{1,2,2,4,2,4,4,8,2,4,4}"); } @Test public void testDigitQ() { check("DigitQ(\"1234\")", // "True"); check("DigitQ(\".\")", // "False"); } @Test public void testDiscreteDelta() { check("DiscreteDelta(0, 0, 0.0)", // "1"); check("DiscreteDelta(0)", // "1"); check("DiscreteDelta(42)", // "0"); check("DiscreteDelta(-1)", // "0"); check("DiscreteDelta(-42)", // "0"); check("DiscreteDelta({1.6, 1.6000000000000000000000000})", // "DiscreteDelta({1.6,1.6})"); check("DiscreteDelta(1.6, 1.6000000000000000000000000)", // "0"); check("DiscreteDelta(1, 2, 3)", // "0"); } @Test public void testDiracDelta() { check("DiracDelta(1+I)", // "DiracDelta(1+I)"); check("DiracDelta(x)", // "DiracDelta(x)"); check("DiracDelta(-x)", // "DiracDelta(x)"); check("DiracDelta(-x, -y)", // "DiracDelta(x,y)"); check("DiracDelta(x, y, z)", // "DiracDelta(x,y,z)"); check("DiracDelta(-x, 0.5, z)", // "0"); check("DiracDelta(0)", // "DiracDelta(0)"); check("DiracDelta(-1)", // "0"); check("DiracDelta(-42)", // "0"); check("DiracDelta({1.6, 1.6000000000000000000000000})", // "{0,0}"); check("DiracDelta({-1, 0, 1})", // "{0,DiracDelta(0),0}"); check("DiracDelta(1, 2, 3)", // "0"); } @Test public void testDirectedInfinity() { check("DirectedInfinity({0,0,0})", // "{ComplexInfinity,ComplexInfinity,ComplexInfinity}"); check("DirectedInfinity(a*b^(-3)*c^2)", // "DirectedInfinity((Sign(a)*Sign(c)^2)/Sign(b)^3)"); check("DirectedInfinity(a*b*c^(-1)*z ^(-2))", // "DirectedInfinity(Sign(a*b)/(Sign(c)*Sign(z)^2))"); check("DirectedInfinity(a/b)", // "DirectedInfinity(Sign(a)/Sign(b))"); check("DirectedInfinity(a)", // "DirectedInfinity(a)"); // message: Infinity: Indeterminate expression 0*DirectedInfinity(a) encountered. check("DirectedInfinity(a)*0", // "Indeterminate"); check("DirectedInfinity(1) + DirectedInfinity(-1)", // "Indeterminate"); check("DirectedInfinity(-2000)", // "-Infinity"); check("DirectedInfinity(2001)", // "Infinity"); check("Table(DirectedInfinity(i), {i, {1, -1, I, -I}})", // "{Infinity,-Infinity,I*Infinity,-I*Infinity}"); check("DirectedInfinity(1 + I)^ -1", // "0"); check("1/DirectedInfinity(1 + I)", // "0"); check("DirectedInfinity(1 + I)", // "DirectedInfinity((1+I)/Sqrt(2))"); check("DirectedInfinity(1+I)+DirectedInfinity(2+I)", // "DirectedInfinity((1+I)/Sqrt(2))+DirectedInfinity((2+I)/Sqrt(5))"); check("DirectedInfinity(Sqrt(3))", // "Infinity"); check("DirectedInfinity(1)", // "Infinity"); check("DirectedInfinity()", // "ComplexInfinity"); check("DirectedInfinity(Indeterminate)", // "ComplexInfinity"); check("ComplexInfinity+b", // "ComplexInfinity"); // Power() check("0^(-1)", // "ComplexInfinity"); check("{Exp(Infinity), Exp(-Infinity)}", // "{Infinity,0}"); check("1^Infinity", // "Indeterminate"); check("1^(-Infinity)", // "Indeterminate"); check("1^ComplexInfinity", // "Indeterminate"); // Times() check("DirectedInfinity(x)*DirectedInfinity(y)", // "DirectedInfinity(x*y)"); check("Table(DirectedInfinity(i), {i, {1, -1, I, -I}})", // "{Infinity,-Infinity,I*Infinity,-I*Infinity}"); check("(1 + I)*Infinity", "DirectedInfinity((1+I)/Sqrt(2))"); check("{DirectedInfinity(), DirectedInfinity(Indeterminate)}", // "{ComplexInfinity,ComplexInfinity}"); check("Infinity/Infinity", // "Indeterminate"); check("3*DirectedInfinity(z)", // "DirectedInfinity(z)"); check("I*DirectedInfinity(z)", // "DirectedInfinity(I*z)"); // Plus() check("1+1", // "2"); check("1+Infinity", // "Infinity"); check("1-Infinity", // "-Infinity"); check("Infinity+Infinity", // "Infinity"); check("-Infinity-Infinity", // "-Infinity"); check("Infinity-Infinity", // "Indeterminate"); check("1+Indeterminate", // "Indeterminate"); check("0+ComplexInfinity", // "ComplexInfinity"); check("ComplexInfinity+ComplexInfinity", // "Indeterminate"); check("ComplexInfinity+Indeterminate", // "Indeterminate"); check("1+ComplexInfinity", // "ComplexInfinity"); check("DirectedInfinity(x) + DirectedInfinity(y)", // "DirectedInfinity(x)+DirectedInfinity(y)"); check("DirectedInfinity(x) + DirectedInfinity(y) /. {x -> 1, y -> -1}", // "Indeterminate"); } @Test public void testDirichletBeta() { check("DirichletBeta(-1)", // "0"); check("DirichletBeta(0)", // "1/2"); check("DirichletBeta(1)", // "Pi/4"); check("DirichletBeta(1.3-I)", // "0.898582+I*(-0.135951)"); check("Table(DirichletBeta(x), {x, -4, 4}) // N", // "{2.5,0.0,-0.5,0.0,0.5,0.785398,0.915966,0.968946,0.988945}"); } @Test public void testDirichletEta() { check("DirichletEta(1)", // "Log(2)"); check("DirichletEta(1.0)", // "0.693147"); check("Table(DirichletEta(x), {x, -4, 4}) // N", // "{0.0,-0.125,0.0,0.25,0.5,0.693147,0.822467,0.901543,0.947033}"); } @Test public void testDiscriminant() { // github #122 check("Discriminant((2*x^5)-(19*x^4)+(58*x^3)-(67*x^2)+(56*x)-48,x)", // "0"); check("Discriminant(x^10 - 5*x^7 - 3*x + 9, x)", // "177945374758153510836"); check("Resultant(f+g*x+h*x^2,g+2*h*x, x)", // "-g^2*h+4*f*h^2"); // print message Discriminant: the function: Discriminant(Sqrt(x),x) has wrong argument Sqrt(x) // at position:1: // Polynomial expected! check("Discriminant(x^(1/2), x)", "Discriminant(Sqrt(x),x)"); check("Discriminant(f+g*x+h*x^2, x)", // "g^2-4*f*h"); check("Discriminant(a*x^2 + b*x + c, x)", // "b^2-4*a*c"); check("Discriminant(x^10 - 5*x^7 - 3*x + 9, x)", // "177945374758153510836"); check("Discriminant(a*x^3 + b*x^2 + c*x + g, x)", // "b^2*c^2-4*a*c^3-4*b^3*g+18*a*b*c*g-27*a^2*g^2"); check("Discriminant(a*x^4 + b*x^3 + c*x^2 + d*x + e, x)", // "b^2*c^2*d^2-4*a*c^3*d^2-4*b^3*d^3+18*a*b*c*d^3-27*a^2*d^4-4*b^2*c^3*e+16*a*c^4*e+\n" + "18*b^3*c*d*e-80*a*b*c^2*d*e-6*a*b^2*d^2*e+144*a^2*c*d^2*e-27*b^4*e^2+144*a*b^2*c*e^\n" + "2-128*a^2*c^2*e^2-192*a^2*b*d*e^2+256*a^3*e^3"); } @Test public void testDisjointQ() { check("DisjointQ(f(d,f,e), f(a, b, c))", // "True"); check("DisjointQ(f(b, a, b), f(a, b, c))", // "False"); // same as ContainsNone check("DisjointQ({d,f,e}, {a, b, c})", // "True"); check("DisjointQ({b, a, b}, {a, b, c})", // "False"); check("DisjointQ({ }, {a, b, c})", // "True"); check("DisjointQ(1, {1,2,3})", // "DisjointQ(1,{1,2,3})"); check("DisjointQ({1,2,3}, 4)", // "DisjointQ({1,2,3},4)"); check("DisjointQ({1.0,2.0}, {1,2,3})", // "True"); check("DisjointQ({1.0,2.0}, {1,2,3}, SameTest->Equal)", // "False"); } @Test public void testDispatch() { check("emptyRul=Dispatch({ })", // "Dispatch({})"); check("{\"a\", b, \"c\", d, e} /. emptyRul", // "{a,b,c,d,e}"); check("rul=Dispatch({\"a\" -> 1, \"b\" -> 2, \"c\" -> 3})", // "Dispatch({a->1,b->2,c->3})"); check("{\"a\", b, \"c\", d, e} /. rul", // "{1,b,3,d,e}"); check("rul // Normal // InputForm", // "{\"a\"->1,\"b\"->2,\"c\"->3}"); check("rul = {a -> b, b -> c, c -> a, d -> e, e -> d};", // ""); check("dis= Dispatch(rul);", // ""); check("{a, b, c, d, e} /. rul", // "{b,c,a,e,d}"); check("{a, b, c, d, e} /. dis", // "{b,c,a,e,d}"); check("Atomq(dis)", // "True"); check("Normal(dis)", // "{a->b,b->c,c->a,d->e,e->d}"); check("dis= Dispatch({1 -> a, 2 -> b, c_?NumericQ -> Infinity})", // "Dispatch({1->a,2->b,c_?NumericQ->Infinity})"); check("{1, 2, 3, Pi, Sin[x], Cos[3]} /. dis", // "{a,b,Infinity,Infinity,Sin(x),Infinity}"); check("dis= Dispatch(<|a -> b, c -> d|>);", // ""); check("{a, b, c, d, e} /. dis", // "{b,b,d,d,e}"); } @Test public void testDistribute() { // check( // "Distribute(x^10 - 1)", // // "-1+x^10"); check("Distribute(Factor(x^10 - 1))", // "-1+x^10"); check("Distribute((a + b).(x + y + z))", // "a.x+a.y+a.z+b.x+b.y+b.z"); check("Distribute(f(a + b, c + d + e))", // "f(a,c)+f(a,d)+f(a,e)+f(b,c)+f(b,d)+f(b,e)"); check("Distribute(f(g(a, b), g(c, d, e)), g)", // "g(f(a,c),f(a,d),f(a,e),f(b,c),f(b,d),f(b,e))"); check("Distribute((a + b + c) (u + v))", // "a*u+b*u+c*u+a*v+b*v+c*v"); check("Distribute((a + b + c) (u + v), Plus)", // "a*u+b*u+c*u+a*v+b*v+c*v"); check("Distribute((a + b + c)*(u + v), Plus, Times)", // "a*u+b*u+c*u+a*v+b*v+c*v"); check("Distribute((a + b + c)^(u + v), Plus, Times)", // "(a+b+c)^(u+v)"); check("Distribute({{a, b}, {x, y, z}, {s, t}}, List)", // "{{a,x,s},{a,x,t},{a,y,s},{a,y,t},{a,z,s},{a,z,t},{b,x,s},{b,x,t},{b,y,s},{b,y,t},{b,z,s},{b,z,t}}"); check("Distribute((x*y*z)^n0, Times)", // "x^n0*y^n0*z^n0"); check("Distribute(And(Or(a, b, c), Or(u, v)), Or, And)", // "(a&&u)||(a&&v)||(b&&u)||(b&&v)||(c&&u)||(c&&v)"); check("Distribute((a + b).(x + y + z))", // "a.x+a.y+a.z+b.x+b.y+b.z"); check("Distribute(f(g(a, b), g(c, d, e)), g, f, gp, fp)", // "gp(fp(a,c),fp(a,d),fp(a,e),fp(b,c),fp(b,d),fp(b,e))"); check("Distribute(Factor(x^10 - 1))", // "-1+x^10"); check("Distribute(Factor(x^6 - 1), Plus, Times, List, Times)", // "{-1,-x,-x^2,x,x^2,x^3,-x^2,-x^3,-x^4,-x,-x^2,-x^3,x^2,x^3,x^4,-x^3,-x^4,-x^5,x,x^\n" + "2,x^3,-x^2,-x^3,-x^4,x^3,x^4,x^5,x^2,x^3,x^4,-x^3,-x^4,-x^5,x^4,x^5,x^6}"); check("Distribute((x*y*z)^n, Times)", // "x^n*y^n*z^n"); // possibly not intended: check("Distribute((a + b)*(a + b))", // "a^2+b^2"); } @Test public void testDivide() { check("Divide(a,b) // FullForm", // "Times(a, Power(b, -1))"); check("1/2/3/5", // "1/30"); check("30 / 5", // "6"); check("1 / 8", // "1/8"); check("Pi / 4", // "Pi/4"); check("Pi / 4.0", // "0.785398"); check("N(1 / 8)", // "0.125"); check("a / b / c", // "a/(b*c)"); check("a / (b / c)", // "(a*c)/b"); check("a / b / (c / (d / e))", // "(a*d)/(b*c*e)"); check("a / (b ^ 2 * c ^ 3 / e)", // "(a*e)/(b^2*c^3)"); check("1 / 4.0", // "0.25"); check("10 / 3 // FullForm", // "Rational(10,3)"); check("a / b // FullForm", // "Times(a, Power(b, -1))"); } @Test public void testDivideBy() { check("a = 10", // "10"); check("a /= 2", // "5"); check("a", // "5"); check("index={1,2,3,4,5,6,7,8,9}", // "{1,2,3,4,5,6,7,8,9}"); check("index[[3]]/=y", // "3/y"); check("index", // "{1,2,3/y,4,5,6,7,8,9}"); } @Test public void testDivisible() { check("Divisible(2*Pi, Pi/2)", // "True"); check("Divisible(42,7)", // "True"); check("Divisible(10,3)", // "False"); check("Divisible(2^100-1,3)", // "True"); check("Divisible({200, 201, 202, 203}, 3)", // "{False,True,False,False}"); check("Divisible(3/4, 1/4)", // "True"); check("Divisible(3 + I, 2 - I)", // "True"); } @Test public void testDivisors() { check("Length(Divisors(Factorial(18)))", // "14688"); check("Divisors(5)", // "{1,5}"); check("Divisors(101)", // "{1,101}"); check("Divisors(-2147483648)", // "{1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,131072,\n" + "262144,524288,1048576,2097152,4194304,8388608,16777216,33554432,67108864,\n" + "134217728,268435456,536870912,1073741824,2147483648}"); check( "a178752(n_):=Sum((1/GCD(n, k))*2^s *EulerPhi(GCD(n, k)/s), {k, 0, n-1}, {s, Divisors(GCD(n, k))})", // ""); check("Table(a178752(n),{n,30})", // "{2,5,8,13,16,28,32,56,80,136,208,400,656,1232,2240,4192,7744,14728,27632,52664,\n" + "99968,190984,364768,699760,1342256,2582120,4971248,9588880,18512848,35795104}"); check("Divisors(990)", // "{1,2,3,5,6,9,10,11,15,18,22,30,33,45,55,66,90,99,110,165,198,330,495,990}"); check("Divisors(341550071728321)", // "{1,10670053,32010157,341550071728321}"); check("Divisors(2010)", // "{1,2,3,5,6,10,15,30,67,134,201,335,402,670,1005,2010}"); check("Divisors(0)", // "Divisors(0)"); check("Divisors(1)", // "{1}"); check("Divisors(6)", // "{1,2,3,6}"); check("Divisors(-2)", // "{1,2}"); check("Divisors(-6)", // "{1,2,3,6}"); check("Divisors(24)", // "{1,2,3,4,6,8,12,24}"); check("Divisors(1729)", // "{1,7,13,19,91,133,247,1729}"); check("FactorInteger(1729)", // "{{7,1},{13,1},{19,1}}"); check("Divisors({605,871,824})", // "{{1,5,11,55,121,605},{1,13,67,871},{1,2,4,8,103,206,412,824}}"); } @Test public void testDivisorSigma() { check("DivisorSigma(17,20)", // "13107300000780119453382"); check("DivisorSigma(0,12)", // "6"); check("DivisorSigma(1,12)", // "28"); check("DivisorSigma(1,20)", // "42"); check("DivisorSigma(2,20)", // "546"); check("DivisorSigma(2, {1, 2, 3, 4, 5})", // "{1,5,10,21,26}"); check("DivisorSigma(k,10)", // "1+2^k+5^k+10^k"); check("DivisorSigma(4,15)", // "51332"); } @Test public void testDivisorSum() { // https://oeis.org/A002791 check("a(n_) := DivisorSum(n, #^2 &, # < 5 &) + 4 * DivisorSum(n, # &, # > 4 &); Array(a,70)", // "{1,5,10,21,21,38,29,53,46,65,45,102,53,89,90,117,69,146,77,161,122,137,93,230,\n" + // "121,161,154,217,117,278,125,245,186,209,189,354,149,233,218,353,165,374,173,329,\n" + // "306,281,189,486,225,365,282,385,213,470,285,473,314,353,237,662,245,377,410,501,\n" + // "333,566,269,497,378,569}"); check("DivisorSum(11, # &, PrimeQ)", // "11"); check("DivisorSum(1000, #^2 &)", // "1383460"); check("DivisorSum(20, # &, # < 5 &)", // "7"); check("DivisorSum(20, # &)", // "42"); check("DivisorSum(30, # &)", // "72"); check("DivisorSum(20, f)", // "f(1)+f(2)+f(4)+f(5)+f(10)+f(20)"); check("DivisorSum({2, 5, 10}, #^2 &)", // "{5,26,130}"); if (Config.EXPENSIVE_JUNIT_TESTS) { check("DivisorSum(10^50 + 1, # &)", // "101023927335579679355031598994389503718340251571328"); } } @Test public void testDo() { check("Do(marray(i,10-i+1)=1, {i,1,10});marray(1,10)", // "1"); check("Do(Print(i0),{})", // "Do(Print(i0),{})"); check("g(x_) := (Do(If(x < 0, Return(0)), {i, {2, 1, 0, -1}}); x)", // ""); check("g(-1)", // "-1"); // http://oeis.org/A005132 - Recaman's sequence check( "a = {1}; Do( If( a[ [ -1 ] ] - n > 0 && Position( a, a[ [ -1 ] ] - n ) == {}, a = Append( a, a[ [ -1 ] ] - n ), a = Append( a, a[ [ -1 ] ] + n ) ), {n, 2, 70} ); a", // "{1,3,6,2,7,13,20,12,21,11,22,10,23,9,24,8,25,43,62,42,63,41,18,42,17,43,16,44,15,\n" + "45,14,46,79,113,78,114,77,39,78,38,79,37,80,36,81,35,82,34,83,33,84,32,85,31,86,\n" + "30,87,29,88,28,89,27,90,26,91,157,224,156,225,155}"); check("Do(Print(i), {i, 2, 4})", // ""); check("Do(Print({i, j}), {i,1,2}, {j,3,5})", // ""); check("Do(If(i > 10, Break(), If(Mod(i, 2) == 0, Continue()); Print(i)), {i, 5, 20})", ""); check("Do(Print(\"hi\"),{1+1})", ""); check("reap(do(if(primeQ(2^n0 - 1), sow(n0)), {n0, 100}))[[2, 1]]", // "{2,3,5,7,13,17,19,31,61,89}"); check("$t = x; Do($t = 1/(1 + $t), {5}); $t", // "1/(1+1/(1+1/(1+1/(1+1/(1+x)))))"); check("Nest(1/(1 + #) &, x, 5)", // "1/(1+1/(1+1/(1+1/(1+1/(1+x)))))"); } @Test public void testDownValues() { check("f(1)=3", // "3"); check("f(x_):=x^3", // ""); check("DownValues(f)", // "{HoldPattern(f(1)):>3,HoldPattern(f(x_)):>x^3}"); } @Test public void testDrop() { // message Drop: Sequence specification (+n,-n,{+n},{-n},{m,n}) or {m,n,s} expected at position // 2 in x. check("Drop({1,2,3}, {3, x})", // "Drop({1,2,3},{3,x})"); check("Drop(SparseArray(Range(1000)), {3, -4})", // "{1,2,998,999,1000}"); check("Drop({a,b,c,d},1317624576693539401)", // "Drop({a,b,c,d},1317624576693539401)"); check("Drop(<|1 -> a, 2 -> b, 3 -> c, 4 -> d|>, {2, -1})", // "<|1->a|>"); check("Drop(<|1 -> a, 2 -> b, 3 -> c|>, {2})", // "<|1->a,3->c|>"); check("Drop({}, 0)", // "{}"); check("Drop({}, 1)", // "Drop({},1)"); check("Drop({a, b, c, d}, 3)", // "{d}"); check("Drop({a, b, c, d}, -2)", // "{a,b}"); check("Drop({a, b, c, d, e}, {2, -2})", // "{a,e}"); check("A = Table(i*10 + j, {i, 4}, {j, 4})", // "{{11,12,13,14},{21,22,23,24},{31,32,33,34},{41,42,43,44}}"); check("Drop(A, {2, 3}, {2, 3})", // "{{11,14},{41,44}}"); check("Drop(Range(10), {-2, -6, -3})", // "{1,2,3,4,5,7,8,10}"); check("Drop(Range(10), {10, 1, -3})", // "{2,3,5,6,8,9}"); check("Drop(Range(6), {-5, -2, -2}) ", // "Drop({1,2,3,4,5,6},{-5,-2,-2})"); check("Drop(Range(6), {0, 3, 1}) ", // "Drop({1,2,3,4,5,6},{0,3,1})"); check("Drop(Range(6), {1, 3, 1}) ", // "{4,5,6}"); check("Drop({a, b, c, d, e, f}, 2)", // "{c,d,e,f}"); check("Drop({a, b, c, d, e, f}, -3)", // "{a,b,c}"); check("Drop({a, b, c, d, e, f}, {2, 4})", // "{a,e,f}"); check("Drop({{11, 12, 13}, {21, 22, 23}, {31, 32, 33}}, 1, 2)", // "{{23},{33}}"); check("Drop({{11, 12, 13}, {21, 22, 23}, a, {31, 32, 33}}, 1, 2)", // "Drop({{11,12,13},{21,22,23},a,{31,32,33}},1,2)"); } // @Test // public void testDSolve() { // check("DSolve({(2*y(x)-x^2)+(2*x-y(x)^2)*y'(x)==0},y(x), x)", // "{{y(x)->1/(x^2-C(1))}}"); // check("DSolve({y'(x)==2*x*y(x)^2},y(x), x)", "{{y(x)->1/(-x^2-C(1))}}"); // check("DSolve({(2*y(x)-x^2)+(2*x-y(x)^2)*y'(x)==0},y(x), x)", // "{{y(x)->1/(x^2-C(1))}}"); // check("DSolve({(6*x*y(x)+y(x)^2)*y'(x)==-2*x-3*y[x]^2},y(x), x)", // "{{y(x)->E^x}}"); // } @Test public void testDSolve() { check("DSolve(y'(x)==2*x*y(x)^2,Null,x)", // "DSolve(y'(x)==2*x*y(x)^2,Null,x)"); check("DSolve({},y,t)", // "DSolve({},y,t)"); check("DSolve(y'(t)==t+y(t), y, t)", // "{{y->Function({t},-1-t+E^t*C(1))}}"); check("DSolve(y'(t)==y(t), y, t)", // "{{y->Function({t},E^t*C(1))}}"); check("DSolve(y'(x)==2*x*y(x)^2, y, x)", // "{{y->Function({x},1/(-x^2-C(1)))}}"); check("DSolve(y'(x)==2*x*y(x)^2, y(x), x)", // "{{y(x)->1/(-x^2-C(1))}}"); check("DSolve({y'(x)==2*x*y(x)^2},y(x), x)", // "{{y(x)->1/(-x^2-C(1))}}"); check("DSolve(D(f(x, y), x) == D(f(x, y), y), f, {x, y})", // "DSolve(Derivative(1,0)[f][x,y]==Derivative(0,1)[f][x,y],f,{x,y})"); // check("DSolve({y'(x)==y(x),y(0)==1},y(x), x)", "{{y(x)->E^x}}"); check("DSolve({y'(x)==y(x)+2,y(0)==1},y(x), x)", "{{y(x)->-2+3*E^x}}"); check("DSolve({y(0)==0,y'(x) + y(x) == a*Sin(x)}, y(x), x)", // "{{y(x)->a/(2*E^x)-1/2*a*Cos(x)+1/2*a*Sin(x)}}"); check("DSolve({y'(x) + y(x) == a*Sin(x),y(0)==0}, y(x), x)", // "{{y(x)->a/(2*E^x)-1/2*a*Cos(x)+1/2*a*Sin(x)}}"); check("DSolve(y'(x) + y(x) == a*Sin(x), y(x), x)", // "{{y(x)->C(1)/E^x-1/2*a*Cos(x)+1/2*a*Sin(x)}}"); check("DSolve(y'(x)-x ==0, y(x), x)", // "{{y(x)->x^2/2+C(1)}}"); check("DSolve(y'(x)+k*y(x) ==0, y(x), x)", // "{{y(x)->C(1)/E^(k*x)}}"); check("DSolve(y'(x)-3/x*y(x)-7==0, y(x), x)", // "{{y(x)->-7/2*x+x^3*C(1)}}"); check("DSolve(y'(x)== 0, y(x), x)", // "{{y(x)->C(1)}}"); check("DSolve(y'(x) + y(x)*Tan(x) == 0, y(x), x)", // "{{y(x)->C(1)*Cos(x)}}"); check("DSolve(y'(x) + y(x)*Cos(x) == 0, y(x), x)", // "{{y(x)->C(1)/E^Sin(x)}}"); check("DSolve(y'(x) == 3*y(x), y(x), x)", // "{{y(x)->E^(3*x)*C(1)}}"); check("DSolve(y'(x) + 2*y(x)/(1-x^2) == 0, y(x), x)", // "{{y(x)->C(1)/E^(2*ArcTanh(x))}}"); check("DSolve(y'(x) == -y(x), y(x), x)", // "{{y(x)->C(1)/E^x}}"); check("DSolve(y'(x) == y(x)+a*Cos(x), y(x), x)", // "{{y(x)->E^x*C(1)-1/2*a*Cos(x)+1/2*a*Sin(x)}}"); // not implemented yet check("DSolve(y'(x) == -3*y(x)^2, y(x), x)", // "{{y(x)->1/(3*x-C(1))}}"); check("DSolve({y'(x) == -3*y(x)^2, y(0)==2}, y(x), x)", // "{{y(x)->1/(1/2+3*x)}}"); } @Test public void testDuplicateFreeQ() { check("DuplicateFreeQ({1, 7, 8, 4, 3, 9, 2})", // "True"); check("DuplicateFreeQ({1, 7, 8, 4, 3, 4, 1, 9, 9, 2})", // "False"); check( "l = {{0, 0, 0, 1, 0}, {1, 0, 1, 0, 1}, {1, 1, 1, 0, 0}, {0, 0, 0, 0, 1}, {1, 1, 1, 0, 1}};", // ""); check("DuplicateFreeQ(l, Total(#1) == Total(#2) &)", // "False"); } @Test public void testEasterSunday() { check("EasterSunday(2000)", // "{2000,4,23}"); check("EasterSunday(2030)", // "{2030,4,21}"); } @Test public void testEcho() { check("{Echo(f(x,y)), Print(g(a,b))}", // // >> f(x,y) // >> g(a,b) "{f(x,y),Null}"); check("Echo(2*2)+Echo(3^4)", // // >> 4 // >> 81 "85"); check("expr1; x = Echo(1 + 1, \"sum: \"); expr2", // // >> sum: 2 "expr2"); check("expr1; x = Echo(f(x,g(y,z)), \"leaf count: \",LeafCount); expr2", // // >> leaf count: 5 "expr2"); check("x = Echo[Unevaluated[1 + 1]]; x^2", // // >> 1+1 "4"); } @Test public void testEchoFunction() { check("{EchoFunction()[f(x,y)], Print(g(a,b))}", // // >> f(x,y) // >> g(a,b) "{f(x,y),Null}"); check("EchoFunction()[2*2]+EchoFunction()[3^4]", // // >> 4 // >> 81 "85"); check("EchoFunction(\"test: \", f)[expr]", // // >> test: f(expr) "expr"); check("EchoFunction(f)[expr]", // // >> f(expr) "expr"); } @Test public void testEffectiveInterest() { // TODO // check("EffectiveInterest({{0, .05}, {3, .065}, {5, .07}, {6, .085}}, 1/12)", // // "{{0,0.0511619},{3,0.0669719},{5,0.0722901},{6,0.0883909}}"); check("EffectiveInterest(a,b)", // "-1+(1+a*b)^(1/b)"); check("EffectiveInterest({.05, .065, .07, .085}, 1/12)", // "{0.0511619,0.0669719,0.0722901,0.0883909}"); check("EffectiveInterest(SparseArray({.05, .065, .07, .085}), 1/12)", // "{0.0511619,0.0669719,0.0722901,0.0883909}"); check("EffectiveInterest({.05, .065, .07, .085}, 1/12)", // "{0.0511619,0.0669719,0.0722901,0.0883909}"); check("EffectiveInterest(.1, 0)", // "0.105171"); check("EffectiveInterest(.06, 3)", // "0.0567218"); check("EffectiveInterest({a,b,c,d})", // "-1+((1+a)*(1+b)*(1+c)*(1+d))^(1/4)"); check("EffectiveInterest(SparseArray({a,b,c,d}))", // "-1+((1+a)*(1+b)*(1+c)*(1+d))^(1/4)"); check("FindRoot(EffectiveInterest(r, 1/4) == .05, {r, .05})", // "{r->0.0490889}"); check("Solve(EffectiveInterest(nr, 1/f) == eff, nr) // Quiet", // "{{nr->(-1+(1+eff)^(1/f))*f}}"); } @Test public void testElement() { check("Element(N(1,50), Integers)", // "1∈Integers"); check("Element(Sqrt(2), #) & /@ {Complexes, Algebraics, Reals, Rationals, Integers, Primes}", // "{True,Sqrt(2)∈Algebraics,True,Sqrt(2)∈Rationals,False,False}"); check("Element(ComplexInfinity, Complexes)", // "False"); check("{x} \\[Element] Reals", // "x∈Reals"); check("{ } \\[Element] Reals", // "True"); check("{x, y, I} \\[Element] Reals", // "False"); check("Element(Undefined, Reals)", // "Undefined"); check("Element(ComplexInfinity, Reals)", // "False"); check("Element(Infinity, Reals)", // "False"); check("Element(-Infinity, Reals)", // "False"); check("Element(a | b | c, Reals)", // "(a|b|c)∈Reals"); check("Element(a | 2 | c, Reals)", // "(a|c)∈Reals"); check("Element(pi, reals)", // "True"); check("Element(sin, reals)", // "Sin∈Reals"); // check("Element(Sqrt(2), #) & /@ {Complexes, Algebraics, Reals, Rationals, Integers, // Primes}",// // ""); check("Element(E, Algebraics)", // "False"); check("Element(Pi, Algebraics)", // "False"); check("Element(ComplexInfinity, Algebraics)", // "False"); check("Element(I, Algebraics)", // "True"); } @Test public void testElementData() { // TODO // check("Length(ElementData(All))", "118"); check("ElementData(74)", // "Tungsten"); check("ElementData(\"He\", \"AbsoluteBoilingPoint\")", // "4.22"); check("ElementData(\"Carbon\", \"IonizationEnergies\")", // "{1086.5,2352.6,4620.5,6222.7,37831,47277.0}"); check("ElementData(16, \"ElectronConfigurationString\")", // "[Ne] 3s2 3p4"); check("ElementData(73, \"ElectronConfiguration\")", // "{{2},{2,6},{2,6,10},{2,6,10,14},{2,6,3},{2}}"); check("ElementData(\"He\", \"ElectroNegativity\")", // "Missing(NotApplicable)"); check("ElementData(\"Tc\", \"SpecificHeat\")", // "Missing(NotAvailable)"); check("ElementData(\"Properties\")", // "{StandardName,AtomicNumber,Abbreviation,AbsoluteBoilingPoint,AbsoluteMeltingPoint,AtomicRadius,AtomicWeight,Block,BoilingPoint,BrinellHardness,BulkModulus,CovalentRadius,CrustAbundance,Density,DiscoveryYear,ElectroNegativity,ElectronAffinity,ElectronConfiguration,ElectronConfigurationString,ElectronShellConfiguration,FusionHeat,Group,IonizationEnergies,LiquidDensity,MeltingPoint,MohsHardness,Name,Period,PoissonRatio,Series,ShearModulus,SpecificHeat,ThermalConductivity,VanDerWaalsRadius,VaporizationHeat,VickersHardness,YoungModulus}"); check("ElementData(6)", "Carbon"); check("ElementData(\"Carbon\", \"Name\")", // "carbon"); check("ElementData(79, \"Abbreviation\")", // "Au"); check("ElementData(\"Au\", \"StandardName\")", // "Gold"); check("ElementData(\"Gold\", \"AtomicNumber\")", // "79"); check("ElementData(\"Carbon\", \"AtomicNumber\")", // "6"); check("ElementData(\"He\", \"AtomicNumber\")", // "2"); check("ElementData(\"Chlorine\", \"BoilingPoint\")", // "-34.04"); check("ElementData(\"C\", \"AtomicWeight\")", // "12.01"); check("ElementData(117, \"AtomicWeight\")", // "294"); // check("ElementData(\"Pd\", \"AtomicRadius\")", "140"); check("ElementData(\"Pd\", \"VanDerWaalsRadius\")", // "163"); // check("ElementData(\"Pd\", \"CovalentRadius\")", "131"); check("ElementData(\"Pd\", \"IonizationEnergies\")", // "{804.4,1870,3177}"); check("ElementData(\"Pd\", \"ElectronAffinity\")", // "54.24"); check("ElementData(\"Pd\", \"ThermalConductivity\")", // "71.8"); check("ElementData(\"Pd\", \"YoungModulus\")", // "121"); check("ElementData(\"Pd\", \"PoissonRatio\")", // "0.39"); check("ElementData(\"Pd\", \"BulkModulus\")", // "180"); check("ElementData(\"Pd\", \"ShearModulus\")", // "44"); check("ElementData(\"Pd\", \"ElectronConfiguration\")", // "{{2},{2,6},{2,6,10},{2,6,10}}"); check("ElementData(\"Pd\", \"ElectronConfigurationString\")", // "[Kr] 4d10"); check("ElementData(\"Pd\", \"ElectronShellConfiguration\")", // "{2,8,18,18}"); // check("ElementData(\"Helium\", \"MeltingPoint\")", // "Missing(NotApplicable)"); // check("ElementData(\"Tungsten\", \"ThermalConductivity\")", "173"); } @Test public void testEliminate() { check("Eliminate({x^2 + y^2 + z^2 == 1, x - y + z == 2, x^3 - y^2 == z + 1}, {y, z})", "-4*x+2*x^2-4*z+2*x*z+2*z^2==-3&&4*x-x^2+x^3+3*z-2*x*z-z^2==5"); // print: Eliminate: y>2 is not a well-formed equation. check("Eliminate({x==y,y>2},{x})", // "Eliminate({x==y,y>2},{x})"); // TODO // check("Eliminate({a0*x^p+a1*x^q==0},x)", // // "(-a1)*x^q == a0*x^p"); check("Eliminate({(a*x + b)/(c*x + d)==y},x)", // "True"); check("Eliminate({x == 2 + y, y == z}, y)", // "x-z==2"); check("Eliminate({x == 2 + y, y == z}, {y,v})", // "x-z==2"); check("Eliminate({2*x + 3*y + 4*z == 1, 9*x + 8*y + 7*z == 2}, z)", // "11/2*x+11/4*y==1/4"); check("Eliminate({x == 2 + y^3, y^2 == z}, y)", // "x-z^(3/2)==2"); // use evaluation step: Cos(ArcSin(y)) => Sqrt(1-y^2) check("Eliminate({Sin(x)==y, Cos(x) == z}, x)", // "Sqrt(1-y^2)-z==0"); check("Eliminate({a^x==y, b^(2*x) == z}, x)", // "b^((2*Log(y))/Log(a))-z==0"); } @Test public void testEllipticE() { // TODO implement second kind arbitrary precision checkNumeric("N(EllipticE(2/3,2),50)", // "EllipticE(0.66666666666666666666666666666666666666666666666666,2)"); // https://github.com/Hipparchus-Math/hipparchus/issues/148 check("EllipticE(3 + 2.5*I, 2.3 - 1.5*I)", // "3.05969+I*11.16503"); check("EllipticE(I-2.0,0.5)", // "-1.47153+I*0.714415"); check("EllipticE(2,0.999999)", // "1.09071"); check("EllipticE(-Pi/2,0.5)", // "-1.35064"); check("Table(EllipticE(x,0.5), {x,-2.0, 2.0, 1/4})", // "{-1.6629,-1.47803,-1.30054,-1.12005,-0.92733,-0.717351,-0.489911,-0.248708,0.0," + // "0.248708,0.489911,0.717351,0.92733,1.12005,1.30054,1.47803,1.6629}"); check("Table(EllipticE(I+x,0.5), {x,-2.0, 2.0, 1/4})", // "{-1.47153+I*0.714415,-1.34791+I*0.585355,-1.37918+I*0.53464,-1.29305+I*0.657158,-1.12766+I*0.789102," + // "-0.901309+I*0.911354,-0.627973+I*1.00908,-0.322266+I*1.07186,I*1.09348,0.322266+I*1.07186,0.627973+I*1.00908," + // "0.901309+I*0.911354,1.12766+I*0.789102,1.29305+I*0.657158,1.37918+I*0.53464,1.34791+I*0.585355,1.47153+I*0.714415}"); checkNumeric("EllipticE(0.4)", // "1.3993921388974322"); checkNumeric("EllipticE(3 + 2.5*I)", // "1.1997488433342685+I*(-1.3570974376009501)"); checkNumeric("N(EllipticE(1/3),50)", // "1.4303152571722197239225284145322837302944509074088"); checkNumeric("EllipticE(0.1234567890000000000)", // "1.521130747104144722"); checkNumeric("EllipticE(0.1234567890000000000000000000000)", // "1.521130747104144722956858486312"); check("EllipticE(0, m)", // "0"); check("EllipticE(z,0)", // "z"); check("EllipticE(1/2)", // "(Pi^2+2*Gamma(3/4)^4)/(4*Sqrt(Pi)*Gamma(3/4)^2)"); check("EllipticE(-1)", // "(Pi^2+2*Gamma(3/4)^4)/(2*Sqrt(2*Pi)*Gamma(3/4)^2)"); check("EllipticE(Pi/2, m)", // "EllipticE(m)"); check("EllipticE(5/4,1)", // "Sin(5/4)"); check("EllipticE(0.4)", // "1.39939"); // needs formula for complex numbers // check("Table(EllipticE(x ), {x,-2.0, 2.0, 1/4})", ""); } @Test public void testEllipticF() { check("EllipticF(0.3,0.8)", // "0.303652"); // https://github.com/paulmasson/math/issues/13 check("EllipticF(-1.5708,1.5708)", // "-1.58877+I*1.39865"); // see github #109 check("EllipticF(3,1/2)//N", // "3.56632"); check("EllipticF(17/2*Pi, m)", // "17*EllipticK(m)"); check("EllipticF(Pi/2, m)", // "EllipticK(m)"); check("EllipticF(a+42*Pi,m)", // "EllipticF(a,m)+84*EllipticK(m)"); check("EllipticF(-z,m)", // "-EllipticF(z,m)"); check("EllipticF(0, m)", // "0"); check("EllipticF(z,0)", // "z"); check("EllipticF(5/4, 1)", // "Log(Sec(5/4)+Tan(5/4))"); check("EllipticF(3, 1)", // "ComplexInfinity"); check("EllipticF(Pi, 1)", // "ComplexInfinity"); check("Table(EllipticF(x,0.5), {x,-2.0, 2.0, 1/4})", // "{-2.44438,-2.10618,-1.75404,-1.4077,-1.08322,-0.785382,-0.510467,-0.251304,0.0,0.251304,0.510467,0.785382,1.08322,1.4077,1.75404,2.10618,2.44438}"); check("Table(EllipticF(I+x,0.5), {x,-2.0, 2.0, 1/4})", // "{-2.77616+I*1.25663,-2.53768+I*1.51416,-1.26198+I*1.69875,-1.03395+I*1.34928,-0.804237+I*1.16274,-0.591003+I*1.04644," + // "-0.388636+I*0.973573,-0.192779+I*0.933104,I*0.920097,0.192779+I*0.933104,0.388636+I*0.973573,0.591003+I*1.04644,0.804237+I*1.16274," + // "1.03395+I*1.34928,1.26198+I*1.69875,2.53768+I*1.51416,2.77616+I*1.25663}"); } @Test public void testEllipticK() { check("N(EllipticK(8/10), 50)", // "2.2572053268208536550832560045233873972354192817399"); check("EllipticK(0.999999999999999990000000000000000)", // "20.9582676515692789828830607366566"); // reducing the accuracy gives ComplexInfinity in MMA: check("EllipticK(0.99999999999999999)", // "20.958267651569278"); checkNumeric("EllipticK(2.5+I)", // "1.1551450606569331+I*0.9528453714670536"); check("EllipticK(0.5)", // "1.85407"); check("EllipticK(-1.0+I)", // "1.26549+I*0.162237"); check("Table(EllipticK(x), {x,-1.0, 1.0, 1/4})", // "{1.31103,1.35906,1.41574,1.48441,1.5708,1.68575,1.85407,2.15652,ComplexInfinity}"); check("Table(EllipticK(x+I), {x,-1.0, 1.0, 1/4})", // "{1.26549+I*0.162237,1.30064+I*0.18478,1.33866+I*0.213052,1.37925+I*0.249038,1.42127+I*0.29538,1.46203+I*0.355241,1.49611+I*0.431362,1.51493+I*0.523542,1.50924+I*0.625146}"); } @Test public void testEllipticPi() { check("EllipticPi(0.4, 0.6)", // "2.59092"); check("EllipticPi(0,-1,1.5708)", // "-1.58877+I*0.451013"); // github #172 check("EllipticPi(I,1+(-1)*1,0.3)", // "0.0"); check("Table(EllipticPi(x+I,0.5), {x,-2.0, 2.0, 1/4})", // "{0.978856+I*0.171427,1.01788+I*0.193752,1.06089+I*0.221026,1.10832+I*0.254803,1.16047+I*0.297252," // + "1.21733+I*0.351426,1.27808+I*0.421604,1.34015+I*0.513624,1.39738+I*0.63483,1.437+I*0.79243," // + "1.43661+I*0.987709,1.36724+I*1.20422,1.21283+I*1.39928,0.996036+I*1.52334,0.768937+I*1.55932," // + "0.57283+I*1.52838,0.420978+I*1.46215}"); // TODO improve see discussion: https://github.com/paulmasson/math/issues/6 // check( // "EllipticPi(2.0, 0.5)", // // "-0.313545+I*(-1.8138)"); check("EllipticPi(0,z,m)", // "EllipticF(z,m)"); check("EllipticPi(n,Pi/2,n)", // "EllipticE(n)/(1-n)"); check("EllipticPi(n,Pi/2,x)", // "EllipticPi(n,x)"); check("EllipticPi(n,0)", // "Pi/(2*Sqrt(1-n))"); check("EllipticPi(n,1)", // "Infinity/Sign(1-n)"); check("EllipticPi(n,n)", // "EllipticE(n)/(1-n)"); check("EllipticPi(0.4,0.6)", // "2.59092"); check("EllipticPi(1/3, Pi/5, 0.3)", // "0.668735"); // TODO improve see discussion: https://github.com/paulmasson/math/issues/6 // check( // "Table(EllipticPi(x,0.5), {x,-2.0, 2.0, 1/4})", // // // "{1.0227,1.07184,1.12843,1.19454,1.27313,1.36859,1.48785,1.64253,1.85407,2.16762,2.70129,3.93061,ComplexInfinity,-0.592756+I*(-4.05578),-0.45672+I*(-2.7207),-0.371748+I*(-2.14612),-0.313545+I*(-1.8138)}"); } @Test public void testEllipticTheta() { check("EllipticTheta(3,0.4,E^(Pi*I*1/3))", // "EllipticTheta(3,0.4,0.5+I*0.866025)"); check("EllipticTheta(1,0,x)", // "0"); check("EllipticTheta(1,x,0)", // "0"); check("EllipticTheta(2,x,0)", // "0"); check("EllipticTheta(3,x,0)", // "1"); check("EllipticTheta(4,x,0)", // "1"); check("EllipticTheta(1,Pi,1/2)", // "0"); check("EllipticTheta({1, 2, 3, 4}, z, q)", // "{EllipticTheta(1,z,q),EllipticTheta(2,z,q),EllipticTheta(3,z,q),EllipticTheta(4,z,q)}"); check("EllipticTheta(3, 0.4+I, 0.5 )", // "2.89461+I*(-6.54061)"); check("EllipticTheta(1, 2., 1/3)", // "1.42788"); check("EllipticTheta(2, 5.0, 0.5)", // "0.183328"); check("EllipticTheta(3, 0.4, 0.5)", // "1.69015"); check("EllipticTheta(3, 1/4, 1/3) // N", // "1.5984"); check("EllipticTheta(1, 0, 0) // N", // "0.0"); check("Table(EllipticTheta(4, x,0.5), {x,-2.0, 2.0, 1/4})", // "{1.63213,2.03256,2.1136,1.83522,1.33069,0.806366," // + "0.411527,0.189666,0.121124,0.189666,0.411527,0.806366," // + "1.33069,1.83522,2.1136,2.03256,1.63213}"); check("Table(EllipticTheta(4, x), {x,-0.9, 0.9, 1/4})", // "{5.46055,2.70051,1.85173,1.30101,0.8002,0.329855,0.0396032,2.24177*10^-6}"); check("Table(EllipticTheta(4, x*I), {x,-0.9, 0.9, 1/4})", // "{2.73027+I*2.73027,1.35904+I*1.34147,1.0512+I*0.800524,1.00101+I*0.3,1.0002+I*(-0.2),1.03001+I*(-0.700158),1.25976+I*(-1.22016),2.19833+I*(-2.19833)}"); // TODO: improve for case "EllipticTheta: Unsupported elliptic nome" check("EllipticTheta(3, 0.4+I, 0.5+I)", // "EllipticTheta(3,0.4+I*1.0,0.5+I*1.0)"); } @Test public void testEntropy() { // Shannon entropy check("Entropy({a, b, b})", // "2/3*Log(3/2)+Log(3)/3"); check("Entropy({a, b, b,c,c,c,d})", // "3/7*Log(7/3)+2/7*Log(7/2)+2/7*Log(7)"); check("Entropy(b,{a,c,c})", // "2/3*Log(3/2)/Log(b)+Log(3)/(3*Log(b))"); } @Test public void testErf() { // assertEquals(org.hipparchus.special.Erf.erf(new Complex(1.0, 1.5)).toString(), // // ""); // check("N(Erf(10000), 30)", // // "1"); check("N(Erf(3/2-I), 50)", // "1.0783992074989334503393327040582123696121612366804+" + "I*0.0279637112386558494484658962059072085066945367208"); check("N(Erf(3/2), 50)", // "0.96610514647531072706697626164594785868141047925763"); checkNumeric("Erf(-10007.0)", // "-1.0"); checkNumeric("Erf(-0.5)", // "-0.5204998778130465"); checkNumeric("Erf(3.0)", // "0.9999779095030015"); check("Erf(-42*I*x)", // "-I*Erfi(42*x)"); check("Erf(43*I*x)", // "I*Erfi(43*x)"); check("Erf(I)", // "I*Erfi(1)"); check("Erf(-I)", // "-I*Erfi(1)"); checkNumeric("Erf(1.5, 2)", // "0.029217118543642062"); check("Erf(-Infinity, Infinity)", // "2"); check("Erf(0.0)", // "0.0"); check("Erf(1.5-I)", // "1.0784+I*0.0279637"); check("Erf({0.5, 1.0, 1.5})", // "{0.5205,0.842701,0.966105}"); check("Erf({Infinity, -Infinity, I Infinity, -I Infinity})", // "{1,-1,I*Infinity,-I*Infinity}"); check("Erf(-x)", // "-Erf(x)"); check("Erf(1.0)", // "0.842701"); check("Erf(0)", // "0"); check("{Erf(0, x), Erf(x, 0)}", // "{Erf(x),-Erf(x)}"); check("Erf(ComplexInfinity)", // "Indeterminate"); checkNumeric("Erf(0.95)", // "0.8208908072732779"); } @Test public void testErfc() { check("N(Erfc(100000000000000000000000000000000035/2*1/Sqrt(2)),30)", // "0"); checkNumeric("Erfc(1.5-I)", // "-0.07839920749893345+I*(-0.02796371123865584)"); check("Erfc({0.5, 1.0, 1.5})", // "{0.4795,0.157299,0.0338949}"); check("Erfc(0.95)", // "0.179109"); checkNumeric("Erfc(5/Sqrt(2))/2 // N", // "2.866515718791936E-7"); check("Erfc(-0.28991)", // "1.31819"); // don't transform negative arg check("Erfc(-x) / 2", // "Erfc(-x)/2"); checkNumeric("Erfc(1.0)", // "0.15729920705028513"); check("Erfc(0)", // "1"); } @Test public void testErfi() { // https://github.com/Hipparchus-Math/hipparchus/issues/278 checkNumeric("Erfi(1.5-I)", // "-0.7013604642514806+I*(-1.8468330146085419)"); checkNumeric("N(Erfi(1/2),50)", // "0.6149520946965109808396811856236413930513456178954"); check("Erfi(0.5000000000000000000000000000000000)", // "0.6149520946965109808396811856236413"); // https://github.com/mtommila/apfloat/issues/31 // checkNumeric("N(Erfi(1/2),50)", // // "0.6149520946965109808396811856236413930513456178954"); check("Erfi({0.5, 1.5, 2.5})", // "{0.614952,4.58473,130.3958}"); check("Erfi(I)", // "I*Erf(1)"); check("Erfi(-I)", // "-I*Erf(1)"); check("Erfi(-42*I*x)", // "-I*Erf(42*x)"); check("Erfi(43*I*x)", // "I*Erf(43*x)"); check("Erfi((-1)^(1/4)*2^2)", // "Erfi(4*(-1)^(1/4))"); check("Erfi((-1)^(1/4)*2.0^2)", // "-0.121816+I*1.07044"); check("Erfi(0)", // "0"); check("Erfi({-Infinity, Infinity, I Infinity, -I Infinity})", // "{-Infinity,Infinity,I,-I}"); check("Erfi(I*Infinity)", // "I"); check("Erfi(-I*Infinity)", // "-I"); check("Erfi(-x)", // "-Erfi(x)"); } @Test public void testEuclideanDistance() { check("EuclideanDistance({-1, -1}, {1.0, 1})", // "2.82843"); check("EuclideanDistance({a, b, c}, {x, y, z})", // "Sqrt(Abs(a-x)^2+Abs(b-y)^2+Abs(c-z)^2)"); check("EuclideanDistance({-1, -1}, {1, 1})", // "2*Sqrt(2)"); check("EuclideanDistance({a, b}, {c, d})", // "Sqrt(Abs(a-c)^2+Abs(b-d)^2)"); } @Test public void testEulerE() { check("EulerE(n,1/2)", // "EulerE(n)/2^n"); check("Table(EulerE(n,z), {n, 0, 15})", // "{1,-1/2+z,-z+z^2,1/4-3/2*z^2+z^3,z-2*z^3+z^4,-1/2+5/2*z^2-5/2*z^4+z^5,-3*z+5*z^3-\n" // + "3*z^5+z^6,17/8-21/2*z^2+35/4*z^4-7/2*z^6+z^7,17*z-28*z^3+14*z^5-4*z^7+z^8,-31/2+\n" // + "153/2*z^2-63*z^4+21*z^6-9/2*z^8+z^9,-155*z+255*z^3-126*z^5+30*z^7-5*z^9+z^10,691/\n" // + "4-1705/2*z^2+2805/4*z^4-231*z^6+165/4*z^8-11/2*z^10+z^11,2073*z-3410*z^3+1683*z^\n" // + "5-396*z^7+55*z^9-6*z^11+z^12,-5461/2+26949/2*z^2-22165/2*z^4+7293/2*z^6-1287/2*z^\n" // + "8+143/2*z^10-13/2*z^12+z^13,-38227*z+62881*z^3-31031*z^5+7293*z^7-1001*z^9+91*z^\n" // + "11-7*z^13+z^14,929569/16-573405/2*z^2+943215/4*z^4-155155/2*z^6+109395/8*z^8-\n" // + "3003/2*z^10+455/4*z^12-15/2*z^14+z^15}"); check("EulerE(10,z)", // "-155*z+255*z^3-126*z^5+30*z^7-5*z^9+z^10"); check("Table(EulerE(k), {k, 0, 15})", // "{1,0,-1,0,5,0,-61,0,1385,0,-50521,0,2702765,0,-199360981,0}"); } @Test public void testEulerGamma() { check("N(EulerGamma,100)", // "0.5772156649015328606065120900824024310421593359399235988057672348848677267776646709369470632917467495"); check("N(EulerGamma)", // "0.577216"); } @Test public void testEulerPhi() { check("Refine(EulerPhi(p^n),Element(p, Primes)&&Element(n, Integers))", // "-1/p^(1-n)+p^n"); check("EulerPhi(-a)", // "EulerPhi(a)"); check("Table(EulerPhi(k), {k, 0, 20})", // "{0,1,1,2,2,4,2,6,4,6,4,10,4,12,6,8,8,16,6,18,8}"); check("Table(EulerPhi(-k), {k, 0, 20})", // "{0,1,1,2,2,4,2,6,4,6,4,10,4,12,6,8,8,16,6,18,8}"); check("EulerPhi(50!)", // "4218559200885839042679312107816703841788854953574400000000000000"); check("Table(EulerPhi(10^k), {k, 0, 10})", // "{1,4,40,400,4000,40000,400000,4000000,40000000,400000000,4000000000}"); } @Test public void testEvaluate() { check("Evaluate(1+1)", // "2"); check("{f(2+2, 1+1, -1+2), f(Evaluate(2+2),Evaluate(1+1),-1+2,Evaluate(-1+2))}", // "{f(4,2,1),f(4,2,1,1)}"); check( "SetAttributes(hr,HoldRest); {hr(2+2, 1+1, -1+2), hr(2+2,Evaluate(1+1),-1+2,Evaluate(-1+2))}", // "{hr(4,1+1,-1+2),hr(4,2,-1+2,1)}"); check("SetAttributes(hf,HoldFirst); {hf(1+1), hf(Evaluate(1+1))}", // "{hf(1+1),hf(2)}"); check("cheb = ChebyshevT(5, x);Function(x, Evaluate(cheb))", // "Function(x,5*x-20*x^3+16*x^5)"); check("Function(x, Evaluate(cheb))[10]", // "1580050"); check("Hold(Evaluate(1+1),2+2)", // "Hold(2,2+2)"); check("Evaluate(a,b)", // "Identity(a,b)"); check("x=Plus; {Attributes(x), Attributes(Evaluate(x))}", // "{{},{Flat,Listable,NumericFunction,OneIdentity,Orderless,Protected}}"); } @Test public void testExactNumberQ() { check("ExactNumberQ(10)", // "True"); check("ExactNumberQ(4.0)", // "False"); check("ExactNumberQ(n)", // "False"); check("ExactNumberQ(1+I)", // "True"); check("ExactNumberQ(1 + 1. * I)", // "False"); } @Test public void testExcept001() { check("Cases({x, a, b, x, c}, Except(x))", // "{a,b,c}"); check("Cases({a, 0, b, 1, c, 2, 3}, Except(1, _Integer))", // "{0,2,3}"); check("Cases({1, 0, 2, 0, 3}, (0|2))", // "{0,2,0}"); check("Cases({1, 0, 2, 0, 3}, Except(0))", // "{1,2,3}"); check("Cases({a, b, 0, 1, 2, x, y}, Except(_Integer))", // "{a,b,x,y}"); check("Cases({a, b, 0, 1, 2, x, y}, Except(0, _Integer))", // "{1,2}"); check("Cases({1, 1, -5, EulerGamma, r, I, 0, Pi, 1/2}, Except(_Integer))", // "{EulerGamma,r,I,Pi,1/2}"); } @Test public void testExcept002() { // https://github.com/mathics/Mathics/issues/1405 check("f(Except(_(___), x_?NumericQ)) := g(x)", // ""); check("f(f(x_)) := x", // ""); check("f(2)", // "g(2)"); check("f(Pi)", // "g(Pi)"); check("f(2*Pi)", // "f(2*Pi)"); check("f(a)", // "f(a)"); check("f(f(a))", // "a"); } @Test public void testExp() { check("\\[ExponentialE]", // "E"); check("Exp(10.*^20)", // "Overflow()"); check("Exp(x*Log(n))", // "n^x"); check("Exp(42+Log(a)+Log(b))", // "a*b*E^42"); check("Exp(1)", // "E"); checkNumeric("Exp(10.0)", // "22026.465794806703"); check("Exp(x) //FullForm", // "Power(E, x)"); check("Exp(a+b)", // "E^(a+b)"); check("E^(I*Pi)", // "-1"); check("E^(2*I*Pi)", // "1"); check("E^(2*I*Pi*3)", // "1"); check("E^(5*I*Pi)", // "-1"); check("E^Infinity", // "Infinity"); check("E^(-Infinity)", // "0"); check("E^(I*Infinity)", // "Indeterminate"); check("E^(-I*Infinity)", // "Indeterminate"); check("E^ComplexInfinity", // "Indeterminate"); check("Conjugate(E^z)", // "E^Conjugate(z)"); } @Test public void testExpand() { check("Expand((a(1)+a(2))*(x(1)+x(2))^2, x(_))", // "(a(1)+a(2))*x(1)^2+2*(a(1)+a(2))*x(1)*x(2)+(a(1)+a(2))*x(2)^2"); check("Expand((a + b)^2*(1 + x)^2, x)", // "(a+b)^2+2*(a+b)^2*x+(a+b)^2*x^2"); check("Expand((1 + x)^2 + (2 + x)^2, 1 + x)", // "1+2*x+x^2+(2+x)^2"); // performance test // check("Expand((x + y + z + w)^15 * ((x + y + z + w)^15+w));", // // "?"); // check("test = (x + y + z + w)^15;Length(Expand(test*(test+w)))", // // "6272"); // check( // // "Expand((1+x+x^2)*(1-x+x^3-x^4+x^6-x^7+x^9-x^10+x^12-x^13+x^15-x^16+x^18-x^19+x^21-x^22+x^\n" // + // "24-x^25+x^27-x^28+x^30-x^31+x^33-x^34+x^36-x^37+x^39-x^40+x^42-x^43+x^45-x^46+x^\n" // + // "48-x^49+x^51-x^52+x^54-x^55+x^57-x^58+x^60-x^61+x^63-x^64+x^66-x^67+x^69-x^70+x^\n" // + // "72-x^73+x^75-x^76+x^78-x^79+x^81-x^82+x^84-x^85+x^87-x^88+x^90-x^91+x^93-x^94+x^\n" // + // "96-x^97+x^99-x^100+x^102-x^103+x^105-x^106+x^108-x^109+x^111-x^112+x^114-x^115+x^\n" // + "117-x^118+x^120-x^121+x^123-x^124+x^126-x^127+x^129-x^130+x^132-x^133+x^135-x^\n" // + "136+x^138-x^139+x^141-x^142+x^144-x^145+x^147-x^148+x^150-x^151+x^153-x^154+x^\n" // + "156-x^157+x^159-x^160+x^162-x^163+x^165-x^166+x^168-x^169+x^171-x^172+x^174-x^\n" // + "175+x^177-x^178+x^180-x^181+x^183-x^184+x^186-x^187+x^189-x^190+x^192-x^193+x^\n" // + "195-x^196+x^198-x^199+x^201-x^202+x^204-x^205+x^207-x^208+x^210-x^211+x^213-x^\n" // + "214+x^216-x^217+x^219-x^220+x^222-x^223+x^225-x^226+x^228-x^229+x^231-x^232+x^\n" // + "234-x^235+x^237-x^238+x^240-x^241+x^243-x^244+x^246-x^247+x^249-x^250+x^252-x^\n" // + "253+x^255-x^256+x^258-x^259+x^261-x^262+x^264-x^265+x^267-x^268+x^270-x^271+x^\n" // + "273-x^274+x^276-x^277+x^279-x^280+x^282-x^283+x^285-x^286+x^288-x^289+x^291-x^\n" // + "292+x^294-x^295+x^297-x^298+x^300-x^301+x^303-x^304+x^306-x^307+x^309-x^310+x^\n" // + "312-x^313+x^315-x^316+x^318-x^319+x^321-x^322+x^324-x^325+x^327-x^328+x^330-x^\n" // + "331+x^333-x^334+x^336-x^337+x^339-x^340+x^342-x^343+x^345-x^346+x^348-x^349+x^\n" // + "351-x^352+x^354-x^355+x^357-x^358+x^360-x^361+x^363-x^364+x^366-x^367+x^369-x^\n" // + "370+x^372-x^373+x^375-x^376+x^378-x^379+x^381-x^382+x^384-x^385+x^387-x^388+x^\n" // + "390-x^391+x^393-x^394+x^396-x^397+x^399-x^400+x^402-x^403+x^405-x^406+x^408-x^\n" // + "409+x^411-x^412+x^414-x^415+x^417-x^418+x^420-x^421+x^423-x^424+x^426-x^427+x^\n" // + "429-x^430+x^432-x^433+x^435-x^436+x^438-x^439+x^441-x^442+x^444-x^445+x^447-x^\n" // + "448+x^450-x^451+x^453-x^454+x^456-x^457+x^459-x^460+x^462-x^463+x^465-x^466+x^\n" // + "468-x^469+x^471-x^472+x^474-x^475+x^477-x^478+x^480-x^481+x^483-x^484+x^486-x^\n" // + "487+x^489-x^490+x^492-x^493+x^495-x^496+x^498-x^499+x^501-x^502+x^504-x^505+x^\n" // + "507-x^508+x^510-x^511+x^513-x^514+x^516-x^517+x^519-x^520+x^522-x^523+x^525-x^\n" // + "526+x^528-x^529+x^531-x^532+x^534-x^535+x^537-x^538+x^540-x^541+x^543-x^544+x^\n" // + "546-x^547+x^549-x^550+x^552-x^553+x^555-x^556+x^558-x^559+x^561-x^562+x^564-x^\n" // + "565+x^567-x^568+x^570-x^571+x^573-x^574+x^576-x^577+x^579-x^580+x^582-x^583+x^\n" // + "585-x^586+x^588-x^589+x^591-x^592+x^594-x^595+x^597-x^598+x^600-x^601+x^603-x^\n" // + "604+x^606-x^607+x^609-x^610+x^612-x^613+x^615-x^616+x^618-x^619+x^621-x^622+x^\n" // + "624-x^625+x^627-x^628+x^630-x^631+x^633-x^634+x^636-x^637+x^639-x^640+x^642-x^\n" // + "643+x^645-x^646+x^648-x^649+x^651-x^652+x^654-x^655+x^657-x^658+x^660-x^661+x^\n" // + "663-x^664+x^666-x^667+x^669-x^670+x^672-x^673+x^675-x^676+x^678-x^679+x^681-x^\n" // + "682+x^684-x^685+x^687-x^688+x^690-x^691+x^693-x^694+x^696-x^697+x^699-x^700+x^\n" // + "702-x^703+x^705-x^706+x^708-x^709+x^711-x^712+x^714-x^715+x^717-x^718+x^720-x^\n" // + "721+x^723-x^724+x^726-x^727+x^729-x^730+x^732-x^733+x^735-x^736+x^738-x^739+x^\n" // + "741-x^742+x^744-x^745+x^747-x^748+x^750-x^751+x^753-x^754+x^756-x^757+x^759-x^\n" // + "760+x^762-x^763+x^765-x^766+x^768-x^769+x^771-x^772+x^774-x^775+x^777-x^778+x^\n" // + "780-x^781+x^783-x^784+x^786-x^787+x^789-x^790+x^792-x^793+x^795-x^796+x^798-x^\n" // + "799+x^801-x^802+x^804-x^805+x^807-x^808+x^810-x^811+x^813-x^814+x^816-x^817+x^\n" // + "819-x^820+x^822-x^823+x^825-x^826+x^828-x^829+x^831-x^832+x^834-x^835+x^837-x^\n" // + "838+x^840-x^841+x^843-x^844+x^846-x^847+x^849-x^850+x^852-x^853+x^855-x^856+x^\n" // + "858-x^859+x^861-x^862+x^864-x^865+x^867-x^868+x^870-x^871+x^873-x^874+x^876-x^\n" // + "877+x^879-x^880+x^882-x^883+x^885-x^886+x^888-x^889+x^891-x^892+x^894-x^895+x^\n" // + "897-x^898+x^900-x^901+x^903-x^904+x^906-x^907+x^909-x^910+x^912-x^913+x^915-x^\n" // + "916+x^918-x^919+x^921-x^922+x^924-x^925+x^927-x^928+x^930-x^931+x^933-x^934+x^\n" // + "936-x^937+x^939-x^940+x^942-x^943+x^945-x^946+x^948-x^949+x^951-x^952+x^954-x^\n" // + "955+x^957-x^958+x^960-x^961+x^963-x^964+x^966-x^967+x^969-x^970+x^972-x^973+x^\n" // + "975-x^976+x^978-x^979+x^981-x^982+x^984-x^985+x^987-x^988+x^990-x^991+x^993-x^\n" // + // "994+x^996-x^997+x^999-x^1000+x^1002-x^1003+x^1005-x^1006+x^1008-x^1009+x^1011-x^\n" // + "1012+x^1014-x^1015+x^1017-x^1018+x^1020-x^1021+x^1023-x^1024+x^1026-x^1027+x^\n" // + "1029-x^1030+x^1032-x^1033+x^1035-x^1036+x^1038-x^1039+x^1041-x^1042+x^1044-x^\n" // + "1045+x^1047-x^1048+x^1050-x^1051+x^1053-x^1054+x^1056-x^1057+x^1059-x^1060+x^\n" // + "1062-x^1063+x^1065-x^1066+x^1068-x^1069+x^1071-x^1072+x^1074-x^1075+x^1077-x^\n" // + "1078+x^1080-x^1081+x^1083-x^1084+x^1086-x^1087+x^1089-x^1090+x^1092-x^1093+x^\n" // + "1095-x^1096+x^1098-x^1099+x^1101-x^1102+x^1104-x^1105+x^1107-x^1108+x^1110-x^\n" // + "1111+x^1113-x^1114+x^1116-x^1117+x^1119-x^1120+x^1122-x^1123+x^1125-x^1126+x^\n" // + "1128-x^1129+x^1131-x^1132+x^1134-x^1135+x^1137-x^1138+x^1140-x^1141+x^1143-x^\n" // + "1144+x^1146-x^1147+x^1149-x^1150+x^1152-x^1153+x^1155-x^1156+x^1158-x^1159+x^\n" // + "1161-x^1162+x^1164-x^1165+x^1167-x^1168+x^1170-x^1171+x^1173-x^1174+x^1176-x^\n" // + "1177+x^1179-x^1180+x^1182-x^1183+x^1185-x^1186+x^1188-x^1189+x^1191-x^1192+x^\n" // + "1194-x^1195+x^1197-x^1198+x^1200-x^1201+x^1203-x^1204+x^1206-x^1207+x^1209-x^\n" // + "1210+x^1212-x^1213+x^1215-x^1216+x^1218-x^1219+x^1221-x^1222+x^1224-x^1225+x^\n" // + "1227-x^1228+x^1229-x^1231+x^1232-x^1234+x^1235-x^1237+x^1238-x^1240+x^1241-x^\n" // + "1243+x^1244-x^1246+x^1247-x^1249+x^1250-x^1252+x^1253-x^1255+x^1256-x^1258+x^\n" // + "1259-x^1261+x^1262-x^1264+x^1265-x^1267+x^1268-x^1270+x^1271-x^1273+x^1274-x^\n" // + "1276+x^1277-x^1279+x^1280-x^1282+x^1283-x^1285+x^1286-x^1288+x^1289-x^1291+x^\n" // + "1292-x^1294+x^1295-x^1297+x^1298-x^1300+x^1301-x^1303+x^1304-x^1306+x^1307-x^\n" // + "1309+x^1310-x^1312+x^1313-x^1315+x^1316-x^1318+x^1319-x^1321+x^1322-x^1324+x^\n" // + "1325-x^1327+x^1328-x^1330+x^1331-x^1333+x^1334-x^1336+x^1337-x^1339+x^1340-x^\n" // + "1342+x^1343-x^1345+x^1346-x^1348+x^1349-x^1351+x^1352-x^1354+x^1355-x^1357+x^\n" // + "1358-x^1360+x^1361-x^1363+x^1364-x^1366+x^1367-x^1369+x^1370-x^1372+x^1373-x^\n" // + "1375+x^1376-x^1378+x^1379-x^1381+x^1382-x^1384+x^1385-x^1387+x^1388-x^1390+x^\n" // + "1391-x^1393+x^1394-x^1396+x^1397-x^1399+x^1400-x^1402+x^1403-x^1405+x^1406-x^\n" // + "1408+x^1409-x^1411+x^1412-x^1414+x^1415-x^1417+x^1418-x^1420+x^1421-x^1423+x^\n" // + "1424-x^1426+x^1427-x^1429+x^1430-x^1432+x^1433-x^1435+x^1436-x^1438+x^1439-x^\n" // + "1441+x^1442-x^1444+x^1445-x^1447+x^1448-x^1450+x^1451-x^1453+x^1454-x^1456+x^\n" // + "1457-x^1459+x^1460-x^1462+x^1463-x^1465+x^1466-x^1468+x^1469-x^1471+x^1472-x^\n" // + "1474+x^1475-x^1477+x^1478-x^1480+x^1481-x^1483+x^1484-x^1486+x^1487-x^1489+x^\n" // + "1490-x^1492+x^1493-x^1495+x^1496-x^1498+x^1499-x^1501+x^1502-x^1504+x^1505-x^\n" // + "1507+x^1508-x^1510+x^1511-x^1513+x^1514-x^1516+x^1517-x^1519+x^1520-x^1522+x^\n" // + "1523-x^1525+x^1526-x^1528+x^1529-x^1531+x^1532-x^1534+x^1535-x^1537+x^1538-x^\n" // + "1540+x^1541-x^1543+x^1544-x^1546+x^1547-x^1549+x^1550-x^1552+x^1553-x^1555+x^\n" // + "1556-x^1558+x^1559-x^1561+x^1562-x^1564+x^1565-x^1567+x^1568-x^1570+x^1571-x^\n" // + "1573+x^1574-x^1576+x^1577-x^1579+x^1580-x^1582+x^1583-x^1585+x^1586-x^1588+x^\n" // + "1589-x^1591+x^1592-x^1594+x^1595-x^1597+x^1598-x^1600+x^1601-x^1603+x^1604-x^\n" // + "1606+x^1607-x^1609+x^1610-x^1612+x^1613-x^1615+x^1616-x^1618+x^1619-x^1621+x^\n" // + "1622-x^1624+x^1625-x^1627+x^1628-x^1630+x^1631-x^1633+x^1634-x^1636+x^1637-x^\n" // + "1639+x^1640-x^1642+x^1643-x^1645+x^1646-x^1648+x^1649-x^1651+x^1652-x^1654+x^\n" // + "1655-x^1657+x^1658-x^1660+x^1661-x^1663+x^1664-x^1666+x^1667-x^1669+x^1670-x^\n" // + "1672+x^1673-x^1675+x^1676-x^1678+x^1679-x^1681+x^1682-x^1684+x^1685-x^1687+x^\n" // + "1688-x^1690+x^1691-x^1693+x^1694-x^1696+x^1697-x^1699+x^1700-x^1702+x^1703-x^\n" // + "1705+x^1706-x^1708+x^1709-x^1711+x^1712-x^1714+x^1715-x^1717+x^1718-x^1720+x^\n" // + "1721-x^1723+x^1724-x^1726+x^1727-x^1729+x^1730-x^1732+x^1733-x^1735+x^1736-x^\n" // + "1738+x^1739-x^1741+x^1742-x^1744+x^1745-x^1747+x^1748-x^1750+x^1751-x^1753+x^\n" // + "1754-x^1756+x^1757-x^1759+x^1760-x^1762+x^1763-x^1765+x^1766-x^1768+x^1769-x^\n" // + "1771+x^1772-x^1774+x^1775-x^1777+x^1778-x^1780+x^1781-x^1783+x^1784-x^1786+x^\n" // + "1787-x^1789+x^1790-x^1792+x^1793-x^1795+x^1796-x^1798+x^1799-x^1801+x^1802-x^\n" // + "1804+x^1805-x^1807+x^1808-x^1810+x^1811-x^1813+x^1814-x^1816+x^1817-x^1819+x^\n" // + "1820-x^1822+x^1823-x^1825+x^1826-x^1828+x^1829-x^1831+x^1832-x^1834+x^1835-x^\n" // + "1837+x^1838-x^1840+x^1841-x^1843+x^1844-x^1846+x^1847-x^1849+x^1850-x^1852+x^\n" // + "1853-x^1855+x^1856-x^1858+x^1859-x^1861+x^1862-x^1864+x^1865-x^1867+x^1868-x^\n" // + "1870+x^1871-x^1873+x^1874-x^1876+x^1877-x^1879+x^1880-x^1882+x^1883-x^1885+x^\n" // + "1886-x^1888+x^1889-x^1891+x^1892-x^1894+x^1895-x^1897+x^1898-x^1900+x^1901-x^\n" // + "1903+x^1904-x^1906+x^1907-x^1909+x^1910-x^1912+x^1913-x^1915+x^1916-x^1918+x^\n" // + "1919-x^1921+x^1922-x^1924+x^1925-x^1927+x^1928-x^1930+x^1931-x^1933+x^1934-x^\n" // + "1936+x^1937-x^1939+x^1940-x^1942+x^1943-x^1945+x^1946-x^1948+x^1949-x^1951+x^\n" // + "1952-x^1954+x^1955-x^1957+x^1958-x^1960+x^1961-x^1963+x^1964-x^1966+x^1967-x^\n" // + "1969+x^1970-x^1972+x^1973-x^1975+x^1976-x^1978+x^1979-x^1981+x^1982-x^1984+x^\n" // + "1985-x^1987+x^1988-x^1990+x^1991-x^1993+x^1994-x^1996+x^1997-x^1999+x^2000-x^\n" // + "2002+x^2003-x^2005+x^2006-x^2008+x^2009-x^2011+x^2012-x^2014+x^2015-x^2017+x^\n" // + "2018-x^2020+x^2021-x^2023+x^2024-x^2026+x^2027-x^2029+x^2030-x^2032+x^2033-x^\n" // + "2035+x^2036-x^2038+x^2039-x^2041+x^2042-x^2044+x^2045-x^2047+x^2048-x^2050+x^\n" // + "2051-x^2053+x^2054-x^2056+x^2057-x^2059+x^2060-x^2062+x^2063-x^2065+x^2066-x^\n" // + "2068+x^2069-x^2071+x^2072-x^2074+x^2075-x^2077+x^2078-x^2080+x^2081-x^2083+x^\n" // + "2084-x^2086+x^2087-x^2089+x^2090-x^2092+x^2093-x^2095+x^2096-x^2098+x^2099-x^\n" // + "2101+x^2102-x^2104+x^2105-x^2107+x^2108-x^2110+x^2111-x^2113+x^2114-x^2116+x^\n" // + "2117-x^2119+x^2120-x^2122+x^2123-x^2125+x^2126-x^2128+x^2129-x^2131+x^2132-x^\n" // + "2134+x^2135-x^2137+x^2138-x^2140+x^2141-x^2143+x^2144-x^2146+x^2147-x^2149+x^\n" // + "2150-x^2152+x^2153-x^2155+x^2156-x^2158+x^2159-x^2161+x^2162-x^2164+x^2165-x^\n" // + "2167+x^2168-x^2170+x^2171-x^2173+x^2174-x^2176+x^2177-x^2179+x^2180-x^2182+x^\n" // + "2183-x^2185+x^2186-x^2188+x^2189-x^2191+x^2192-x^2194+x^2195-x^2197+x^2198-x^\n" // + "2200+x^2201-x^2203+x^2204-x^2206+x^2207-x^2209+x^2210-x^2212+x^2213-x^2215+x^\n" // + "2216-x^2218+x^2219-x^2221+x^2222-x^2224+x^2225-x^2227+x^2228-x^2230+x^2231-x^\n" // + "2233+x^2234-x^2236+x^2237-x^2239+x^2240-x^2242+x^2243-x^2245+x^2246-x^2248+x^\n" // + "2249-x^2251+x^2252-x^2254+x^2255-x^2257+x^2258-x^2260+x^2261-x^2263+x^2264-x^\n" // + "2266+x^2267-x^2269+x^2270-x^2272+x^2273-x^2275+x^2276-x^2278+x^2279-x^2281+x^\n" // + "2282-x^2284+x^2285-x^2287+x^2288-x^2290+x^2291-x^2293+x^2294-x^2296+x^2297-x^\n" // + "2299+x^2300-x^2302+x^2303-x^2305+x^2306-x^2308+x^2309-x^2311+x^2312-x^2314+x^\n" // + "2315-x^2317+x^2318-x^2320+x^2321-x^2323+x^2324-x^2326+x^2327-x^2329+x^2330-x^\n" // + "2332+x^2333-x^2335+x^2336-x^2338+x^2339-x^2341+x^2342-x^2344+x^2345-x^2347+x^\n" // + "2348-x^2350+x^2351-x^2353+x^2354-x^2356+x^2357-x^2359+x^2360-x^2362+x^2363-x^\n" // + "2365+x^2366-x^2368+x^2369-x^2371+x^2372-x^2374+x^2375-x^2377+x^2378-x^2380+x^\n" // + "2381-x^2383+x^2384-x^2386+x^2387-x^2389+x^2390-x^2392+x^2393-x^2395+x^2396-x^\n" // + "2398+x^2399-x^2401+x^2402-x^2404+x^2405-x^2407+x^2408-x^2410+x^2411-x^2413+x^\n" // + "2414-x^2416+x^2417-x^2419+x^2420-x^2422+x^2423-x^2425+x^2426-x^2428+x^2429-x^\n" // + "2431+x^2432-x^2434+x^2435-x^2437+x^2438-x^2440+x^2441-x^2443+x^2444-x^2446+x^\n" // + "2447-x^2449+x^2450-x^2452+x^2453-x^2455+x^2456))", // // "1+x^1229+x^2458"); check("Expand((x + 3)^(5/2)+(x + 1)^(3/2))", // "Sqrt(1+x)+x*Sqrt(1+x)+9*Sqrt(3+x)+6*x*Sqrt(3+x)+x^2*Sqrt(3+x)"); check("Expand((x + 1)^(5/2))", // "Sqrt(1+x)+2*x*Sqrt(1+x)+x^2*Sqrt(1+x)"); check("Expand((x + 1)^(-5/2))", // "1/(1+x)^(5/2)"); check("Expand((x + y) ^ 3) ", // "x^3+3*x^2*y+3*x*y^2+y^3"); check("Expand((a + b)*(a + c + d))", // "a^2+a*b+a*c+b*c+a*d+b*d"); check("Expand((a + b)*(a + c + d)*(e + f) + e*a*a)", // "2*a^2*e+a*b*e+a*c*e+b*c*e+a*d*e+b*d*e+a^2*f+a*b*f+a*c*f+b*c*f+a*d*f+b*d*f"); check("Expand((a + b) ^ 2 * (c + d))", // "a^2*c+2*a*b*c+b^2*c+a^2*d+2*a*b*d+b^2*d"); check("Expand((x + y) ^ 2 + x*y)", // "x^2+3*x*y+y^2"); check("Expand(((a + b)*(c + d)) ^ 2 + b (1 + a))", // "a^2*c^2+2*a*b*c^2+b^2*c^2+2*a^2*c*d+4*a*b*c*d+2*b^2*c*d+a^2*d^2+2*a*b*d^2+b^2*d^\n" + "2+b(1+a)"); // TODO return {4 x + 4 y, 2 x + 2 y -> 4 x + 4 y} check("Expand({4*(x + y), 2*(x + y) -> 4*(x + y)})", // "{4*x+4*y,2*(x+y)->4*(x+y)}"); check("Expand(Sin(x*(1 + y)))", // "Sin(x*(1+y))"); check("a*(b*(c+d)+e) // Expand ", // "a*b*c+a*b*d+a*e"); check("(y^2)^(1/2)/(2*x+2*y)//Expand", // "Sqrt(y^2)/(2*x+2*y)"); check("2*(3+2*x)^2/(5+x^2+3*x)^3 // Expand ", // "18/(5+3*x+x^2)^3+(24*x)/(5+3*x+x^2)^3+(8*x^2)/(5+3*x+x^2)^3"); check("Expand({x*(1+x)})", // "{x+x^2}"); check("Expand((-g^2+4*f*h)*h)", // "-g^2*h+4*f*h^2"); check("expand((1 + x)^10)", // "1+10*x+45*x^2+120*x^3+210*x^4+252*x^5+210*x^6+120*x^7+45*x^8+10*x^9+x^10"); check("expand((1 + x + y)*(2 - x)^3)", // "8-4*x-6*x^2+5*x^3-x^4+8*y-12*x*y+6*x^2*y-x^3*y"); check("expand((x + y)/z)", // "x/z+y/z"); check("expand((x^s + y^s)^4)", // "x^(4*s)+4*x^(3*s)*y^s+6*x^(2*s)*y^(2*s)+4*x^s*y^(3*s)+y^(4*s)"); check("Expand((1 + x)*(2 + x)*(3 + x))", // "6+11*x+6*x^2+x^3"); check("Distribute((1 + x)*(2 + x)*(3 + x))", // "6+11*x+6*x^2+x^3"); check("expand(2*(x + y)^2*Sin(x))", // "2*x^2*Sin(x)+4*x*y*Sin(x)+2*y^2*Sin(x)"); check("expand(4*(a+b)*(c+d)*(f+g)^(-2))", // "(4*a*c)/(f+g)^2+(4*b*c)/(f+g)^2+(4*a*d)/(f+g)^2+(4*b*d)/(f+g)^2"); } @Test public void testExpandAll() { // IExpr[] temp= // Apart.getFractionalPartsTimes(F.Times(F.Plus(F.c,F.b),F.Power(F.a,F.CN1),F.b), // true); // issue#122 // check("ExpandAll(( ( ( X3 - X1$c) * ( ( X1 + ( ( X4$c * X3 ) + X5$c)) // + X3$b)) * ( ( X3 - X1 ) + ( X3$c + X5 ))))", // ""); check("ExpandAll(a+f(Log((1+x)^3)))", // "a+f(Log(1+3*x+3*x^2+x^3))"); check("ExpandAll(Sum(9*x,{x,x,2*x}))", // "27/2*x+27/2*x^2"); // github #113 - endless recursion check("ExpandAll(Sum(9*x,{x,x,x}))", // "9*x"); // github #111 - loss of precision if you expand the expression check("t=ExpandAll((Pi*E-9)^13)", // "-2541865828329+3671583974253*E*Pi-2447722649502*E^2*Pi^2+997220338686*E^3*Pi^3-\n" + "277005649635*E^4*Pi^4+55401129927*E^5*Pi^5-8207574804*E^6*Pi^6+911952756*E^7*Pi^\n" + "7-75996063*E^8*Pi^8+4691115*E^9*Pi^9-208494*E^10*Pi^10+6318*E^11*Pi^11-117*E^12*Pi^\n" + "12+E^13*Pi^13"); check("N(t)", // "0.174561"); // shorten the result because of failing bitbucket pipeline check("N(t, 30)", // "-0.0000416<>", 10); check("N((Pi*E-9)^13)", // "-0.0000416019"); check( "ExpandAll(( ( ( X3 - X1_c) * ( ( X1 + ( ( X4_c * X3 ) + X5_c)) + X3_b)) * ( ( X3 - X1 ) + ( X3_c + X5 ))))", // "-x1^2*x3+x1*x3^2+x1*x3*x5+x1^2*x1_c-x1*x3*x1_c-x1*x5*x1_c-x1*x3*x3_b+x3^2*x3_b+x3*x5*x3_b+x1*x1_c*x3_b-x3*x1_c*x3_b-x5*x1_c*x3_b+x1*x3*x3_c-x1*x1_c*x3_c+x3*x3_b*x3_c-x1_c*x3_b*x3_c-x1*x3^\n" + "2*x4_c+x3^3*x4_c+x3^2*x5*x4_c+x1*x3*x1_c*x4_c-x3^2*x1_c*x4_c-x3*x5*x1_c*x4_c+x3^\n" + "2*x3_c*x4_c-x3*x1_c*x3_c*x4_c-x1*x3*x5_c+x3^2*x5_c+x3*x5*x5_c+x1*x1_c*x5_c-x3*x1_c*x5_c-x5*x1_c*x5_c+x3*x3_c*x5_c-x1_c*x3_c*x5_c"); check("ExpandAll(1/(1 + x)^3 + Sin((1 + x)^3))", // "1/(1+3*x+3*x^2+x^3)+Sin(1+3*x+3*x^2+x^3)"); check("Expand(1/(1 + x)^3 + Sin((1 + x)^3))", // "1/(1+x)^3+Sin((1+x)^3)"); check("ExpandAll(2*x*(x^2-x+1)^(-1))", // "(2*x)/(1-x+x^2)"); check("ExpandAll((2+x)*(x^2-x+1)^(-1))", // "2/(1-x+x^2)+x/(1-x+x^2)"); check("ExpandAll(2*(2*x^3-4*x+5)*x^3*(3*x^2+2)^(-1))", // "(10*x^3)/(2+3*x^2)+(-8*x^4)/(2+3*x^2)+(4*x^6)/(2+3*x^2)"); check("ExpandAll((b+c)*((b+c)*(a)^(-1)+1))", // "b+b^2/a+c+(2*b*c)/a+c^2/a"); check("ExpandAll((-2*x^3+4*x-5)*((-2*x^3+4*x-5)*(a)^(-1)-2*x))", // "25/a+10*x+(-40*x)/a-8*x^2+(16*x^2)/a+(20*x^3)/a+4*x^4+(-16*x^4)/a+(4*x^6)/a"); check("ExpandAll((-(-2*x^3+4*x-5)*(-(-2*x^3+4*x-5)*(3*x^2+2)^(-1)-2*x)*(3*x^2+2)^(-1)+x^2-2))", // "-2+x^2+(-10*x)/(2+3*x^2)+(8*x^2)/(2+3*x^2)+(-4*x^4)/(2+3*x^2)+25/(4+12*x^2+9*x^4)+(-\n" + "40*x)/(4+12*x^2+9*x^4)+(16*x^2)/(4+12*x^2+9*x^4)+(20*x^3)/(4+12*x^2+9*x^4)+(-16*x^\n" + "4)/(4+12*x^2+9*x^4)+(4*x^6)/(4+12*x^2+9*x^4)"); check("ExpandAll(Sqrt((1 + x)^2))", // "Sqrt(1+2*x+x^2)"); // TODO return a ^ 2 / (c ^ 2 + 2 c d + d ^ 2) + 2 a b / (c ^ 2 + 2 c d // + d ^ 2) + b ^ 2 / (c ^ 2 + 2 c d + d ^ 2) check("ExpandAll((a + b) ^ 2 / (c + d)^2)", // "a^2/(c^2+2*c*d+d^2)+(2*a*b)/(c^2+2*c*d+d^2)+b^2/(c^2+2*c*d+d^2)"); check("ExpandAll((a + Sin(x*(1 + y)))^2)", // "a^2+2*a*Sin(x+x*y)+Sin(x+x*y)^2"); check("ExpandAll(((1 + x)*(1 + y))[x])", // "(1+x+y+x*y)[x]"); } @Test public void testExponent() { check("Exponent(1 + x^(-2) + a*x^(-42), x, List)", // "{-42,-2,0}"); check("Exponent(c*x^(-2)+a+b*x,x,-2)", // "-2[-2,0,1]"); check("Exponent(7*y^w, y, List)", // "{w}"); check("Exponent((2*x )^7*y+5*x^3,x^3)", // "7/3"); check("Exponent(2*x *y+5*x^3,x^3)", // "1"); check("Exponent(2*x*y+5*x^3,2*x)", // "1"); check("Exponent(Cos(x*y), Cos(x*y))", // "1"); check("Exponent(x^3,x^2)", // "3/2"); check("Exponent(x^a,x^2)", // "a/2"); check("Exponent(x^a,x^(2/3))", // "3/2*a"); check("Exponent(2*x^a,x^(2/3))", // "3/2*a"); check("Exponent(2*x^a,f(x))", // "0"); check("Exponent((1+2*x)/Sqrt(3),x,List)", // "{0,1}"); check("Exponent(Together((1+2*x)/Sqrt(3)),x,List)", // "{0,1}"); check("Exponent((1+2*x)/Sqrt(3),x,List)", // "{0,1}"); check("Exponent(a+b*x,x,List)", // "{0,1}"); check("Exponent(SeriesData(x, 0, {1, 1, 0, 1, 1, 0, 1, 1}, 0, 9, 1), x)", // "7"); check("Exponent(x*y,y,List)", // "{1}"); check("Exponent(Sin(x*y),y)", // "0"); check("Exponent(f(x^2),x)", // "0"); check("Exponent(f(x^2),x,List)", // "{0}"); check("Exponent(x*(b+a),x)", // "1"); check("Exponent(x*(b+a),{a,b,x})", // "{1,1,1}"); check("Exponent(x*(b+a),x,List)", // "{1}"); check("Exponent(0, x)", // "-Infinity"); check("Exponent(2, x)", // "0"); check("Exponent(2*x, x)", // "1"); check("Exponent(x, x)", // "1"); check("Exponent(x^3, x)", // "3"); check("Exponent(a*x^(-1), x)", // "-1"); check("Exponent(x^(-3), x)", // "-3"); check("Exponent(x^(-3)+x^(-2), x)", // "-2"); check("Exponent(x+42, x)", // "1"); check("Exponent(1 + x^2 + a*x^3, x)", // "3"); check("Exponent((x^2 + 1)^3 + 1, x)", // "6"); check("Exponent(x^(n0 + 1) + 2*Sqrt(x) + 1, x)", // "Max(1/2,1+n0)"); check("Exponent((x^2 + 1)^3 - 1, x, Min)", // "2"); check("Exponent((x^2 + 1)^3 + 1, x)", // "6"); check("Exponent(1 + x^2 + a*x^3, x, List)", // "{0,2,3}"); check("Exponent((a+b)/c, c)", // "-1"); check("Exponent(a/c+b/c, c)", // "-1"); } @Test public void testExpToTrig() { check("TrigToExp(Sin(x))", // "(I*1/2)/E^(I*x)-I*1/2*E^(I*x)"); check("ExpToTrig((I*1/2)/E^(I*x))", // "I*1/2*Cos(x)+Sin(x)/2"); check("ExpToTrig(TrigToExp(Sin(x)))", // "Sin(x)"); check("ExpToTrig((-1)^(1/3))", // "1/2+I*1/2*Sqrt(3)"); check("ExpToTrig(Sqrt(I))", // "(1+I)/Sqrt(2)"); check("Log(-17)", // "I*Pi+Log(17)"); check("Cosh(a+b) // TrigExpand", // "Cosh(a)*Cosh(b)+Sinh(a)*Sinh(b)"); check("ExpToTrig((-17)^a)", // "(Cos(a*Pi)+I*Sin(a*Pi))*(Cosh(a*Log(17))+Sinh(a*Log(17)))"); check("ExpToTrig((-17/19)^a)", // "(Cos(a*Pi)+I*Sin(a*Pi))*(Cosh(a*Log(19/17))-Sinh(a*Log(19/17)))"); check("ExpToTrig(I^a)", // "Cos(1/2*a*Pi)+I*Sin(1/2*a*Pi)"); check("ExpToTrig(Exp(x) - Exp(-x))", // "2*Sinh(x)"); check("ExpToTrig(Exp(x) - Exp(-x))", // "2*Sinh(x)"); check("ExpToTrig(Exp(I*x) == -1)", // "Cos(x)+I*Sin(x)==-1"); check("ExpToTrig(Exp(x)-Exp(-x))", // "2*Sinh(x)"); check("ExpToTrig(E^(I*x))", // "Cos(x)+I*Sin(x)"); check("ExpToTrig(E^(c*x))", // "Cosh(c*x)+Sinh(c*x)"); } @Test public void testExtendedGCD() { check("ExtendedGCD(2,3)", // "{1,{-1,1}}"); check("ExtendedGCD(550,420,3515)", // "{5,{-4563,5967,1}}"); check("ExtendedGCD(6,15,30)", // "{3,{-2,1,0}}"); check("ExtendedGCD(3,{5,15})", // "{{1,{2,-1}},{3,{1,0}}}"); check("ExtendedGCD(6,21)", // "{3,{-3,1}}"); check("GCD(6,21)", // "3"); check("ExtendedGCD(10, 15)", // "{5,{-1,1}}"); check("ExtendedGCD(10, 15, 7)", // "{1,{-3,3,-2}}"); check("$numbers = {10, 20, 14};", // ""); check("{$gcd, $factors} = ExtendedGCD(Sequence @@ $numbers)", // "{2,{3,0,-2}}"); check("Plus @@ ($numbers * $factors)", // "2"); } @Test public void testExpIntegralE() { check("ExpIntegralE(0,z)", // "1/(E^z*z)"); check("ExpIntegralE(n,0)", // "ExpIntegralE(n,0)"); check("ExpIntegralE(17,0)", // "1/16"); check("ExpIntegralE(-17,0)", // "ComplexInfinity"); // https://github.com/paulmasson/math/issues/14 check("Table(ExpIntegralE(x, 2/3), {x,-4.0, 4.0, 1/4})", // "{182.1347,113.6881,71.99039,46.27989,30.22743,20.0743,13.56576,9.33534,6.54607,4.6798,3.41217," // + "2.53784,1.92531,1.4894,1.17424,0.942781,0.770126,0.639355,0.538822,0.460414,0.398409,0.348723," // + "0.308405,0.275299,0.247811,0.224748,0.205209,0.188505,0.174105,0.161593,0.150644,0.140999,0.132449}"); } @Test public void testExpIntegralEi() { checkNumeric("ExpIntegralEi(I*1.0)", // "0.3374039229009681+I*2.5168793971620795"); checkNumeric("ExpIntegralEi(-I*1.0)", // "0.3374039229009681+I*(-2.5168793971620795)"); checkNumeric("ExpIntegralEi(-1.0)", // "-0.21938393439552029"); checkNumeric("ExpIntegralEi(1.0)", // "1.895117816355937"); check("ExpIntegralEi(I*Infinity)", // "I*Pi"); check("ExpIntegralEi(-I*Infinity)", // "-I*Pi"); check("Table(ExpIntegralEi(x), {x,-4.0, 4.0, 1/4})", // "{-0.00377935,-0.0051241,-0.00697014,-0.00951651,-0.0130484,-0.0179789,-0.0249149,-0.0347621," // + "-0.0489005,-0.0694887,-0.10002,-0.146413,-0.219384,-0.340341,-0.559774,-1.04428,-Infinity," // + "-0.542543,0.45422,1.20733,1.89512,2.58105,3.30129,4.08365,4.95423,5.94057,7.07377,8.3903," // + "9.93383,11.7573,13.92535,16.51732,19.63087}"); check("Table(ExpIntegralEi(x), {x, -3.0, 3.0, 0.25})", // "{-0.0130484,-0.0179789,-0.0249149,-0.0347621,-0.0489005,-0.0694887,-0.10002,-0.146413,-0.219384,-0.340341," // + "-0.559774,-1.04428,-Infinity,-0.542543,0.45422,1.20733,1.89512,2.58105,3.30129,4.08365,4.95423,5.94057," // + "7.07377,8.3903,9.93383}"); check("ExpIntegralEi(1.8)", // "4.24987"); } @Test public void testExtract() { // Extract: Position specification {{rr},{3}} in Extract(a+b+c,{{rr},{3}}) is not applicable. check("Extract(a+b+c,{{rr},{3}})", // "Extract(a+b+c,{{rr},{3}})"); check("Extract(a+b+c,{{2},{3}},Hold)", // "{Hold(b),Hold(c)}"); check("Extract(<|test->f(a,b,c)|>,{Key(test),2})", // "b"); check("Extract(a+b+c,{})", // "{}"); check("Extract(a+b+c,{{}})", // "{a+b+c}"); check("Extract(2)[Infinity]", // "Extract(2)[Infinity]"); check("Extract(2)[{a, b, c, d}]", // "b"); check("Extract(a+b+c,2)", // "b"); check("Extract(a+b+c,0)", // "Plus"); check("Extract(a+b+c,-4)", // "Extract(a+b+c,-4)"); check("Extract(a+b+c, {2})", // "b"); check("Extract(a+b+c,{{2},{3}})", // "{b,c}"); check("Extract({{a, b}, {c, d}}, {{1}, {2, 2}})", // "{{a,b},d}"); } @Test public void testFactor() { // TODO message is printed to many times // print message "rvalue" Increment: y is not a variable with a value, so its value cannot be // changed. check("Factor(a*x+b*x+a*y++b*y)", // "a*x+b*x+a*b*y*y++"); // for (int i = 0; i < 2_000_000; i++) { // check( // "Factor(a*Cosh(x) + I*b*Cosh(x) - I*a*Sinh(x) + b*Sinh(x))", // // " (-I*a+b)*(I*Cosh(x)+Sinh(x))"); // } // flaky test - depends on random generator: // check("Factor(2*y^6 - x*y^3 - 3*x^2)", // // "(x+y^3)*(-3*x+2*y^3)"); // doc examples check("Factor({x + x^2, 2*x + 2*y + 2})", // "{x*(1+x),2*(1+x+y)}"); check("Factor(x*a == x*b+x*c)", // "a*x==(b+c)*x"); check("Factor(x^3 + 3*x^2*y + 3*x*y^2 + y^3) ", // "(x+y)^3"); check("a == d*b + d*c // Factor", // "a==(b+c)*d"); // Use heuristic? check("Factor(x^34 + x^17 + 1)", // "(1+x+x^2)*(1-x+x^3-x^4+x^6-x^7+x^9-x^10+x^12-x^13+x^15-x^16+x^17-x^19+x^20-x^22+x^\n" + "23-x^25+x^26-x^28+x^29-x^31+x^32)"); System.out.println(); if (Config.EXPENSIVE_JUNIT_TESTS) { // "Computer Algebra - Concepts and Techniques" p.200 E.Lamagna check("Factor(x^2458 + x^1229 + 1)", // "(1+x+x^2)*(1-x+x^3-x^4+x^6-x^7+x^9-x^10+x^12-x^13+x^15-x^16+x^18-x^19+x^21-x^22+x^\n" + "24-x^25+x^27-x^28+x^30-x^31+x^33-x^34+x^36-x^37+x^39-x^40+x^42-x^43+x^45-x^46+x^\n" + "48-x^49+x^51-x^52+x^54-x^55+x^57-x^58+x^60-x^61+x^63-x^64+x^66-x^67+x^69-x^70+x^\n" + "72-x^73+x^75-x^76+x^78-x^79+x^81-x^82+x^84-x^85+x^87-x^88+x^90-x^91+x^93-x^94+x^\n" + "96-x^97+x^99-x^100+x^102-x^103+x^105-x^106+x^108-x^109+x^111-x^112+x^114-x^115+x^\n" + "117-x^118+x^120-x^121+x^123-x^124+x^126-x^127+x^129-x^130+x^132-x^133+x^135-x^\n" + "136+x^138-x^139+x^141-x^142+x^144-x^145+x^147-x^148+x^150-x^151+x^153-x^154+x^\n" + "156-x^157+x^159-x^160+x^162-x^163+x^165-x^166+x^168-x^169+x^171-x^172+x^174-x^\n" + "175+x^177-x^178+x^180-x^181+x^183-x^184+x^186-x^187+x^189-x^190+x^192-x^193+x^\n" + "195-x^196+x^198-x^199+x^201-x^202+x^204-x^205+x^207-x^208+x^210-x^211+x^213-x^\n" + "214+x^216-x^217+x^219-x^220+x^222-x^223+x^225-x^226+x^228-x^229+x^231-x^232+x^\n" + "234-x^235+x^237-x^238+x^240-x^241+x^243-x^244+x^246-x^247+x^249-x^250+x^252-x^\n" + "253+x^255-x^256+x^258-x^259+x^261-x^262+x^264-x^265+x^267-x^268+x^270-x^271+x^\n" + "273-x^274+x^276-x^277+x^279-x^280+x^282-x^283+x^285-x^286+x^288-x^289+x^291-x^\n" + "292+x^294-x^295+x^297-x^298+x^300-x^301+x^303-x^304+x^306-x^307+x^309-x^310+x^\n" + "312-x^313+x^315-x^316+x^318-x^319+x^321-x^322+x^324-x^325+x^327-x^328+x^330-x^\n" + "331+x^333-x^334+x^336-x^337+x^339-x^340+x^342-x^343+x^345-x^346+x^348-x^349+x^\n" + "351-x^352+x^354-x^355+x^357-x^358+x^360-x^361+x^363-x^364+x^366-x^367+x^369-x^\n" + "370+x^372-x^373+x^375-x^376+x^378-x^379+x^381-x^382+x^384-x^385+x^387-x^388+x^\n" + "390-x^391+x^393-x^394+x^396-x^397+x^399-x^400+x^402-x^403+x^405-x^406+x^408-x^\n" + "409+x^411-x^412+x^414-x^415+x^417-x^418+x^420-x^421+x^423-x^424+x^426-x^427+x^\n" + "429-x^430+x^432-x^433+x^435-x^436+x^438-x^439+x^441-x^442+x^444-x^445+x^447-x^\n" + "448+x^450-x^451+x^453-x^454+x^456-x^457+x^459-x^460+x^462-x^463+x^465-x^466+x^\n" + "468-x^469+x^471-x^472+x^474-x^475+x^477-x^478+x^480-x^481+x^483-x^484+x^486-x^\n" + "487+x^489-x^490+x^492-x^493+x^495-x^496+x^498-x^499+x^501-x^502+x^504-x^505+x^\n" + "507-x^508+x^510-x^511+x^513-x^514+x^516-x^517+x^519-x^520+x^522-x^523+x^525-x^\n" + "526+x^528-x^529+x^531-x^532+x^534-x^535+x^537-x^538+x^540-x^541+x^543-x^544+x^\n" + "546-x^547+x^549-x^550+x^552-x^553+x^555-x^556+x^558-x^559+x^561-x^562+x^564-x^\n" + "565+x^567-x^568+x^570-x^571+x^573-x^574+x^576-x^577+x^579-x^580+x^582-x^583+x^\n" + "585-x^586+x^588-x^589+x^591-x^592+x^594-x^595+x^597-x^598+x^600-x^601+x^603-x^\n" + "604+x^606-x^607+x^609-x^610+x^612-x^613+x^615-x^616+x^618-x^619+x^621-x^622+x^\n" + "624-x^625+x^627-x^628+x^630-x^631+x^633-x^634+x^636-x^637+x^639-x^640+x^642-x^\n" + "643+x^645-x^646+x^648-x^649+x^651-x^652+x^654-x^655+x^657-x^658+x^660-x^661+x^\n" + "663-x^664+x^666-x^667+x^669-x^670+x^672-x^673+x^675-x^676+x^678-x^679+x^681-x^\n" + "682+x^684-x^685+x^687-x^688+x^690-x^691+x^693-x^694+x^696-x^697+x^699-x^700+x^\n" + "702-x^703+x^705-x^706+x^708-x^709+x^711-x^712+x^714-x^715+x^717-x^718+x^720-x^\n" + "721+x^723-x^724+x^726-x^727+x^729-x^730+x^732-x^733+x^735-x^736+x^738-x^739+x^\n" + "741-x^742+x^744-x^745+x^747-x^748+x^750-x^751+x^753-x^754+x^756-x^757+x^759-x^\n" + "760+x^762-x^763+x^765-x^766+x^768-x^769+x^771-x^772+x^774-x^775+x^777-x^778+x^\n" + "780-x^781+x^783-x^784+x^786-x^787+x^789-x^790+x^792-x^793+x^795-x^796+x^798-x^\n" + "799+x^801-x^802+x^804-x^805+x^807-x^808+x^810-x^811+x^813-x^814+x^816-x^817+x^\n" + "819-x^820+x^822-x^823+x^825-x^826+x^828-x^829+x^831-x^832+x^834-x^835+x^837-x^\n" + "838+x^840-x^841+x^843-x^844+x^846-x^847+x^849-x^850+x^852-x^853+x^855-x^856+x^\n" + "858-x^859+x^861-x^862+x^864-x^865+x^867-x^868+x^870-x^871+x^873-x^874+x^876-x^\n" + "877+x^879-x^880+x^882-x^883+x^885-x^886+x^888-x^889+x^891-x^892+x^894-x^895+x^\n" + "897-x^898+x^900-x^901+x^903-x^904+x^906-x^907+x^909-x^910+x^912-x^913+x^915-x^\n" + "916+x^918-x^919+x^921-x^922+x^924-x^925+x^927-x^928+x^930-x^931+x^933-x^934+x^\n" + "936-x^937+x^939-x^940+x^942-x^943+x^945-x^946+x^948-x^949+x^951-x^952+x^954-x^\n" + "955+x^957-x^958+x^960-x^961+x^963-x^964+x^966-x^967+x^969-x^970+x^972-x^973+x^\n" + "975-x^976+x^978-x^979+x^981-x^982+x^984-x^985+x^987-x^988+x^990-x^991+x^993-x^\n" + "994+x^996-x^997+x^999-x^1000+x^1002-x^1003+x^1005-x^1006+x^1008-x^1009+x^1011-x^\n" + "1012+x^1014-x^1015+x^1017-x^1018+x^1020-x^1021+x^1023-x^1024+x^1026-x^1027+x^\n" + "1029-x^1030+x^1032-x^1033+x^1035-x^1036+x^1038-x^1039+x^1041-x^1042+x^1044-x^\n" + "1045+x^1047-x^1048+x^1050-x^1051+x^1053-x^1054+x^1056-x^1057+x^1059-x^1060+x^\n" + "1062-x^1063+x^1065-x^1066+x^1068-x^1069+x^1071-x^1072+x^1074-x^1075+x^1077-x^\n" + "1078+x^1080-x^1081+x^1083-x^1084+x^1086-x^1087+x^1089-x^1090+x^1092-x^1093+x^\n" + "1095-x^1096+x^1098-x^1099+x^1101-x^1102+x^1104-x^1105+x^1107-x^1108+x^1110-x^\n" + "1111+x^1113-x^1114+x^1116-x^1117+x^1119-x^1120+x^1122-x^1123+x^1125-x^1126+x^\n" + "1128-x^1129+x^1131-x^1132+x^1134-x^1135+x^1137-x^1138+x^1140-x^1141+x^1143-x^\n" + "1144+x^1146-x^1147+x^1149-x^1150+x^1152-x^1153+x^1155-x^1156+x^1158-x^1159+x^\n" + "1161-x^1162+x^1164-x^1165+x^1167-x^1168+x^1170-x^1171+x^1173-x^1174+x^1176-x^\n" + "1177+x^1179-x^1180+x^1182-x^1183+x^1185-x^1186+x^1188-x^1189+x^1191-x^1192+x^\n" + "1194-x^1195+x^1197-x^1198+x^1200-x^1201+x^1203-x^1204+x^1206-x^1207+x^1209-x^\n" + "1210+x^1212-x^1213+x^1215-x^1216+x^1218-x^1219+x^1221-x^1222+x^1224-x^1225+x^\n" + "1227-x^1228+x^1229-x^1231+x^1232-x^1234+x^1235-x^1237+x^1238-x^1240+x^1241-x^\n" + "1243+x^1244-x^1246+x^1247-x^1249+x^1250-x^1252+x^1253-x^1255+x^1256-x^1258+x^\n" + "1259-x^1261+x^1262-x^1264+x^1265-x^1267+x^1268-x^1270+x^1271-x^1273+x^1274-x^\n" + "1276+x^1277-x^1279+x^1280-x^1282+x^1283-x^1285+x^1286-x^1288+x^1289-x^1291+x^\n" + "1292-x^1294+x^1295-x^1297+x^1298-x^1300+x^1301-x^1303+x^1304-x^1306+x^1307-x^\n" + "1309+x^1310-x^1312+x^1313-x^1315+x^1316-x^1318+x^1319-x^1321+x^1322-x^1324+x^\n" + "1325-x^1327+x^1328-x^1330+x^1331-x^1333+x^1334-x^1336+x^1337-x^1339+x^1340-x^\n" + "1342+x^1343-x^1345+x^1346-x^1348+x^1349-x^1351+x^1352-x^1354+x^1355-x^1357+x^\n" + "1358-x^1360+x^1361-x^1363+x^1364-x^1366+x^1367-x^1369+x^1370-x^1372+x^1373-x^\n" + "1375+x^1376-x^1378+x^1379-x^1381+x^1382-x^1384+x^1385-x^1387+x^1388-x^1390+x^\n" + "1391-x^1393+x^1394-x^1396+x^1397-x^1399+x^1400-x^1402+x^1403-x^1405+x^1406-x^\n" + "1408+x^1409-x^1411+x^1412-x^1414+x^1415-x^1417+x^1418-x^1420+x^1421-x^1423+x^\n" + "1424-x^1426+x^1427-x^1429+x^1430-x^1432+x^1433-x^1435+x^1436-x^1438+x^1439-x^\n" + "1441+x^1442-x^1444+x^1445-x^1447+x^1448-x^1450+x^1451-x^1453+x^1454-x^1456+x^\n" + "1457-x^1459+x^1460-x^1462+x^1463-x^1465+x^1466-x^1468+x^1469-x^1471+x^1472-x^\n" + "1474+x^1475-x^1477+x^1478-x^1480+x^1481-x^1483+x^1484-x^1486+x^1487-x^1489+x^\n" + "1490-x^1492+x^1493-x^1495+x^1496-x^1498+x^1499-x^1501+x^1502-x^1504+x^1505-x^\n" + "1507+x^1508-x^1510+x^1511-x^1513+x^1514-x^1516+x^1517-x^1519+x^1520-x^1522+x^\n" + "1523-x^1525+x^1526-x^1528+x^1529-x^1531+x^1532-x^1534+x^1535-x^1537+x^1538-x^\n" + "1540+x^1541-x^1543+x^1544-x^1546+x^1547-x^1549+x^1550-x^1552+x^1553-x^1555+x^\n" + "1556-x^1558+x^1559-x^1561+x^1562-x^1564+x^1565-x^1567+x^1568-x^1570+x^1571-x^\n" + "1573+x^1574-x^1576+x^1577-x^1579+x^1580-x^1582+x^1583-x^1585+x^1586-x^1588+x^\n" + "1589-x^1591+x^1592-x^1594+x^1595-x^1597+x^1598-x^1600+x^1601-x^1603+x^1604-x^\n" + "1606+x^1607-x^1609+x^1610-x^1612+x^1613-x^1615+x^1616-x^1618+x^1619-x^1621+x^\n" + "1622-x^1624+x^1625-x^1627+x^1628-x^1630+x^1631-x^1633+x^1634-x^1636+x^1637-x^\n" + "1639+x^1640-x^1642+x^1643-x^1645+x^1646-x^1648+x^1649-x^1651+x^1652-x^1654+x^\n" + "1655-x^1657+x^1658-x^1660+x^1661-x^1663+x^1664-x^1666+x^1667-x^1669+x^1670-x^\n" + "1672+x^1673-x^1675+x^1676-x^1678+x^1679-x^1681+x^1682-x^1684+x^1685-x^1687+x^\n" + "1688-x^1690+x^1691-x^1693+x^1694-x^1696+x^1697-x^1699+x^1700-x^1702+x^1703-x^\n" + "1705+x^1706-x^1708+x^1709-x^1711+x^1712-x^1714+x^1715-x^1717+x^1718-x^1720+x^\n" + "1721-x^1723+x^1724-x^1726+x^1727-x^1729+x^1730-x^1732+x^1733-x^1735+x^1736-x^\n" + "1738+x^1739-x^1741+x^1742-x^1744+x^1745-x^1747+x^1748-x^1750+x^1751-x^1753+x^\n" + "1754-x^1756+x^1757-x^1759+x^1760-x^1762+x^1763-x^1765+x^1766-x^1768+x^1769-x^\n" + "1771+x^1772-x^1774+x^1775-x^1777+x^1778-x^1780+x^1781-x^1783+x^1784-x^1786+x^\n" + "1787-x^1789+x^1790-x^1792+x^1793-x^1795+x^1796-x^1798+x^1799-x^1801+x^1802-x^\n" + "1804+x^1805-x^1807+x^1808-x^1810+x^1811-x^1813+x^1814-x^1816+x^1817-x^1819+x^\n" + "1820-x^1822+x^1823-x^1825+x^1826-x^1828+x^1829-x^1831+x^1832-x^1834+x^1835-x^\n" + "1837+x^1838-x^1840+x^1841-x^1843+x^1844-x^1846+x^1847-x^1849+x^1850-x^1852+x^\n" + "1853-x^1855+x^1856-x^1858+x^1859-x^1861+x^1862-x^1864+x^1865-x^1867+x^1868-x^\n" + "1870+x^1871-x^1873+x^1874-x^1876+x^1877-x^1879+x^1880-x^1882+x^1883-x^1885+x^\n" + "1886-x^1888+x^1889-x^1891+x^1892-x^1894+x^1895-x^1897+x^1898-x^1900+x^1901-x^\n" + "1903+x^1904-x^1906+x^1907-x^1909+x^1910-x^1912+x^1913-x^1915+x^1916-x^1918+x^\n" + "1919-x^1921+x^1922-x^1924+x^1925-x^1927+x^1928-x^1930+x^1931-x^1933+x^1934-x^\n" + "1936+x^1937-x^1939+x^1940-x^1942+x^1943-x^1945+x^1946-x^1948+x^1949-x^1951+x^\n" + "1952-x^1954+x^1955-x^1957+x^1958-x^1960+x^1961-x^1963+x^1964-x^1966+x^1967-x^\n" + "1969+x^1970-x^1972+x^1973-x^1975+x^1976-x^1978+x^1979-x^1981+x^1982-x^1984+x^\n" + "1985-x^1987+x^1988-x^1990+x^1991-x^1993+x^1994-x^1996+x^1997-x^1999+x^2000-x^\n" + "2002+x^2003-x^2005+x^2006-x^2008+x^2009-x^2011+x^2012-x^2014+x^2015-x^2017+x^\n" + "2018-x^2020+x^2021-x^2023+x^2024-x^2026+x^2027-x^2029+x^2030-x^2032+x^2033-x^\n" + "2035+x^2036-x^2038+x^2039-x^2041+x^2042-x^2044+x^2045-x^2047+x^2048-x^2050+x^\n" + "2051-x^2053+x^2054-x^2056+x^2057-x^2059+x^2060-x^2062+x^2063-x^2065+x^2066-x^\n" + "2068+x^2069-x^2071+x^2072-x^2074+x^2075-x^2077+x^2078-x^2080+x^2081-x^2083+x^\n" + "2084-x^2086+x^2087-x^2089+x^2090-x^2092+x^2093-x^2095+x^2096-x^2098+x^2099-x^\n" + "2101+x^2102-x^2104+x^2105-x^2107+x^2108-x^2110+x^2111-x^2113+x^2114-x^2116+x^\n" + "2117-x^2119+x^2120-x^2122+x^2123-x^2125+x^2126-x^2128+x^2129-x^2131+x^2132-x^\n" + "2134+x^2135-x^2137+x^2138-x^2140+x^2141-x^2143+x^2144-x^2146+x^2147-x^2149+x^\n" + "2150-x^2152+x^2153-x^2155+x^2156-x^2158+x^2159-x^2161+x^2162-x^2164+x^2165-x^\n" + "2167+x^2168-x^2170+x^2171-x^2173+x^2174-x^2176+x^2177-x^2179+x^2180-x^2182+x^\n" + "2183-x^2185+x^2186-x^2188+x^2189-x^2191+x^2192-x^2194+x^2195-x^2197+x^2198-x^\n" + "2200+x^2201-x^2203+x^2204-x^2206+x^2207-x^2209+x^2210-x^2212+x^2213-x^2215+x^\n" + "2216-x^2218+x^2219-x^2221+x^2222-x^2224+x^2225-x^2227+x^2228-x^2230+x^2231-x^\n" + "2233+x^2234-x^2236+x^2237-x^2239+x^2240-x^2242+x^2243-x^2245+x^2246-x^2248+x^\n" + "2249-x^2251+x^2252-x^2254+x^2255-x^2257+x^2258-x^2260+x^2261-x^2263+x^2264-x^\n" + "2266+x^2267-x^2269+x^2270-x^2272+x^2273-x^2275+x^2276-x^2278+x^2279-x^2281+x^\n" + "2282-x^2284+x^2285-x^2287+x^2288-x^2290+x^2291-x^2293+x^2294-x^2296+x^2297-x^\n" + "2299+x^2300-x^2302+x^2303-x^2305+x^2306-x^2308+x^2309-x^2311+x^2312-x^2314+x^\n" + "2315-x^2317+x^2318-x^2320+x^2321-x^2323+x^2324-x^2326+x^2327-x^2329+x^2330-x^\n" + "2332+x^2333-x^2335+x^2336-x^2338+x^2339-x^2341+x^2342-x^2344+x^2345-x^2347+x^\n" + "2348-x^2350+x^2351-x^2353+x^2354-x^2356+x^2357-x^2359+x^2360-x^2362+x^2363-x^\n" + "2365+x^2366-x^2368+x^2369-x^2371+x^2372-x^2374+x^2375-x^2377+x^2378-x^2380+x^\n" + "2381-x^2383+x^2384-x^2386+x^2387-x^2389+x^2390-x^2392+x^2393-x^2395+x^2396-x^\n" + "2398+x^2399-x^2401+x^2402-x^2404+x^2405-x^2407+x^2408-x^2410+x^2411-x^2413+x^\n" + "2414-x^2416+x^2417-x^2419+x^2420-x^2422+x^2423-x^2425+x^2426-x^2428+x^2429-x^\n" + "2431+x^2432-x^2434+x^2435-x^2437+x^2438-x^2440+x^2441-x^2443+x^2444-x^2446+x^\n" + "2447-x^2449+x^2450-x^2452+x^2453-x^2455+x^2456)"); } check("Factor(x^34+x^17+1)", // "(1+x+x^2)*(1-x+x^3-x^4+x^6-x^7+x^9-x^10+x^12-x^13+x^15-x^16+x^17-x^19+x^20-x^22+x^\n" + "23-x^25+x^26-x^28+x^29-x^31+x^32)"); check("Factor(I,GaussianIntegers->True)", // "I"); // https://github.com/kredel/java-algebra-system/issues/12 // for (int i = 0; i < 100000; i++) { // System.out.println(i); // String[] vars = new String[] { "a", "c", "d", "e", "x" }; // GenPolynomialRing fac; // fac = new GenPolynomialRing(edu.jas.arith.BigInteger.ZERO, // vars.length, // new TermOrder(TermOrder.INVLEX), vars); // // GenPolynomial poly = fac.parse("a*d*e + c*d^2*x + a*e^2*x + // c*d*e*x^2"); // System.out.println("A: " + poly.toString()); // FactorAbstract factorAbstract = FactorFactory // .getImplementation(edu.jas.arith.BigInteger.ZERO); // SortedMap, Long> map = factorAbstract.factors(poly); // } // System.out.println(); check("Factor(1+x^2, Extension->I)", // "(-I+x)*(I+x)"); check("Factor(x^(-6)+1)", // "((1+x^2)*(1-x^2+x^4))/x^6"); System.out.println(); System.out.print('.'); check("Factor(x+2*Sqrt(x)+1)", // "(1+Sqrt(x))^2"); // check("Factor(E^x+E^(2*x))", // // "E^x*(1+E^x)"); System.out.print('.'); check("Factor(r^2+k*q*Q*r^4-E*r^6)", // "r^2*(1+k*q*Q*r^2-E*r^4)"); System.out.print('.'); check("Factor(x+2*Sqrt(x)+1)", // "(1+Sqrt(x))^2"); System.out.print('.'); check("Factor((a*d*e+(c*d^2+a*e^2)*x+c*d*e*x^2)^(3/2))", // "((a*e+c*d*x)*(d+e*x))^(3/2)"); System.out.print('.'); check("Factor(Cos(x)-I*Sin(x) )", // "Cos(x)-I*Sin(x)"); System.out.print('.'); check("Factor((Cos(x)-I*Sin(x))/(I*Cos(x)-Sin(x)))", // "(Cos(x)-I*Sin(x))/(I*Cos(x)-Sin(x))"); System.out.print('.'); check("Factor(12 * x^2 -75 * y^2)", // "3*(2*x-5*y)*(2*x+5*y)"); // example from paper // https://www.research.ed.ac.uk/portal/files/413486/Solving_Symbolic_Equations_%20with_PRESS.pdf System.out.print('.'); check("Factor(4^(2*x+1)*5^(x-2)-6^(1-x))", // "(2^(1-x)*(-75+2^(1+5*x)*15^x))/(25*3^x)"); System.out.print('.'); check("Factor(E^x+E^(2*x))", // "E^x*(1+E^x)"); // example from paper // https://www.research.ed.ac.uk/portal/files/413486/Solving_Symbolic_Equations_%20with_PRESS.pdf System.out.print('.'); check("Factor(Log(2,x)+4*Log(x,2)-5)", // "((-4*Log(2)+Log(x))*(-Log(2)+Log(x)))/(Log(2)*Log(x))"); // TODO reduce negative signs // ((Log(2) - Log(x))*(4*Log(2) - Log(x)))/(Log(2)*Log(x)) System.out.print('.'); check("Factor( (4*a^2-5*a*b+b^2)/(a*b) )", // "((-4*a+b)*(-a+b))/(a*b)"); // example from paper System.out.print('.'); check("Factor(3*Tan(3*x)-Tan(x)+2)", // "2-Tan(x)+3*Tan(3*x)"); System.out.print('.'); check("TrigToExp(3*Tan(3*x)-Tan(x)+2)", // "2+(-I*(E^(-I*x)-E^(I*x)))/(E^(-I*x)+E^(I*x))+(I*3*(E^(-I*3*x)-E^(I*3*x)))/(E^(-\n" + "I*3*x)+E^(I*3*x))"); System.out.print('.'); check( "Factor(2+(-I*(E^(-I*x)-E^(I*x)))/(E^(-I*x)+E^(I*x))+(I*3*(E^(-I*3*x)-E^(I*3*x)))/(E^(-I*3*x)+E^(I*3*x)))", // "((2-I*2)*(I+(-1/2-I*1/2)*E^(I*2*x)+E^(I*4*x)))/((-1-I*E^(I*x)+E^(I*2*x))*(-1+I*E^(I*x)+E^(\n" + "I*2*x)))"); // example from paper System.out.print('.'); check("Factor(3*Sech(x)^2+4*Tanh(x)+1)", // "1+3*Sech(x)^2+4*Tanh(x)"); System.out.print('.'); check("TrigToExp(3*Sech(x)^2+4*Tanh(x)+1)", // "1+12/(E^(-x)+E^x)^2+4*(-1/(E^x*(E^(-x)+E^x))+E^x/(E^(-x)+E^x))"); // example from paper System.out.print('.'); check("Factor(Log(x+1)+Log(x-1)-3)", // "-3+Log(-1+x)+Log(1+x)"); System.out.print('.'); check("TrigToExp(Log(x+1)+Log(x-1)-3)", // "-3+Log(-1+x)+Log(1+x)"); check("-3+Log(1+x)+Log(-1+x)", // "-3+Log(-1+x)+Log(1+x)"); // example from paper System.out.print('.'); check("Factor(E^(3*x)-4*E^x+3*E^(-x))", // "((-1+E^x)*(1+E^x)*(-3+E^(2*x)))/E^x"); // example from paper System.out.print('.'); check("Factor(Cosh(x)-3*Sinh(y))", // "Cosh(x)-3*Sinh(y)"); // 1/(E^x*2) + E^x/2 + 3/(E^y*2) - (3*E^y)/2 System.out.print('.'); check("TrigToExp(Cosh(x)-3*Sinh(y))", // "1/(2*E^x)+E^x/2-3*(-1/(2*E^y)+E^y/2)"); System.out.print('.'); check("TrigToExp(Cosh(x))", // "1/(2*E^x)+E^x/2"); System.out.print('.'); check("TrigToExp(Sinh(x))", // "-1/(2*E^x)+E^x/2"); // example from paper System.out.print('.'); check("Factor(2*Sinh(x)+6*Cosh(y)-5)", // "-5+6*Cosh(y)+2*Sinh(x)"); System.out.print('.'); check("TrigToExp(2*Sinh(x)+6*Cosh(y)-5)", // "-5+2*(-1/(2*E^x)+E^x/2)+6*(1/(2*E^y)+E^y/2)"); // example from paper System.out.print('.'); check("TrigToExp(Cos(x) + Cos(3*x) + Cos(5*x))", // "1/(2*E^(I*5*x))+1/(2*E^(I*3*x))+1/(2*E^(I*x))+E^(I*x)/2+E^(I*3*x)/2+E^(I*5*x)/2"); // // // TODO determine more factors System.out.print('.'); check("Factor(1/(2*E^(I*5*x))+1/(2*E^(I*3*x))+1/(2*E^(I*x))+E^(I*x)/2+E^(I*3*x)/2+E^(I*5*x)/2)", // "((-I+E^(I*x))*(I+E^(I*x))*(1-E^(I*x)+E^(I*2*x))*(-1-I*E^(I*x)+E^(I*2*x))*(-1+I*E^(I*x)+E^(\n" + "I*2*x))*(1+E^(I*x)+E^(I*2*x)))/(2*E^(I*5*x))"); // ((1/2)*(1 + E^(2*I*x))*(1 - E^(I*x) + E^(2*I*x))*(1 + E^(I*x) + E^(2*I*x))* // (1 - E^(2*I*x) + E^(4*I*x)))/E^(5*I*x) System.out.print('.'); check("Factor(TrigToExp(Cos(x) + Cos(3*x) + Cos(5*x)))", // "((-I+E^(I*x))*(I+E^(I*x))*(1-E^(I*x)+E^(I*2*x))*(-1-I*E^(I*x)+E^(I*2*x))*(-1+I*E^(I*x)+E^(\n" + "I*2*x))*(1+E^(I*x)+E^(I*2*x)))/(2*E^(I*5*x))"); System.out.print('.'); // (a+I*b)*(Cosh(x)-I*Sinh(x)) check("Factor(a*Cosh(x) + I*b*Cosh(x) - I*a*Sinh(x) + b*Sinh(x))", // "(-I*a+b)*(I*Cosh(x)+Sinh(x))"); System.out.print('.'); check("Factor(a*b+(4+4*x+x^2)^2)", // "16+a*b+32*x+24*x^2+8*x^3+x^4"); // github #121 System.out.print('.'); check("Factor(x^(12)-y^(12), GaussianIntegers->True)", // "(x-y)*(-I*x+y)*(I*x+y)*(x+y)*(x^2+x*y+y^2)*(x^2-x*y+y^2)*(-x^2-I*x*y+y^2)*(-x^2+I*x*y+y^\n" + // "2)"); System.out.print('.'); check("Factor(x^(2)+y^(2), GaussianIntegers->True)", // "(-I*x+y)*(I*x+y)"); System.out.print('.'); check("Factor(Sin(x), GaussianIntegers->True)", // "Sin(x)"); System.out.print('.'); check("Factor(1+x^2, GaussianIntegers->True)", // "(-I+x)*(I+x)"); System.out.print('.'); check("Factor(1+x^2, Extension->I)", // "(-I+x)*(I+x)"); check("Factor(x^(2)+y^(2), GaussianIntegers->False)", // "x^2+y^2"); // Homogenization example from // https://www.research.ed.ac.uk/portal/files/413486/Solving_Symbolic_Equations_%20with_PRESS.pdf System.out.print('.'); check("Factor(E^(3*x)-4*E^x+3*E^(-x))", // "((-1+E^x)*(1+E^x)*(-3+E^(2*x)))/E^x"); System.out.print('.'); check("Factor(E^x+E^(2*x))", // "E^x*(1+E^x)"); System.out.print('.'); check("Factor(Sin(x))", // "Sin(x)"); // TODO https://github.com/kredel/java-algebra-system/issues/8 System.out.print('.'); check("Factor(a*c+(b*c+a*d)*x+b*d*x^2)", // "(a+b*x)*(c+d*x)"); System.out.print('.'); check("Factor(b*c*n-a*d*n)", // "(b*c-a*d)*n"); System.out.print('.'); check("Factor(a*b*(4+4*x+x^2)^2)", // "a*b*(2+x)^4"); System.out.print('.'); check("Factor(x^2 - y^2)", // "(x-y)*(x+y)"); System.out.print('.'); check("Factor(1 / (x^2+2*x+1) + 1 / (x^4+2*x^2+1))", // "(2+2*x+3*x^2+x^4)/((1+x)^2*(1+x^2)^2)"); System.out.print('.'); check("Factor({x+x^2})", // "{x*(1+x)}"); System.out.print('.'); if (Config.EXPENSIVE_JUNIT_TESTS) { check("Factor(x^259+1)", // "(1+x)*(1-x+x^2-x^3+x^4-x^5+x^6)*(1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8-x^9+x^10-x^11+x^\n" + "12-x^13+x^14-x^15+x^16-x^17+x^18-x^19+x^20-x^21+x^22-x^23+x^24-x^25+x^26-x^27+x^\n" + "28-x^29+x^30-x^31+x^32-x^33+x^34-x^35+x^36)*(1+x-x^7-x^8+x^14+x^15-x^21-x^22+x^\n" + "28+x^29-x^35-x^36-x^37-x^38+x^42+x^43+x^44+x^45-x^49-x^50-x^51-x^52+x^56+x^57+x^\n" + "58+x^59-x^63-x^64-x^65-x^66+x^70+x^71+x^72+x^73+x^74+x^75-x^77-x^78-x^79-x^80-x^\n" + "81-x^82+x^84+x^85+x^86+x^87+x^88+x^89-x^91-x^92-x^93-x^94-x^95-x^96+x^98+x^99+x^\n" + "100+x^101+x^102+x^103-x^105-x^106-x^107-x^108-x^109-x^110-x^111+x^113+x^114+x^\n" + "115+x^116+x^117+x^118-x^120-x^121-x^122-x^123-x^124-x^125+x^127+x^128+x^129+x^\n" + "130+x^131+x^132-x^134-x^135-x^136-x^137-x^138-x^139+x^141+x^142+x^143+x^144+x^\n" + "145+x^146-x^150-x^151-x^152-x^153+x^157+x^158+x^159+x^160-x^164-x^165-x^166-x^\n" + "167+x^171+x^172+x^173+x^174-x^178-x^179-x^180-x^181+x^187+x^188-x^194-x^195+x^\n" + "201+x^202-x^208-x^209+x^215+x^216)"); System.out.print('.'); check("Factor(x^258-1)", // "(-1+x)*(1+x)*(1-x+x^2)*(1+x+x^2)*(1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8-x^9+x^10-x^11+x^\n" + "12-x^13+x^14-x^15+x^16-x^17+x^18-x^19+x^20-x^21+x^22-x^23+x^24-x^25+x^26-x^27+x^\n" + "28-x^29+x^30-x^31+x^32-x^33+x^34-x^35+x^36-x^37+x^38-x^39+x^40-x^41+x^42)*(1+x+x^\n" + "2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^\n" + "20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30+x^31+x^32+x^33+x^34+x^35+x^\n" + "36+x^37+x^38+x^39+x^40+x^41+x^42)*(1-x+x^3-x^4+x^6-x^7+x^9-x^10+x^12-x^13+x^15-x^\n" + "16+x^18-x^19+x^21-x^22+x^24-x^25+x^27-x^28+x^30-x^31+x^33-x^34+x^36-x^37+x^39-x^\n" + "40+x^42-x^44+x^45-x^47+x^48-x^50+x^51-x^53+x^54-x^56+x^57-x^59+x^60-x^62+x^63-x^\n" + "65+x^66-x^68+x^69-x^71+x^72-x^74+x^75-x^77+x^78-x^80+x^81-x^83+x^84)*(1+x-x^3-x^\n" + "4+x^6+x^7-x^9-x^10+x^12+x^13-x^15-x^16+x^18+x^19-x^21-x^22+x^24+x^25-x^27-x^28+x^\n" + "30+x^31-x^33-x^34+x^36+x^37-x^39-x^40+x^42-x^44-x^45+x^47+x^48-x^50-x^51+x^53+x^\n" + "54-x^56-x^57+x^59+x^60-x^62-x^63+x^65+x^66-x^68-x^69+x^71+x^72-x^74-x^75+x^77+x^\n" + "78-x^80-x^81+x^83+x^84)"); } System.out.print('.'); check("Factor(4*x^2+3, Extension->I)", // "4*(3/4+x^2)"); System.out.print('.'); check("Factor(3/4*x^2+9/16, Extension->I)", // "3/4*(3/4+x^2)"); System.out.print('.'); check("Factor(x^10 - 1, Modulus -> 2)", // "(1+x)^2*(1+x+x^2+x^3+x^4)^2"); System.out.print('.'); check("factor(-1+x^16)", // "(-1+x)*(1+x)*(1+x^2)*(1+x^4)*(1+x^8)"); System.out.print('.'); check("factor((-3)*x^3 +10*x^2-11*x+4)", // "(1-x)^2*(4-3*x)"); System.out.print('.'); check("factor(x^2-a^2)", // "(-a+x)*(a+x)"); // is sometimes slow, if it calls // FactorAbstract#factorsSquarefreeKronecker() System.out.print('.'); check("factor(2*x^3*y - 2*a^2*x*y - 3*a^2*x^2 + 3*a^4)", // "(-a+x)*(a+x)*(-3*a^2+2*x*y)"); System.out.print('.'); check("expand((x+a)*(-x+a)*(-2*x*y+3*a^2))", // "3*a^4-3*a^2*x^2-2*a^2*x*y+2*x^3*y"); } @Test public void testFactorialPower() { check("N(FactorialPower(1/3, 7, 3), 50)", // "131965.39551897576588934613625971650663008687700045"); checkNumeric("FactorialPower(1 + I, I, 3.)", // "0.6161330645515811+I*1.0098175021356184"); check("FactorialPower(-5, 3, 0.5)", // "-165.0"); check("FactorialPower(x,n,0)", // "x^n"); check("FactorialPower(2-I, 2)", // "1-I*3"); check("Gamma(2.0+1.0)/Gamma(2.0-0.9+1.0)", // "1.91116"); check("FactorialPower(2, 0.9)", // "1.91116"); check("FactorialPower(1,3)", // "0"); check("FactorialPower(19,1317624576693539401)", // "0"); check("FactorialPower(-1,1317624576693539401,1+Sqrt(2))", // "FactorialPower(-1,1317624576693539401,1+Sqrt(2))"); check("FactorialPower(E^(I*1/3*Pi),1317624576693539401)", // "FactorialPower(1/2+I*1/2*Sqrt(3),1317624576693539401)"); check("FactorialPower(3, 2)", // "6"); check("FactorialPower(2, 2)", // "2"); check("FactorialPower(1, 2)", // "0"); check("FactorialPower(0, 2)", // "0"); check("FactorialPower(9, 1)", // "9"); check("FactorialPower(1, 1)", // "1"); check("FactorialPower(100, 0)", // "1"); check("FactorialPower(100, 3)", // "970200"); check("FactorialPower(-1, 2)", // "2"); check("FactorialPower(-1, 3)", // "-6"); check("FactorialPower(-2, 2)", // "6"); check("FactorialPower(-3, 2)", // "12"); check("FactorialPower(100, 3)", // "970200"); check("FactorialPower(-100, 3)", // "-1030200"); check("FactorialPower(0.5, 1)", // "0.5"); check("FactorialPower(0.5, 2)", // "-0.25"); check("FactorialPower(0.1, 3)", // "0.171"); check("FactorialPower(8, 2, 2)", // "48"); check("FactorialPower(1, 2, 2)", // "-1"); check("FactorialPower(-0.5, 3, 2)", // "-5.625"); check("FactorialPower(0.5, 2, 3)", // "-1.25"); check("FactorialPower(10, 3, 5)", // "0"); check("FactorialPower(0.5, 3, 0.5)", // "0.0"); check("FactorialPower(0.5, 3, 0.1)", // "0.06"); check("FactorialPower(-5, 3, 0.5)", // "-165.0"); check("FactorialPower(2-I, 1)", // "2-I"); check("FactorialPower(1-5I, 0)", // "1"); check("FactorialPower(2-I, 2)", // "1-I*3"); check("FactorialPower(2-I, 2, 2)", // "-1-I*2"); check("FactorialPower(2-I, 2, 0)", // "3-I*4"); check("FactorialPower(2-I, 2, -1)", // "5-I*5"); check("FactorialPower(1+I, 3, -2)", // "6+I*22"); check("FactorialPower(5+6I, 2, -1.5)", // "-3.5+I*69.0"); } @Test public void testFactorial() { check("Factorial(5.211111111111111111)", // "172.7183563387097672"); check("(5/2)!", // "15/8*Sqrt(Pi)"); check("(-7/2)!", // "-8/15*Sqrt(Pi)"); check("(-121/2)!", // "1152921504606846976/6972993461801137628817411854132406856519268086997480719774989309037307630499025\\\n" + "82163482720947265625*Sqrt(Pi)"); check("Factorial(I*Infinity)", // "0"); check("Factorial(-I*Infinity)", // "0"); check("Factorial(ComplexInfinity)", // "Indeterminate"); check("Factorial(Factorial(x))", // "(x!)!"); check("Factorial(2.5)", // "3.32335"); check("Factorial(Infinity)", // "Infinity"); check("Factorial(-1/2)", // "Sqrt(Pi)"); check("Factorial(1/2)", // "Sqrt(Pi)/2"); check("Factorial(0)", // "1"); check("Factorial(1)", // "1"); check("Factorial(-1)", // "ComplexInfinity"); check("Factorial(10)", // "3628800"); check("Factorial(-10)", // "ComplexInfinity"); check("Factorial(11)", // "39916800"); check("Factorial(-11)", // "ComplexInfinity"); check("Factorial(19)", // "121645100408832000"); check("Factorial(20)", // "2432902008176640000"); check("Factorial(21)", // "51090942171709440000"); checkNumeric("10.5!", // "1.1899423083962249E7"); check("!a! //FullForm", // "Not(Factorial(a))"); } @Test public void testFactorial2() { check("N(Factorial2(3/13), 10)", // "0.9953739588"); check("Factorial2(5.211111111111111111)", // "18.6046636633029321"); check("Factorial2(2.0 + I)", // "5.15473+I*3.27618"); check("Factorial2(-1)", // "1"); check("Factorial2(-2)", // "ComplexInfinity"); check("Factorial2(-3)", // "-1"); check("Factorial2(-4)", // "ComplexInfinity"); check("Factorial2(-5)", // "1/3"); check("Factorial2(-6)", // "ComplexInfinity"); check("Factorial2(-7)", // "-1/15"); check("Factorial2(10)", // "3840"); check("Factorial2(Infinity)", // "Infinity"); check("Factorial(-Infinity)", // "Indeterminate"); check("Factorial2(-Infinity)", // "Indeterminate"); check("3!", "6"); check("3!!", "3"); } @Test public void testFactorSquareFree() { check("a == d b + d c // FactorSquareFree", // "a==(b+c)*d"); check("FactorSquareFree((b*c*x^2*Log(F))/(e^2-b^2*c^2*Log(F)^2))", // "(b*c*x^2*Log(F))/(e^2-b^2*c^2*Log(F)^2)"); check("FactorSquareFree(x^2147483647)", // "x^2147483647"); check("FactorSquareFree(x^2)", // "x^2"); check("FactorSquareFree(c^(1/4)*g^(1/4)*(5+2*m+3*n)^(1/4)*x)", // "c^(1/4)*g^(1/4)*(5+2*m+3*n)^(1/4)*x"); check("p = Expand((x + 1)^2 (x + 2)^2 (x + 3)^3)", // "108+432*x+711*x^2+625*x^3+318*x^4+94*x^5+15*x^6+x^7"); check("FactorSquareFree(p)", // "(3+x)^3*(2+3*x+x^2)^2"); } @Test public void testFactorSquareFreeList() { // bug endless loop ? check("FactorSquareFreeList(x^2147483647)", // "{{x,2147483647}}"); check("FactorSquareFreeList(42)", // "{{42,1}}"); check("FactorSquareFreeList(x)", // "{{1,1},{x,1}}"); check("FactorSquareFreeList(x^5 - x^3 - x^2 + 1)", // "{{-1+x,2},{1+2*x+2*x^2+x^3,1}}"); check( "FactorSquareFreeList(x^8 + 11*x^7 + 43*x^6 + 59*x^5 - 35*x^4 - 151*x^3 - 63*x^2 + 81*x + 54)", // "{{2+x,1},{3+x,3},{-1+x^2,2}}"); check("FactorSquareFreeList((-3)*x^3 +10*x^2-11*x+4)", // "{{-1,1},{-1+x,2},{-4+3*x,1}}"); } @Test public void testFactorTerms() { check("FactorTerms(-41*Im(z)-82*Re(z))", // "-41*(Im(z)+2*Re(z))"); check("FactorTerms(Cosh(E^(2*x)*Sin(2*y)))", // "Cosh(E^(2*x)*Sin(2*y))"); // check("Expand((3 + 2 x)^2*(x + 2 y)^2)",// // "9*x^2+12*x^3+4*x^4+36*x*y+48*x^2*y+16*x^3*y+36*y^2+48*x*y^2+16*x^2*y^2"); // check("FactorTerms(9*x^2+12*x^3+4*x^4+36*x*y+48*x^2*y+16*x^3*y+36*y^2+48*x*y^2+16*x^2*y^2, // y)",// // ""); // TODO create simpler form // check("FactorTerms(2*a*x^2*y + 2*x^2*y + 4*a*x^2 + 4*x^2 + 4*a^2*y^2 + 4*a*y^2 + 8*a^2*y + // 2*a*y - 6*y - // 12*a- 12, x)", // // ""); check("FactorTerms(4*Im(z)^2+4*Re(z)^2)", // "4*(Im(z)^2+Re(z)^2)"); check("FactorTerms(100*Log(2))", // "100*Log(2)"); check("FactorTerms(-136+40*Sqrt(17))", // "8*(-17+5*Sqrt(17))"); check("FactorTerms(x^2 - y^2, x)", // "x^2-y^2"); check("factorterms(3 + 6*x + 3*x^2)", // "3*(1+2*x+x^2)"); } @Test public void testFactorTermsList() { check("FactorTermsList(6*a^2 + 9*x^2 + 12*b^2)", // "{3,2*a^2+4*b^2+3*x^2}"); check("FactorTermsList(3 + 3*a + 6*a*x + 6*x + 12*a*x^2 + 12*x^2, x)", // "{3,1+a+2*x+2*a*x+4*x^2+4*a*x^2}"); // FactorTermsList: {g(x,y)} is not a polynomial. check("FactorTermsList({g(x,y)})", // "FactorTermsList({g(x,y)})"); check("FactorTermsList(g(x,y))", // "{1,g(x,y)}"); check("FactorTermsList(100*Log(2))", // "{100,Log(2)}"); check("FactorTermsList(I*Log(2))", // "{I,Log(2)}"); check("FactorTermsList(x^2 - y^2 )", // "{1,x^2-y^2}"); check("FactorTermsList(3 + 6*x + 3*x^2)", // "{3,1+2*x+x^2}"); check("FactorTermsList(5*x^2 - 5)", // "{5,-1+x^2}"); check("FactorTermsList(-136+40*Sqrt(17))", // "{8,-17+5*Sqrt(17)}"); check("FactorTermsList(3+3/4*x^3+12/17*x^2)", // "{3/68,68+16*x^2+17*x^3}"); } @Test public void testFibonacci() { checkNumeric("Fibonacci(5.8, 3)", // "283.4827308329499"); // check("Fibonacci(10007,Quantity(1.2,\"m\"))", // // "Fibonacci(10007,1.2[m])"); // Fibonacci(11,{13,2,3,a}) check("Fibonacci(11,{13,2,3,a})", // "{145336221161,5741,141481,1+15*a^2+35*a^4+28*a^6+9*a^8+a^10}"); // message Polynomial degree 151 exceeded check("Fibonacci(151,11/9223372036854775807)", // "Fibonacci(151,11/9223372036854775807)"); // iter limit check("Fibonacci(2147483647)", // "Hold(Fibonacci(2147483647))"); check("Fibonacci(0.2114411444411100011, 5)", // "0.1598551917369153725"); check("Fibonacci(5.8)", // "7.26639"); check("Fibonacci(1+I/2)//N", // "1.3763+I*0.00716945"); check("Fibonacci(-10, x)", // "-5*x-20*x^3-21*x^5-8*x^7-x^9"); check("Fibonacci(11, x)", // "1+15*x^2+35*x^4+28*x^6+9*x^8+x^10"); check("Fibonacci(50, x)", // "25*x+2600*x^3+80730*x^5+1184040*x^7+10015005*x^9+54627300*x^11+206253075*x^13+\n" + "565722720*x^15+1166803110*x^17+1855967520*x^19+2319959400*x^21+2310789600*x^23+\n" + "1852482996*x^25+1203322288*x^27+635745396*x^29+273438880*x^31+95548245*x^33+\n" + "26978328*x^35+6096454*x^37+1086008*x^39+148995*x^41+15180*x^43+1081*x^45+48*x^47+x^\n" + "49"); check("Table(Fibonacci(n, x), {n, 5})", // "{1,x,1+x^2,2*x+x^3,1+3*x^2+x^4}"); check("Table(Fibonacci(n), {n, 45})", // "{1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,\n" + "28657,46368,75025,121393,196418,317811,514229,832040,1346269,2178309,3524578,\n" + "5702887,9227465,14930352,24157817,39088169,63245986,102334155,165580141,\n" + "267914296,433494437,701408733,1134903170}"); // check("Fibonacci(10000)", "0"); check("Fibonacci(0)", // "0"); check("Fibonacci(1)", // "1"); check("Fibonacci(10)", // "55"); check("Fibonacci(-51)", // "20365011074"); check("Fibonacci(-52)", // "-32951280099"); check("Fibonacci(200)", // "280571172992510140037611932413038677189525"); check("Table(Fibonacci(-n), {n, 10})", // "{1,-1,2,-3,5,-8,13,-21,34,-55}"); check("Fibonacci(1000)", // "4346655768693745643568852767504062580256466051737178040248172908953655541794905\\\n" + "1890403879840079255169295922593080322634775209689623239873322471161642996440906\\\n" + "533187938298969649928516003704476137795166849228875"); } @Test public void testFileFormat() { check("FileFormat(\"example/picture.jpg\")", // "JPEG"); check("FileFormat(\"example/picture.test\")", // "None"); } @Test public void testFilterRules() { check("FilterRules({a -> 1, b -> 2, c -> 3}, {b, a})", // "{a->1,b->2}"); check("Options(f) = {a -> 1, b -> 2}", // "{a->1,b->2}"); check("FilterRules({b -> 3, MaxIterations -> 5}, Options(f))", // "{b->3}"); } @Test public void testFindClusters() { check("FindClusters(DirectedInfinity({-1,-2,3}),Times())", // "FindClusters({-Infinity,-Infinity,Infinity},1)"); // check( // "FindClusters({{2, 3}, {5, 10}, {4, 5}, {2, 2}}, DistanceFunction -> CorrelationDistance)", // // // "{{{2.0,3.0},{4.0,5.0},{2.0,2.0}},{{5.0,10.0}},{}}"); // Test data generator http://people.cs.nctu.edu.tw/~rsliang/dbscan/testdatagen.html // check("FindClusters({{83.08303244924173,58.83387754182331},{45.05445510940626,23.469642649637535},{14.96417921432294,69.0264096390456},{73.53189604333602,34.896145021310076},{73.28498173551634,33.96860806993209},{73.45828098873608,33.92584423092194},{73.9657889183145,35.73191006924026},{74.0074097183533,36.81735596177168},{73.41247541410848,34.27314856695011},{73.9156256353017,36.83206791547127},{74.81499205809087,37.15682749846019},{74.03144880081527,37.57399178552441},{74.51870941207744,38.674258946906775},{74.50754595105536,35.58903978415765},{74.51322752749547,36.030572259100154},{59.27900996617973,46.41091720294207},{59.73744793841615,46.20015558367595},{58.81134076672606,45.71150126331486},{58.52225539437495,47.416083617601544},{58.218626647023484,47.36228902172297},{60.27139669447206,46.606106348801404},{60.894962462363765,46.976924697402865},{62.29048673878424,47.66970563563518},{61.03857608977705,46.212924720020965}}, // 2.0, \r\n" + // "5, Method->\"DBSCAN\", DistanceFunction->EuclideanDistance)",// // "{{{73.5319,34.89615},{73.28498,33.96861},{73.45828,33.92584},{73.96579,35.73191},{74.00741,36.81736},{73.41248,34.27315},{73.91563,36.83207},{74.50755,35.58904},{74.51323,36.03057},{74.81499,37.15683},{74.03145,37.57399},{74.51871,38.67426}},{{59.27901,46.41092},{59.73745,46.20016},{58.81134,45.7115},{58.52226,47.41608},{58.21863,47.36229},{60.2714,46.60611},{60.89496,46.97692},{61.03858,46.21292},{62.29049,47.66971}}}"); // check("FindClusters({{ 83.08303244924173, 58.83387754182331 },\n" + // // "{ 45.05445510940626, 23.469642649637535 },\n" + // // "{ 14.96417921432294, 69.0264096390456 },\n" + // // "{ 73.53189604333602, 34.896145021310076 },\n" + // // "{ 73.28498173551634, 33.96860806993209 },\n" + // // "{ 73.45828098873608, 33.92584423092194 },\n" + // // "{ 73.9657889183145, 35.73191006924026 },\n" + // // "{ 74.0074097183533, 36.81735596177168 },\n" + // // "{ 73.41247541410848, 34.27314856695011 },\n" + // // "{ 73.9156256353017, 36.83206791547127 },\n" + // // "{ 74.81499205809087, 37.15682749846019 },\n" + // // "{ 74.03144880081527, 37.57399178552441 },\n" + // // "{ 74.51870941207744, 38.674258946906775 },\n" + // // "{ 74.50754595105536, 35.58903978415765 },\n" + // // "{ 74.51322752749547, 36.030572259100154 },\n" + // // "{ 59.27900996617973, 46.41091720294207 },\n" + // // "{ 59.73744793841615, 46.20015558367595 },\n" + // // "{ 58.81134076672606, 45.71150126331486 },\n" + // // "{ 58.52225539437495, 47.416083617601544 },\n" + // // "{ 58.218626647023484, 47.36228902172297 },\n" + // // "{ 60.27139669447206, 46.606106348801404 },\n" + // // "{ 60.894962462363765, 46.976924697402865 },\n" + // // "{ 62.29048673878424, 47.66970563563518 },\n" + // // "{ 61.03857608977705, 46.212924720020965 },\n" + // // "{ 60.16916214139201, 45.18193661351688 },\n" + // // "{ 59.90036905976012, 47.555364347063005 },\n" + // // "{ 62.33003634144552, 47.83941489877179 },\n" + // // "{ 57.86035536718555, 47.31117930193432 },\n" + // // "{ 58.13715479685925, 48.985960494028404 },\n" + // // "{ 56.131923963548616, 46.8508904252667 },\n" + // // "{ 55.976329887053, 47.46384037658572 },\n" + // // "{ 56.23245975235477, 47.940035191131756 },\n" + // // "{ 58.51687048212625, 46.622885352699086 },\n" + // // "{ 57.85411081905477, 45.95394361577928 },\n" + // // "{ 56.445776311447844, 45.162093662656844 },\n" + // // "{ 57.36691949656233, 47.50097194337286 },\n" + // // "{ 58.243626387557015, 46.114052729681134 },\n" + // // "{ 56.27224595635198, 44.799080066150054 },\n" + // // "{ 57.606924816500396, 46.94291057763621 },\n" + // // "{ 30.18714230041951, 13.877149710431695 },\n" + // // "{ 30.449448810657486, 13.490778346545994 },\n" + // // "{ 30.295018390286714, 13.264889000216499 },\n" + // // "{ 30.160201832884923, 11.89278262341395 },\n" + // // "{ 31.341509791789576, 15.282655921997502 },\n" + // // "{ 31.68601630325429, 14.756873246748 },\n" + // // "{ 29.325963742565364, 12.097849250072613 },\n" + // // "{ 29.54820742388256, 13.613295356975868 },\n" + // // "{ 28.79359608888626, 10.36352064087987 },\n" + // // "{ 31.01284597092308, 12.788479208014905 },\n" + // // "{ 27.58509216737002, 11.47570110601373 },\n" + // // "{ 28.593799561727792, 10.780998203903437 },\n" + // // "{ 31.356105766724795, 15.080316198524088 },\n" + // // "{ 31.25948503636755, 13.674329151166603 },\n" + // // "{ 32.31590076372959, 14.95261758659035 },\n" + // // "{ 30.460413702763617, 15.88402809202671 },\n" + // // "{ 32.56178203062154, 14.586076852632686 },\n" + // // "{ 32.76138648530468, 16.239837325178087 },\n" + // // "{ 30.1829453331884, 14.709592407103628 },\n" + // // "{ 29.55088173528202, 15.0651247180067 },\n" + // // "{ 29.004155302187428, 14.089665298582986 },\n" + // // "{ 29.339624439831823, 13.29096065578051 },\n" + // // "{ 30.997460327576846, 14.551914158277214 },\n" + // // "{ 30.66784126125276, 16.269703107886016 }},2.0,5,Method->\"DBSCAN\", // DistanceFunction->EuclideanDistance)", // // // "{{{73.5319,34.89615},{73.28498,33.96861},{73.45828,33.92584},{73.96579,35.73191},{74.00741,36.81736},{73.41248,34.27315},{73.91563,36.83207},{74.50755,35.58904},{74.51323,36.03057},{74.81499,37.15683},{74.03145,37.57399},{74.51871,38.67426}},"// // + // "{{59.27901,46.41092},{59.73745,46.20016},{58.81134,45.7115},{58.52226,47.41608},{58.21863,47.36229},{60.2714,46.60611},{60.89496,46.97692},{61.03858,46.21292},{60.16916,45.18194},{59.90037,47.55536},{57.86036,47.31118},{58.51687,46.62289},{57.85411,45.95394},{58.24363,46.11405},{57.60692,46.94291},{58.13715,48.98596},{57.36692,47.50097},{62.29049,47.66971},{62.33004,47.83941},{56.13192,46.85089},{55.97633,47.46384},{56.23246,47.94004},{56.44578,45.16209},{56.27225,44.79908}}," // + // "{{30.18714,13.87715},{30.44945,13.49078},{30.29502,13.26489},{30.1602,11.89278},{31.34151,15.28266},{31.68602,14.75687},{29.32596,12.09785},{29.54821,13.6133},{31.01285,12.78848},{31.35611,15.08032},{31.25949,13.67433},{30.18295,14.70959},{29.55088,15.06512},{29.00416,14.08967},{29.33962,13.29096},{30.99746,14.55191},{28.5938,10.781},{32.3159,14.95262},{30.46041,15.88403},{32.56178,14.58608},{32.76139,16.23984},{30.66784,16.2697},{28.7936,10.36352},{27.58509,11.4757}}}"); // check("FindClusters({{2.5, 3.1}, {5.9, 3.4}, {10, 15}, {2.2, 1.5}, {100, 7.5}})", // // "{{{2.5,3.1},{5.9,3.4},{2.2,1.5}},{{100.0,7.5}},{{10.0,15.0}}}"); // check("FindClusters({1, 2, 3, 4, 5, 6, 7, 8, 9})", // // "{{1.0,2.0,3.0},{6.0,7.0,8.0,9.0},{4.0,5.0}}"); // check("FindClusters({1, 2, 10, 12, 3, 1, 13, 25},4)", // // "{{1.0,2.0,3.0,1.0},{12.0,13.0},{25.0},{10.0}}"); } @Test public void testFindFit() { // https://stackoverflow.com/a/51696587/24819 check( "FindFit({ {1.3,0.5}, {2.8,0.9}, {5.0,2.6}, {10.2,7.1}, {16.5,12.3}, {21.3,15.3},{ 31.8,20.4}, {52.2,24.4}}, " // + "d+((a-d)/ (1+(x/c)^ b)), {{a, 1}, {b,2}, {c,20}, {d,20}}, x)", // "{a->0.174321,b->1.75938,c->19.69032,d->28.83068}"); // initial guess [1.0, 1.0, 1.0] gives bad result: check("FindFit(Table({t, 3*Sin(3*t + 1)}, {t, -3, 3, 0.1}), a* Sin(w*t + f), {a,w,f}, t)", // "{a->0.599211,w->1.51494,f->3.80421}"); // initial guess [2.0, 1.0, 1.0] gives better result: check( "FindFit(Table({t, 3*Sin(3*t + 1)}, {t, -3, 3, 0.1}), a* Sin(w*t + f), {{a, 2}, {w,1}, {f,1}}, t)", // "{a->3.0,w->3.0,f->1.0}"); // initial guess [2.0, 1.0, 1.0] with 1.0 by default: check( "FindFit(Table({t, 3*Sin(3*t + 1)}, {t, -3, 3, 0.1}), a* Sin(w*t + f), {{a, 2}, w, f}, t)", // "{a->3.0,w->3.0,f->1.0}"); check("FindFit({{1,1},{2,4},{3,9},{4,16}}, " // + "a+b*x+c*x^2, {a, b, c}, x)", // "{a->-6.10623*10^-16,b->7.21645*10^-16,c->1.0}"); check("FindFit({{15.2,8.9},{31.1,9.9},{38.6,10.3},{52.2,10.7},{75.4,11.4}}, " // + "a*Log(b*x), {a, b}, x)", // "{a->1.54503,b->20.28258}"); check("FindFit(Table(Prime(x), {x, 20}), a*x*Log(b + c*x), {a, b, c}, x)", // "{a->1.42076,b->1.65558,c->0.534644}"); check("FindFit({{1.0, 12.}, {1.9, 10.}, {2.6, 8.2}, {3.4, 6.9}, {5.0, 5.9}}, " // + "a*Exp(-k*t), {a, k}, t)", // "{a->14.38886,k->0.198208}"); // initial guess [0, 0, 0] doesn't work check("FindFit(Table(Prime(x), {x, 20}), a*x*Log(b + c*x), {{a,0},{b,0},{c,0}}, x)", // "FindFit({2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71},a*x*Log(b+c*x),{{a,\n" + "0},{b,0},{c,0}},x)"); } @Test public void testFindLinearRecurrence() { check("FindLinearRecurrence({{1,0},Sqrt(2)/2})", // "FindLinearRecurrence({{1,0},1/Sqrt(2)})"); check("FindLinearRecurrence({1, 2, 4, 7, 28, 128, 582, 2745, 13021, 61699, 292521, 1387138})", // "{5,-2,6,-11}"); check("FindLinearRecurrence(Table(2^k, {k, 10}))", // "{2}"); check("FindLinearRecurrence(Table(Fibonacci(k)*Fibonacci(k-1)^2, {k, 10}))", // "{3,6,-3,-1}"); check("data = LinearRecurrence({4, 3, 2, 1}, {1, 2, 3, 4}, 10)", // "{1,2,3,4,30,140,661,3128,14805,70066}"); check("FindLinearRecurrence(data)", // "{4,3,2,1}"); } @Test public void testFindMaximum() { // print message: The Function value False is not a real number at {x}={2.0}. check("FindMaximum(False,{x, 2})", // "FindMaximum(False,{x,2})"); check("FindMaximum(-Abs(x + 1) - Abs(x + 1.01) - Abs(y + 1),{x, y})", // "{-0.01,{x->-1.00719,y->-1.0}}"); check("FindMaximum(x*Cos(x), {x,2.0} )", // "{0.561096,{x->0.860334}}"); check("FindMaximum(Sin(x)*Sin(2*y), {{x, 2}, {y, 2}})", // "{1.0,{x->4.71239,y->2.35619}}"); check("FindMaximum(Sin(x), {x, 0.5})", // "{1.0,{x->1.5708}}"); check("FindMaximum(Sin(x)*Sin(2*y), {{x, 2}, {y, 2}}, Method -> \"ConjugateGradient\")", // "{1.0,{x->-1.5708,y->-0.785398}}"); } @Test public void testFindMinimum() { check( "FindMinimum({x+y,3*x+2*y >= 7 , x >= 0 , y >= 0}, {x, y},Method -> \"SequentialQuadratic\")", // "{2.33333,{x->2.33333,y->-8.32917*10^-11}}"); check( "FindMinimum({x+y,3*x+2*y >= 7 && x >= 0 && y >= 0}, {x, y},Method -> \"SequentialQuadratic\")", // "{2.33333,{x->2.33333,y->-8.32917*10^-11}}"); // TODO Less and Greater are not allowed at the moment // message: FindMinimum: Constraints in `1` are not all 'equality' or 'less // equal' or 'greater equal' linear constraints. Constraints with Unequal(!=) are not supported. check( "FindMinimum({x+y,3*x+2*y > 7 && x > 0 && y > 0}, {x, y},Method -> \"SequentialQuadratic\")", // "FindMinimum({x+y,3*x+2*y>7&&x>0&&y>0},{x,y},Method->SequentialQuadratic)"); // check("FindMinimum({Sin(x)*Sin(2*y),x^2 + y^2 < 3}, {{x, 2}, {y, 2}})", // // ""); check("FindMinimum(Abs(x + 1) + Abs(x + 1.01) + Abs(y + 1),{x, y})", // "{0.01,{x->-1.00719,y->-1.0}}"); check( "FindMinimum(Abs(x + 1) + Abs(x + 1.01) + Abs(y+1), {x, y}, Method -> \"ConjugateGradient\")", // "{0.01,{x->-1.01,y->-1.0}}"); check("FindMinimum(Sin(x), {x,1} )", // "{-1.0,{x->-1.5708}}"); check("FindMinimum(x*Cos(x), {x,5.0} )", // "{-3.28837,{x->3.42562}}"); check("FindMinimum(x*Cos(x), {x,10.0} )", // "{-9.47729,{x->9.52933}}"); check("FindMinimum(Sin(x)*Sin(2*y), {{x, 2}, {y, 2}})", // "{-1.0,{x->1.5708,y->2.35619}}"); check("FindMinimum(Sin(x), {x, 0.5})", // "{-1.0,{x->-1.5708}}"); check("FindMinimum(Sin(x), {x,1}, Method -> \"ConjugateGradient\")", // "{-1.0,{x->-7.85398}}"); check("FindMinimum(x*Cos(x), {x,5.0}, Method -> \"ConjugateGradient\")", // "{-3.28837,{x->3.42562}}"); check("FindMinimum(x*Cos(x), {x,10.0}, Method -> \"ConjugateGradient\")", // "{-9.47729,{x->9.52934}}"); check("FindMinimum(Sin(x)*Sin(2*y), {{x, 2}, {y, 2}}, Method -> \"ConjugateGradient\")", // "{-1.0,{x->1.5708,y->2.35619}}"); } // https://github.com/Hipparchus-Math/hipparchus/issues/40 // @Test // public void testBisection() { // BisectionSolver solver = new BisectionSolver(); // System.out.println(solver.solve(100, x->Math.cos(x)+2, 0.0, 5.0)); // } @Test public void testFindRoot() { // automatic: AccuracyGoal->6 checkNumeric("10-x /. FindRoot(Sin(x - 10) - x + 10, {x, 0})", // "1.498271155142561E-6"); checkNumeric("10-x /. FindRoot(Sin(x - 10) - x + 10, {x, 0},AccuracyGoal->4)", // "1.9439351756744827E-4"); // Message FindRoot: interval does not bracket a root: f(NaN) = NaN, f(NaN) = NaN. checkNumeric("10-x /. FindRoot(Sin(x - 10) - x + 10, {x, 0},AccuracyGoal->8)", // "10-x/.FindRoot(10-x-Sin(10-x),{x,0},AccuracyGoal->8)"); // Message FindRoot: Value of option AccuracyGoal->test is not Automatic or a machine-sized // integer. checkNumeric("10-x /. FindRoot(Sin(x - 10) - x + 10, {x, 0},AccuracyGoal->test)", // "10-x/.FindRoot(10-x-Sin(10-x),{x,0},AccuracyGoal->test)"); // multivariate cases check("FindRoot({2*x1+x2==E^(-x1), -x1+2*x2==E^(-x2)},{{x1, 0.0},{x2, 1.0}})", // "{x1->0.197594,x2->0.425514}"); check( "FindRoot({Exp(-Exp(-(x1+x2)))-x2*(1+x1^2), x1*Cos(x2)+x2*Sin(x1)-0.5},{{x1, 0.0},{x2,0.0}})", // "{x1->0.353247,x2->0.606082}"); check("FindRoot({Exp(x - 2) == y, y^2 == x}, {{x, 1}, {y, 1}})", // "{x->0.019026,y->0.137935}"); check("FindRoot({y == E^x, x + y == 2}, {{x, 1}, {y, 1}})", // "{x->0.442854,y->1.55715}"); check("FindRoot({Sin(x + y), Cos(x - y), x^2 + y^2 - z}, {{x, 1}, {y, 0}, {z, 0}})", // "{x->0.785398,y->-0.785398,z->1.2337}"); // univariate cases check("FindRoot(sin(x)==x^2, {x, -6.6, 3.99999999})", // "{x->-1.84448*10^-19}"); check("v1:= E^x - 3*x ;v2:={x, 2};", // ""); check("FindRoot(v1,v2)", // "{x->1.51213}"); check("{v1,v2,x}", // "{E^x-3*x,{x,2},x}"); check("FindRoot(Surd(x, 2) == 1.5, {x, 1})", // "{x->2.25}"); check("Exp(1.243624090168953 * E - 16) - 1", // "-0.999997"); checkNumeric("FindRoot(30*x/0.000002==30, {x, 0, 5}, Method->brent)", // "{x->2.0E-6}"); // github issue #60 // Message FindRoot: Method->brent is only applicable for univariate real functions and requires // two real starting values that bracket the root. check("FindRoot(cos(x) + 2, {x, 0, 5}, Method->brent)", // "FindRoot(2+Cos(x),{x,0,5},Method->brent)"); // FindRoot: Method->bisection is only applicable for univariate real functions and requires two // real starting values that bracket the root. check("FindRoot(cos(x) + 2, {x, 0, 5}, Method->bisection)", // "FindRoot(2+Cos(x),{x,0,5},Method->bisection)"); check("FindRoot(cos(x) + 2, {x, 0, 5}, Method->newton)", // "FindRoot(2+Cos(x),{x,0,5},Method->newton)"); // github issue #43 check("findroot(abs(x-1)-2x-3==0, {x, -10, 10})", // "{x->-0.666667}"); // github issue #103 check("FindRoot(2^x==0,{x,-100, 100}, Method->Brent)", // "FindRoot(2^x==0,{x,-100,100},Method->brent)"); // FindRoot: interval does not bracket a root: f(-1) = 0.5, f(100) = // 1,267,650,600,228,229,400,000,000,000,000 check("FindRoot(2^x==0,{x,-1,100}, Method->Brent)", // "FindRoot(2^x==0,{x,-1,100},Method->brent)"); checkNumeric("N(2^(-100))", // "7.888609052210118E-31"); check("FindRoot(Exp(x)-1 == 0,{x,-50,100}, Method->Muller)", // "{x->1.24362*10^-16}"); if (!ParserConfig.EXPLICIT_TIMES_OPERATOR) { // implicit times operator '*' allowed check("Exp(1.243624090168953 * E - 16) - 1", // "-0.999997"); check("Exp(1.243624090168953E-16) - 1", // "-0.999997"); } else { check("Exp(1.243624090168953E-16) - 1", // "0.0"); } checkNumeric("FindRoot(Exp(x)==Pi^3,{x,-1,10})", // "{x->3.4341896575482007}"); checkNumeric("$K=10000;\n" + "$g=0.0;\n" + "$n=10*12;\n" + "$Z=12;\n" + "$AA=0.0526;\n" + "$R=100;\n" + "$d=0.00;\n" + "$vn=0;\n" + "$EAj=0;\n" + "$zj=0;\n" + "$sz=1;\n" + "FindRoot((($K*(1+p-$g)^($n/$Z))/(1+$AA))+(Sum((($R*(1+$d)^(Floor(i0/$Z)))/(1+$AA))*(1+p-$g)^(($n-i0-$vn)/$Z),{i0,0,$n-1}))+(Sum(($EAj*(1+p-$g)^(($n-$zj)/$Z))/(1+$AA),{j,1,$sz})) - 30199, {p, 0, 0.1})", // "{p->0.04999709393822403}"); checkNumeric( "$K=10000;\n" + "$g=0.0;\n" + "$n=10*12;\n" + "$Z=12;\n" + "$AA=0.0526;\n" + "$res=15474;\n" + "FindRoot((($K*(1+p-$g)^($n/$Z))/(1+$AA)) - $res, {p, 0, 0.1})", // "{p->0.049993464334866594}"); checkNumeric("Exp(3.4341896)", // "31.006274895944433"); checkNumeric("Pi^3.0", // "31.006276680299816"); // default to Newton method checkNumeric("FindRoot(Exp(x)==Pi^3,{x,-1,10})", // "{x->3.4341896575482007}"); checkNumeric("FindRoot(Exp(x)==Pi^3,{x,-1,10}, Method->Brent)", // "{x->3.434189629596888}"); // only a start value is given: checkNumeric("FindRoot(Exp(x)==Pi^3,{x,3}, Method->Newton)", "{x->3.4341896575482007}"); checkNumeric("FindRoot(Exp(x)==Pi^3,{x,-1,10}, Method->Bisection)", // "{x->3.434189647436142}"); checkNumeric("FindRoot(Exp(x)==Pi^3,{x,-1,10}, Method->Brent)", // "{x->3.434189629596888}"); checkNumeric("FindRoot(Exp(x)==Pi^3,{x,-1,10}, Muller)", // "{x->3.4341896575483015}"); checkNumeric("FindRoot(Exp(x)==Pi^3,{x,-1,10}, Ridders)", // "{x->3.4341896575482007}"); checkNumeric("FindRoot(Exp(x)==Pi^3,{x,1,10}, Secant)", // "{x->3.4341896575036097}"); // FindRoot: maximal count (100) exceeded checkNumeric("FindRoot(Exp(x)==Pi^3,{x,1,10}, Method->RegulaFalsi, MaxIterations->100)", // "FindRoot(E^x==Pi^3,{x,1,10},Method->regulafalsi,MaxIterations->100)"); // FindRoot: convergence failed checkNumeric("FindRoot(Exp(x)==Pi^3,{x,1,10}, Method->RegulaFalsi, MaxIterations->32000)", // "FindRoot(E^x==Pi^3,{x,1,10},Method->regulafalsi,MaxIterations->32000)"); checkNumeric("FindRoot(Exp(x)==Pi^3,{x,1,10}, Illinois)", // "{x->3.4341896915055257}"); checkNumeric("FindRoot(Exp(x)==Pi^3,{x,1,10}, Pegasus)", // "{x->3.4341896575481976}"); checkNumeric("FindRoot(Exp(x)==Pi^3,{x,-1,10}, Brent)", // "{x->3.434189629596888}"); check("FindRoot(Sin(x),{x,-0.5,0.5}, Secant)", // "{x->0.0}"); } @Test public void testFirst() { check("First(<||>)", // "First(<||>)"); check("First(<|1 :> a, 2 -> b, 3 :> c|>)", // "a"); check("First(Infinity)", // "1"); check("First(ComplexInfinity)", // "First(ComplexInfinity)"); check("First({a, b, c})", // "a"); check("First(a + b + c)", // "a"); check("First(a)", // "First(a)"); check("First(a, b)", // "b"); check("First({}, b)", // "b"); check("First({a,b}, x)", // "a"); } @Test public void testFirstCase() { check("FirstCase({a, 5, \\[Pi]}, _Symbol, Heads -> True)", // "List"); check("FirstCase({1, 1, f(a), 2, 3, y, f(8), 9, f(10)}, f(x_) :> x)", // "a"); check("FirstCase({a, b, c, 5, 6, 7}, _Integer)", // "5"); check("FirstCase({1, 1, f(a), 2, 3, y, f[8], 9, f[10]}, Except(_Integer))", // "f(a)"); check("FirstCase(<|1 -> \"a\", 2 -> \"b\", 3 -> c, 4 -> d|>, _Symbol)", // "c"); check("FirstCase(<|1 -> 5, 2 -> <|3 -> 1, a -> b|>|>, _Symbol, Missing(), Infinity)", // "b"); check("FirstCase({a, 5, \\[Pi]}, _Symbol, Heads -> True)", // "List"); check("FirstCase({1, b -> Automatic, c -> 3}, _ -> Automatic )", // "Automatic"); check("FirstCase({1, b -> Automatic, c -> 3}, HoldPattern(_ -> Automatic))", // "b->Automatic"); } @Test public void testFirstPosition() { check("FirstPosition(x^2 + y^2, Power, Heads->False)", // "Missing(NotFound)"); check("FirstPosition({a, b, a, a, b, c, b}, b)", // "{2}"); check("FirstPosition({{a, a, b}, {b, a, a}, {a, b, a}}, b)", // "{1,3}"); check("FirstPosition({1 + x^2, 5, x^4, a + (1 + x^2)^2}, x^_)", // "{1,2}"); check( "FirstPosition(<|{1 -> 1 + x^2, 2 -> <|\"a\" -> x^2|>, 3 -> x^4, 4 -> a + (1 + x^2)^2}|>, x^_)", // "{Key(1),2}"); check("FirstPosition(<|\"a\" -> 1, \"b\" -> 2, \"c\" -> 3, \"d\" -> 4|>, _Integer?PrimeQ)", // "{Key(b)}"); check("FirstPosition({1, 2, 3}, _?StringQ, \"NoStrings\")", // "NoStrings"); check("FirstPosition(x^2 + y^2, Power)", // "{1,0}"); check("FirstPosition(Range(-1, 1, 0.05), 0.1)", // "Missing(NotFound)"); check("FirstPosition(Range(-1, 1, 0.05), n_ /; n == 0.1)", // "{23}"); } @Test public void testFit() { check("Fit({2,3,5,7,11,13},3,x)", // "3.0-1.95238*x+1.10714*x^2-0.0833333*x^3"); check("Fit({{1,1},{2,4},{3,9},{4,16}},2,x)", // "x^2"); check("Fit({1,4,9,16},2,x)", // "x^2"); check("Fit({x,-3,-1/2},2147483647,ComplexInfinity)", // "Fit({x,-3,-1/2},2147483647,ComplexInfinity)"); check("Fit({1->0},1,x)", // "Fit({1->0},1,x)"); check("Fit({{0, 1}, {1, 0}, {3, 2}, {5, 4}}, 1, x)", // "0.186441+0.694915*x"); check("Fit({{1,1},{2,4},{3,9},{4,16}},2,x)", // "x^2"); } @Test public void testFiveNum() { // example from https://en.wikipedia.org/wiki/Five-number_summary check("FiveNum({0, 0, 1, 2, 63, 61, 27, 13})", // "{0,1/2,15/2,44,63}"); check("FiveNum({20,12,16,32,27,65,44,45,22,18})", // "{12,18,49/2,44,65}"); check("FiveNum(SparseArray({20,12,16,32,27,65,44,45,22,18}))", // "{12,18,49/2,44,65}"); } @Test public void testFixedPoint() { check("FixedPoint((# + 2/# )/2 &, 1`20, SameTest -> (Abs(#1 - #2) < 1*^-10 &))", // "1.4142135623730950488"); check("FixedPoint((# + 2/# )/2 &, 1, SameTest -> (Abs(#1 - #2) < 1*^-10 &))", // "886731088897/627013566048"); check("FixedPoint((# + 2/#)/2 &, 1, SameTest -> (Equal(N(#1), N(#2)) &))", // "1572584048032918633353217/1111984844349868137938112"); // $IterationLimit: Iteration limit of 500 exceeded for FixedPoint(-1/2,14). check("FixedPoint(-1/2,14)", // "Hold(FixedPoint(-1/2,14))"); check("FixedPoint(Cos, 1.0)", // "0.739085"); check("FixedPoint(#+1 &, 1, 20)", // "21"); check("FixedPoint(f, x, 0)", // "x"); check("FixedPoint(f, x, -1)", // "FixedPoint(f,x,-1)"); checkNumeric("FixedPoint(Cos, 1.0, Infinity)", // "0.7390851332151607"); checkNumeric("FixedPoint((# + 2/#)/2 &, 1.)", // "1.414213562373095"); check("FixedPoint(1 + Floor(#/2) &, 1000)", // "2"); check("21!=0", // "True"); check("{28, 21} /. {a_, b_} -> {b, Mod(a, b)}", // "{21,7}"); check("{28, 21} /. {a_, b_} /; b != 0 -> {b, Mod(a, b)}", // "{21,7}"); check("{21, 7} /. {a_, b_} /; b != 0 -> {b, Mod(a, b)}", // "{7,0}"); check("{7, 0} /. {a_, b_} /; b != 0 -> {b, Mod(a, b)}", // "{7,0}"); check("FixedPoint(# /. {a_, b_} /; b != 0 -> {b, Mod(a, b)} &, {28, 21})", // "{7,0}"); } @Test public void testFixedPointList() { check("FixedPointList((# + 2/# )/2 &, 1`20, SameTest -> (Abs(#1 - #2) < 1*^-10 &))", // "{1,1.5,1.4166666666666666666,1.4142156862745098039,1.4142135623746899106,1.4142135623730950488}"); check("FixedPointList(Function((# + 3/#)/2), 1.)", // "{1.0,2.0,1.75,1.73214,1.73205,1.73205,1.73205}"); // message $IterationLimit: Iteration limit of 500 exceeded for FixedPointList(-1+I,{x,-2,3}). check("FixedPointList(-1+I,{x,-2,3})", // "Hold(FixedPointList(-1+I,{x,-2,3}))"); check("FixedPointList(x_,Null)", // "Hold(FixedPointList(x_,Null))"); // recursion or iteration limit exceeded check("FixedPointList(x^2,1.5707963267948966)", // "Hold(FixedPointList(x^2,1.5708))"); // message: $IterationLimit: Iteration limit of 500 exceeded for FixedPointList(-1/2,14). check("FixedPointList(-1/2,14)", // "Hold(FixedPointList(-1/2,14))"); check("FixedPointList(Cos, 1.0, 4)", // "{1.0,0.540302,0.857553,0.65429,0.79348}"); checkNumeric("newton(n_) := FixedPointList(.5*(# + n/#) &, 1.); newton(9)", // "{1.0,5.0,3.4,3.023529411764706,3.00009155413138,3.000000001396984,3.0,3.0}"); // Get the "hailstone" sequence of a number: check("collatz(1) := 1", // ""); check("collatz(x_ ? EvenQ) := x / 2", // ""); check("collatz(x_) := 3*x + 1", // ""); check("FixedPointList(collatz, 14)", // "{14,7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1,1}"); check("FixedPointList(f, x, 0)", // "{x}"); check("FixedPointList(f, x, -1) ", // "FixedPointList(f,x,-1)"); check("Last(FixedPointList(Cos, 1.0, Infinity))", // "0.739085"); } @Test public void testFlat() { System.out.println(""); // see test https://github.com/mathics/Mathics/issues/747 check("SetAttributes(eqv, Flat);eqv(p, q, q, p) /. eqv(x_, y_) :> {x, y}", // "{eqv(p),eqv(q,q,p)}"); System.out.print("."); check("SetAttributes(f, Flat)", // ""); System.out.print("."); check("f(a, b, c) /. f(a, b) -> d", // "f(d,c)"); System.out.print("."); check("f(a, f(b, c))", // "f(a,b,c)"); System.out.print("."); check("SetAttributes({u, v}, Flat)", // ""); System.out.print("."); check("u(x_) := {x}", // ""); System.out.print("."); check("u()", // "u()"); // `Flat` is taken into account in pattern matching check("u(a)", // "{a}"); System.out.print("."); // stack overflow? // check("u(a, b)", "Iteration limit of 500 exceeded."); // check("u(a, b, c)", "Iteration limit of 500 exceeded."); check("v(x_) := x ", // ""); System.out.print("."); check("v()", // "v()"); System.out.print("."); check("v(a)", // "a"); System.out.print("."); // iteration limit exceeded check("v(a, b)", // "Hold(v(a,b))"); System.out.print("."); // Iteration limit check("v(a, b, c)", // "Hold(v(a,b,c))"); } @Test public void testOnlyFlat() { // see test https://github.com/mathics/Mathics/issues/1485 check("SetAttributes(fl, Flat)", // ""); check("fl(fl(a, b), c)", // "fl(a,b,c)"); check("fl(x_, x_) := fl(x)", // ""); check("fl(b, b, b, c, c)", // "fl(b,c)"); check("fl(a, a, a, b, b, b, c, c)", // "fl(a,b,c)"); } @Test public void testFlatOrderlessOneIdentity() { check("pm(y_,x_+y_+z_):={x,y,z}", // ""); check("pm(g,e+f+g+h+k)", // "{e,g,f+h+k}"); // see github issue 89 check("SetAttributes(oi, {OneIdentity})", // ""); check("oi(p, q, r) /. {oi(x_,y_) :> {x,y}}", // "oi(p,q,r)"); check("First@( oi(p, q, r) /. {oi(x_,y_) :> {x,y}} )", // "p"); check("Rest@( oi(p, q, r) /. {oi(x_,y_) :> {x,y}} )", "oi(q,r)"); check("SetAttributes(fo, {Flat, Orderless})", ""); check("fo(p, q, r) /. {fo(x_,y_) :> {x,y}}", // "{p,fo(q,r)}"); check("First@( fo(p, q, r) /. {fo(x_,y_) :> {x,y}} )", // "p"); check("Rest@( fo(p, q, r) /. {fo(x_,y_) :> {x,y}} )", "{fo(q,r)}"); check("Flatten(Table(Union(Sort/@Permutations({Flat,Orderless,OneIdentity}, {i})), {i,3}), 1)", // // "{{Flat}," // + "{OneIdentity}," // + "{Orderless}," // + "{Flat,OneIdentity}," // + "{Flat,Orderless}," // + "{OneIdentity,Orderless}," // + "{Flat,OneIdentity,Orderless}}"); // Check when substitution is defined BEFORE setting attributes. check("Table(Module({ e = (eqv(p,q,r) /. {eqv(x_,y_) :> {x,y}}) }, ClearAll(eqv); " // + "SetAttributes(eqv,j); " // + "{j, First@e, Rest@e})," // + " {j, Flatten(Table(Union(Sort/@Permutations({Flat,Orderless,OneIdentity}, {i})), {i,3}), 1)})", // // "{{{Flat},p,eqv(q,r)}," // + "{{OneIdentity},eqv(p),{eqv(q,r)}}," // + "{{Orderless},p,eqv(q,r)}," // + "{{Flat,OneIdentity},p,eqv(q,r)}," // + "{{Flat,Orderless},p,{eqv(q,r)}}," // + "{{OneIdentity,Orderless},p,{eqv(q,r)}}," // + "{{Flat,OneIdentity,Orderless},p,eqv(q,r)}}"); // Check when substitution is defined AFTER setting attributes. check("Table(Module({e},ClearAll(eqv);" // + "SetAttributes(eqv,j);" // + "e=(eqv(p,q,r)/.{eqv(x_,y_):>{x,y}});{j,First@e,Rest@e})," // + "{j,Flatten(Table(Union(Sort/@Permutations({Flat,Orderless,OneIdentity},{i})),{i,3}),1)})", // // "{{{Flat},eqv(p),{eqv(q,r)}}," // + "{{OneIdentity},p,eqv(q,r)}," // + "{{Orderless},p,eqv(q,r)}," // + "{{Flat,OneIdentity},p,{eqv(q,r)}}," // + "{{Flat,Orderless},p,{eqv(q,r)}}," // + "{{OneIdentity,Orderless},p,eqv(q,r)}," // + "{{Flat,OneIdentity,Orderless},p,{eqv(q,r)}}}"); } @Test public void testFlatten() { // message Flatten: Level specification value greater equal 0 expected instead of -Infinity. check("Flatten(f(g(u, v), f(x, y)), -Infinity, f)", // "Flatten(f(g(u,v),f(x,y)),-Infinity,f)"); check("Flatten(RandomReal(1, {3, 5, 7}), {{2, 3}, {1}})", // "Flatten(RandomReal(1,{3,5,7}),{{2,3},{1}})"); check("Flatten(3.14)", // "Flatten(3.14)"); // https://oeis.org/A049615 check( "Table(Length(Select(Flatten(Table({x, y}, {x, 0, n - k}, {y, 0, k}), 1), GCD @@ # > 1 &)), {n, 0, 11}, {k, 0, n}) // Flatten", // "{0,0,0,1,0,1,2,1,1,2,3,2,3,2,3,4,3,4,4,3,4,5,4,6,6,6,4,5,6,5,7,8,8,7,5,6,7,6,9,9,\n" + "11,9,9,6,7,8,7,10,12,12,12,12,10,7,8,9,8,12,13,16,14,16,13,12,8,9,10,9,13,15,17,\n" + "18,18,17,15,13,9,10}"); check("Flatten({{a, b}, {c, {d}, e}, {f, {g, h}}})", // "{a,b,c,d,e,f,g,h}"); check("Flatten({{a, b}, {c, {d}, e}, {f, {g, h}}}, 1)", // "{a,b,c,{d},e,f,{g,h}}"); check("Flatten(f(f(x, y), z))", // "f(x,y,z)"); check("Flatten({0, {1}, {{2, -2}}, {{{3}, {-3}}}, {{{{4}}}}}, 0)", // "{0,{1},{{2,-2}},{{{3},{-3}}},{{{{4}}}}}"); check("Flatten(f(g(u, v), f(x, y)), Infinity, g)", // "f(u,v,f(x,y))"); check("Flatten(f(g(u, v), f(x, y)), Infinity, f)", // "f(g(u,v),x,y)"); check("m = {{{1, 2}, {3}}, {{4}, {5, 6}}}", // "{{{1,2},{3}},{{4},{5,6}}}"); // check("Flatten(m, {2})", ""); // check("Flatten(m, {{2}})", ""); // check("Flatten(m, {{2}, {1}})", ""); // check("Flatten(m, {{2}, {1}, {3}})", ""); // check("m = {{{1, 2}, {3}}, {{4}, {5, 6}}}", ""); // check("m = {{{1, 2}, {3}}, {{4}, {5, 6}}}", ""); } @Test public void testFlattenAt() { check("FlattenAt(2)[{a, {b, c}, {d, e}, {f}}]", // "{a,b,c,{d,e},{f}}"); check("FlattenAt({a, {b, c}, {d, e}, {f}}, 2)", // "{a,b,c,{d,e},{f}}"); check("FlattenAt({a, g(b,c), {d, e}, {f}}, 2)", // "{a,b,c,{d,e},{f}}"); check("FlattenAt(f(a, g(b,c), {d, e}, {f}), -2)", // "f(a,g(b,c),d,e,{f})"); check("FlattenAt(f(a, g(b,c), {d, e}, {f}), 4)", // "f(a,g(b,c),{d,e},f)"); check("Table(FlattenAt(f({a}, {b}, {c}, {d}), i), {i, 4})", // "{f(a,{b},{c},{d}),f({a},b,{c},{d}),f({a},{b},c,{d}),f({a},{b},{c},d)}"); } @Test public void testFloor() { check("Floor(Quantity(8.5, \"Meters\"))", // "8[Meters]"); check("Floor(DirectedInfinity(0))", // "ComplexInfinity"); check("Floor(DirectedInfinity((1/2-I*1/2)*Sqrt(2)))", // "DirectedInfinity((1/2-I*1/2)*Sqrt(2))"); check("Floor(-Infinity)", // "-Infinity"); check("Floor(Infinity)", // "Infinity"); check("Floor(-9/4)", // "-3"); check("Floor(1/3)", // "0"); check("Floor(-1/3)", // "-1"); check("Floor(10.4)", // "10"); check("Floor(10/3)", // "3"); check("Floor(10)", // "10"); check("Floor(21, 2)", // "20"); check("Floor(2.6, 0.5)", // "2.5"); check("Floor(-10.4)", // "-11"); check("Floor(1.5 + 2.7*I)", // "1+I*2"); check("Floor(10.4, -1)", // "11"); check("Floor(-10.4, -1) ", // "-10"); check("Floor(1.5)", // "1"); check("Floor(1.5 + 2.7*I)", // "1+I*2"); } @Test public void testFold() { // message: Fold: Fold called with 5 arguments; 1 or 3 arguments are expected. check("Fold(f)[{a, b, c, d},x,y,z]", // "Fold(f)[{a,b,c,d},x,y,z]"); check("Fold(f, {})", // "Fold(f,{})"); check("Fold(test, t1, {a, b, c, d})", // "test(test(test(test(t1,a),b),c),d)"); check("Fold(f, x, {a, b, c, d})", // "f(f(f(f(x,a),b),c),d)"); check("Fold(f)[x,{a, b, c, d}]", // "f(f(f(f(x,a),b),c),d)"); check("Fold(List, x, {a, b, c, d})", // "{{{{x,a},b},c},d}"); check("Fold(Times, 1, {a, b, c, d})", // "a*b*c*d"); check("Fold(#1^#2 &, x, {a, b, c, d})", // "(((x^a)^b)^c)^d"); check("Catch(Fold(If(# > 10^6, Throw(#), #^2 + #1) &, 2, Range(6)))", // "3263442"); check("Fold(g(#2, #1) &, x, {a, b, c, d})", // "g(d,g(c,g(b,g(a,x))))"); check("Fold(x *#1 + #2 &, 0, {a, b, c, d, e})", // "e+x*(d+x*(c+x*(b+a*x)))"); check("Fold(f)[{a, b, c, d}]", // "f(f(f(a,b),c),d)"); check("Fold(Cross, {{1, -1, 1}, {0, 1, 1}, {1, 1, -1}})", // "{0,-1,-1}"); } @Test public void testFoldList() { check("FoldList(f, e1, h(e2, e3, e4))", // "h(e1,f(e1,e2),f(f(e1,e2),e3),f(f(f(e1,e2),e3),e4))"); // message: FoldList: FoldList called with 5 arguments; 1 or 3 arguments are expected. check("FoldList(f)[{a, b, c, d},x,y,z]", // "FoldList(f)[{a,b,c,d},x,y,z]"); // A002110 Primorial numbers: product of first n primes. // https://oeis.org/A002110 check("FoldList(Times, 1, Prime(Range(20)))", // "{1,2,6,30,210,2310,30030,510510,9699690,223092870,6469693230,200560490130,\n" + "7420738134810,304250263527210,13082761331670030,614889782588491410,\n" + "32589158477190044730,1922760350154212639070,117288381359406970983270,\n" + "7858321551080267055879090,557940830126698960967415390}"); check("FoldList(f, {})", // "{}"); check("FoldList(f,h,{})", // "{h}"); check("FoldList(f, g(a))", // "g(a)"); check("FoldList(f, {a, b, c, d})", // "{a,f(a,b),f(f(a,b),c),f(f(f(a,b),c),d)}"); check("FoldList(Plus,{1,2,3})", // "{1,3,6}"); check("foldlist(f, x, h())", // "h(x)"); check("foldlist(f, x, h(c))", // "h(x,f(x,c))"); check("foldlist(#^2 + #1 &, 2, range(6))", // "{2,6,42,1806,3263442,10650056950806,113423713055421844361000442}"); check("foldlist(f, x, {a, b, c, d})", // "{x,f(x,a),f(f(x,a),b),f(f(f(x,a),b),c),f(f(f(f(x,a),b),c),d)}"); // check("FoldList(Times, 1, Array(Prime, 10))", ""); check("foldlist(1/(#2 + #1) &, x, reverse({a, b, c}))", // "{x,1/(c+x),1/(b+1/(c+x)),1/(a+1/(b+1/(c+x)))}"); check("FoldList(f)[{a, b, c, d}]", // "{a,f(a,b),f(f(a,b),c),f(f(f(a,b),c),d)}"); } @Test public void testFor() { check("For(n = 1, n < 1000, n++, If(PrimeQ(n) && (n > 7), Return())); n ", // "11"); check("n := 1; For(i=1, i<=10, i=i+1, n = n * i);n", // "3628800"); check("n==10!", // "True"); check("n := 1;For(i=1, i<=10, i=i+1, If(i > 5, Return(i)); n = n * i)", // "6"); check("n", // "120"); check("For($i = 0, $i < 4, $i++, Print($i))", // ""); check("For($i = 0, $i < 4, $i++)", // ""); check("$i = 0;For($j = 0, $i < 4, $i++, Print($i));$i", // "4"); check("$i = 0;For($j = 0, $i < 4, $i++);$i", // "4"); check("$i = 0;For($j = 0, $i < 4, $i++)", // ""); check("For($ = 1, $i < 1000, $i++, If($i > 10, Break())); $i", // "11"); check( "For($t = 1; $k = 1, $k <= 5, $k++, $t *= $k; Print($t); If($k < 2, Continue()); $t += 2)", // ""); } @Test public void testFourier() { check("Fourier({1, 1, 2, 2, 1, 1, 0, 0})", // "{2.82843,-0.5+I*1.20711,0.0,0.5+I*(-0.207107),0.0,0.5+I*0.207107,0.0,-0.5+I*(-1.20711)}"); check("Fourier({1,0,0,1,0,0,1,0})", // "{1.06066,0.103553+I*(-0.103553),I*(-0.353553),0.603553+I*0.603553,0.353553,0.603553+I*(-0.603553),I*0.353553,0.103553+I*0.103553}"); check("Fourier({1,2-I, -I, -1+2*I})", // "{1.0,2.0+I*2.0,I*(-1.0),-1.0+I*(-1.0)}"); check("Fourier({1 + 2*I, 3 + 11*I})", // "{2.82843+I*9.19239,-1.41421+I*(-6.36396)}"); check("Fourier({1,2,0,0})", // "{1.5,0.5+I*1.0,-0.5,0.5+I*(-1.0)}"); // Fourier: Argument {1,2,0,0,7} is restricted to vectors with a length of power of 2. check("Fourier({1,2,0,0,7})", // "Fourier({1,2,0,0,7})"); } @Test public void testFractionalPart() { check("FractionalPart(Quantity(-1.1, \"Meters\"))", // "-0.1[Meters]"); check("FractionalPart(235/47 + 53/10*I)", // "I*3/10"); check("FractionalPart(235/47 + 5.3*I)", // "I*0.3"); check("FractionalPart(ArcCosh(7/17))", // "-I+ArcCosh(7/17)"); check("FractionalPart(ArcSinh(7/17))", // "ArcSinh(7/17)"); check("FractionalPart(-Infinity)", // "Interval({-1,0})"); check("FractionalPart(test)", // "FractionalPart(test)"); check("FractionalPart({-2.4, -2.5, -3.0})", // "{-0.4,-0.5,0.0}"); check("FractionalPart(14/32)", // "7/16"); check("FractionalPart(4/(1 + 3 I))", // "2/5-I*1/5"); check("FractionalPart(Pi^20)", // "-8769956796+Pi^20"); check("FractionalPart(I*Infinity)", // "I*Interval({0,1})"); check("FractionalPart(-I*Infinity)", // "-I*Interval({0,1})"); check("FractionalPart(ComplexInfinity)", // "Interval({0,1})"); check("FractionalPart(2.4+3.1*I)", // "0.4+I*0.1"); check("FractionalPart(-5/3-(7/3)*I)", // "-2/3-I*1/3"); check("FractionalPart(Cos(Pi/2))", // "0"); check("FractionalPart(Sin(7/17))", // "Sin(7/17)"); check("FractionalPart(Sin(-7/17))", // "-Sin(7/17)"); check("FractionalPart(-Pi)", // "3-Pi"); check("FractionalPart(GoldenRatio)", // "-1+GoldenRatio"); check("FractionalPart(-9/4)", // "-1/4"); check("FractionalPart(-9/4)+IntegerPart(-9/4)", // "-9/4"); check("FractionalPart(-2.25)+IntegerPart(-2.25)", // "-2.25"); check("FractionalPart(9/4)+IntegerPart(9/4)", // "9/4"); check("FractionalPart(2.25)+IntegerPart(2.25)", // "2.25"); check("FractionalPart(-2.25)+IntegerPart(-2.25)", // "-2.25"); check("FractionalPart(0)+IntegerPart(0)", // "0"); check("FractionalPart(0.0)+IntegerPart(0.0)", // "0.0"); check("FractionalPart(1)+IntegerPart(1)", // "1"); check("FractionalPart(1.0)+IntegerPart(1.0)", // "1.0"); check("FractionalPart(-1)+IntegerPart(-1)", // "-1"); check("FractionalPart(-1.0)+IntegerPart(-1.0)", // "-1.0"); checkNumeric("FractionalPart(2.4)", // "0.3999999999999999"); checkNumeric("FractionalPart(-2.4)", // "-0.3999999999999999"); checkNumeric("FractionalPart({-2.4, -2.5, -3.0})", // "{-0.3999999999999999,-0.5,0.0}"); } @Test public void testFreeQ() { // see notes for MemberQ check("FreeQ(a*x*Log(x), x*Log(x))", // "False"); check("FreeQ(a*x*Log(x)+ b*(x*Log(x)), x*Log(x))", // "False"); check("FreeQ(Sin(x*y),Sin)", // "False"); check("s=Sin;FreeQ(Sin(x*y),s)", // "False"); check("FreeQ(x_+y_+z_)[a+b]", // "True"); check("FreeQ(a + b + c, a + c)", // "False"); } @Test public void testFresnelC() { check("N(FresnelC(2),50)", // "0.48825340607534075450022350335726103768836715450921"); check("FresnelC(1.8)", // "0.333633"); check("FresnelC(2.0)", // "0.488253"); checkNumeric("FresnelC(2.5+I)", // "116.64806138055195+I*(-105.22873567055956)"); checkNumeric("FresnelC({1.5, 2.5, 3.5})", // "{0.4452611760398215,0.45741300964177706,0.5325724350280008}"); check("FresnelC(0)", // "0"); check("FresnelC(Infinity)", // "1/2"); check("FresnelC(-Infinity)", // "-1/2"); check("FresnelC(I*Infinity)", // "I*1/2"); check("FresnelC(-I*Infinity)", // "-I*1/2"); check("FresnelC(-z)", // "-FresnelC(z)"); check("FresnelC(I*z)", // "I*FresnelC(z)"); checkNumeric("FresnelC(1.8)", // "0.33363292722155713"); check("D(FresnelC(x),x)", // "Cos(1/2*Pi*x^2)"); } @Test public void testFresnelS() { check("N(FresnelS(2),50)", // "0.34341567836369824219530081595806845688654181220252"); check("FresnelS(1.8)", // "0.450939"); check("FresnelS(2.0)", // "0.343416"); checkNumeric("FresnelS(2.5+I)", // "105.72873498286874+I*116.14801684869202"); checkNumeric("FresnelS({1.5, 2.5, 3.5})", // "{0.6975049600820931,0.619181755819593,0.41524801197243755}"); check("FresnelS(0)", // "0"); check("FresnelS(Infinity)", // "1/2"); check("FresnelS(-Infinity)", // "-1/2"); check("FresnelS(I*Infinity)", // "-I*1/2"); check("FresnelS(-I*Infinity)", // "I*1/2"); check("FresnelS(-z)", // "-FresnelS(z)"); check("FresnelS(I*z)", // "-I*FresnelS(z)"); checkNumeric("FresnelS(1.8)", // "0.45093876926758314"); check("D(Fresnels(x),x)", // "Sin(1/2*Pi*x^2)"); } @Test public void testFrobeniusNumber() { // message FrobeniusNumber: The first argument {0,0,0,0} of FrobeniusNumber should be a // non-empty list of positive integers. check("FrobeniusNumber({0,0,0,0})", // "FrobeniusNumber({0,0,0,0})"); check("FrobeniusNumber({1,-2,3})", // "FrobeniusNumber({1,-2,3})"); check("FrobeniusNumber({ })", // "FrobeniusNumber({})"); check("FrobeniusNumber({1->0})", // "FrobeniusNumber({1->0})"); check("FrobeniusNumber({1000, 1476, 3764, 4864, 4871, 7773})", // "47350"); check("FrobeniusNumber({12,16,20,27})", // "89"); check("Table(FrobeniusNumber({i, i + 1}), {i, 15})", // "{-1,1,5,11,19,29,41,55,71,89,109,131,155,181,209}"); } @Test public void testFrobeniusSolve() { // iter limit check("FrobeniusSolve({1,5,10,25},1317624576693539401)", // "Hold(FrobeniusSolve({1,5,10,25},1317624576693539401))"); check("FrobeniusSolve({-1/2,-2,3},89)", // "FrobeniusSolve({-1/2,-2,3},89)"); check("FrobeniusSolve({-1,-2,3}, 47349, 3)", // "FrobeniusSolve({-1,-2,3},47349,3)"); check("FrobeniusSolve(Null, Null)", // "FrobeniusSolve(Null,Null)"); check("FrobeniusSolve({1000, 1476, 3764, 4864, 4871, 7773}, 47349)", // "{{5,2,4,2,3,0},{6,1,0,4,1,2},{7,5,1,3,3,0},{15,9,3,0,0,1},{17,12,0,1,0,1}}"); check("FrobeniusSolve({1000, 1476, 3764, 4864, 4871, 7773}, 47350)", // "{}"); check("FrobeniusSolve({1000, 1476, 3764, 4864, 4871, 7773}, 47351)", // "{{1,2,3,3,2,1},{3,5,0,4,2,1},{9,3,1,0,3,2},{12,13,3,0,1,0},{14,16,0,1,1,0},{32,2,\n" + "2,0,1,0}}"); check("FrobeniusSolve({2, 3, 4}, 29)", // "{{0,3,5},{0,7,2},{1,1,6},{1,5,3},{1,9,0},{2,3,4},{2,7,1},{3,1,5},{3,5,2},{4,3,3},{\n" + "4,7,0},{5,1,4},{5,5,1},{6,3,2},{7,1,3},{7,5,0},{8,3,1},{9,1,2},{10,3,0},{11,1,1},{\n" + "13,1,0}}"); check("frobeniussolve({ 12, 16, 20, 27},123 )", // "{{0,1,4,1},{0,6,0,1},{1,4,1,1},{2,2,2,1},{3,0,3,1},{4,3,0,1},{5,1,1,1},{8,0,0,1}}"); check("frobeniussolve({ 12, 16, 20, 27},89 )", // "{}"); check("frobeniussolve({1, 5, 10, 25}, 42)", // "{{2,0,4,0},{2,1,1,1},{2,2,3,0},{2,3,0,1},{2,4,2,0},{2,6,1,0},{2,8,0,0},{7,0,1,1},{\n" + "7,1,3,0},{7,2,0,1},{7,3,2,0},{7,5,1,0},{7,7,0,0},{12,0,3,0},{12,1,0,1},{12,2,2,0},{\n" + "12,4,1,0},{12,6,0,0},{17,0,0,1},{17,1,2,0},{17,3,1,0},{17,5,0,0},{22,0,2,0},{22,\n" + "2,1,0},{22,4,0,0},{27,1,1,0},{27,3,0,0},{32,0,1,0},{32,2,0,0},{37,1,0,0},{42,0,0,\n" + "0}}"); check("FrobeniusSolve({12, 16, 20, 27}, 123, 2)", // "{{0,1,4,1},{0,6,0,1}}"); } @Test public void testFromCharacterCode() { check("FromCharacterCode({97,45,51})", // "a-3"); // undefined negative codes check("FromCharacterCode(-42)", // "FromCharacterCode(-42)"); check("FromCharacterCode({65,-10,67})", // "FromCharacterCode({65,-10,67})"); check("FromCharacterCode({65,66,67,68,32,97,98,99,100})", // "ABCD abcd"); check("ToCharacterCode(\"ABCD abcd\")", // "{65,66,67,68,32,97,98,99,100}"); } @Test public void testFromContinuedFraction() { // check( // "Sqrt(63)/3", // // "Sqrt(7)"); check("Sqrt(20541813482020954028041088271392963168222371159)/4727827637485585077281", // "Sqrt(919)"); check("FromContinuedFraction({1, 4, 2, {3, 1}})", // "1/238*(287+Sqrt(21))"); // check( // // "FromContinuedFraction({30,{3,5,1,2,1,2,1,1,1,2,3,1,19,2,3,1,1,4,9,1,7,1,3,6,2,11,1,1,1,29,1,1,1,11,2,6,3,1,7,1,9,4,1,1,3,2,19,1,3,2,1,1,1,2,1,2,1,5,3,60}}) // ", // // "Sqrt(919)"); check("FromContinuedFraction({1, 4, 2, {3, 1}}) ", // "1/238*(287+Sqrt(21))"); check("FromContinuedFraction({1, 2, 3, 4, 5})", // "225/157"); check("FromContinuedFraction({-2, 1, 9, 7, 1, 2})", // "-256/233"); check("FromContinuedFraction({2, 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8}) // N", // "2.71828"); check("FromContinuedFraction({{1}}) ", // "1/2*(1+Sqrt(5))"); check("FromContinuedFraction({0,-7,{-1,-1,-18,-1,-1,-9,-76,-9}})", // "2/11*(1-Sqrt(3))"); check("FromContinuedFraction({-16,{-1,-1,-2,-1,-1,-32}})", // "-5*Sqrt(11)"); check("FromContinuedFraction({-8,{-2,-1,-2,-1,-2,-16}})", // "-Sqrt(70)"); check("FromContinuedFraction({a/b,{1,2,13,2,2,1,54}})", // "-15617/578+Sqrt(256224053)/578+a/b"); check("FromContinuedFraction({27,{1,2,2,13,2,2,1,54}})", // "16*Sqrt(3)"); check("FromContinuedFraction({8,{2,1,2,1,2,16}})", // "Sqrt(70)"); check("FromContinuedFraction({16,{1,1,2,1,1,32}})", // "5*Sqrt(11)"); check("FromContinuedFraction({0,1,1,1,{2}})", // "1/7*(3+Sqrt(2))"); check("FromContinuedFraction({3,{1,1,1,1,6}})", // "Sqrt(13)"); check("FromContinuedFraction({0,1,{8,3,34,3}})", // "1/5*(1+2*Sqrt(3))"); check("FromContinuedFraction({8,{2,1,2,1,2,16}})", // "Sqrt(70)"); check("FromContinuedFraction({0,1,{108,2,4,4,4,2}})", // "1/11*(1+7*Sqrt(2))"); check("FromContinuedFraction({1,1,1,1,1})", // "8/5"); check("FromContinuedFraction({2,3,4,5})", // "157/68"); check("ContinuedFraction(157/68)", // "{2,3,4,5}"); } @Test public void testFromDigits() { // https://oeis.org/A023391 check("NestList(FromDigits(IntegerDigits(#, 8), 9) &, 8, 50)", // "{8,9,10,11,12,13,14,15,16,18,20,22,24,27,30,33,37,41,46,51,57,64,81,100,121,145,\n" + "181,221,275,345,433,541,761,1036,1471,2014,2787,3927,5533,8537,13555,21441,34102,\n" + "60891,103386,185033,329032,651411,1286139,2551404,5654254}"); check("FromDigits({0})", // "0"); check("FromDigits({1,2,3})", // "123"); check("FromDigits({1,1,1,1,0,1,1}, 2)", // "123"); check("FromDigits /@ IntegerDigits(Range(-10, 10))", // "{10,9,8,7,6,5,4,3,2,1,0,1,2,3,4,5,6,7,8,9,10}"); check("FromDigits(\"123\")", // "123"); check("FromDigits(\"1111011\", 2)", // "123"); check("FromDigits(\"0\")", // "0"); check("FromDigits(\"789ABC\")", // "790122"); check("FromDigits(\"789ABC\", 16)", // "7903932"); check("FromDigits(\"789abc\")", // "790122"); check("FromDigits(\"789abc\", 16)", // "7903932"); check("FromDigits(\"1A3C\")", // "2042"); } @Test public void testFromRomanNumeral() { check("FromRomanNumeral(\"MDCLXVI\")", // "1666"); // TODO add message for invalid roman number check("FromRomanNumeral(\"MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM\")", // "36000"); // zero as special case represented by 'N' check("FromRomanNumeral(\"N\")", // "0"); check("FromRomanNumeral(\"MCMXXXVII\")", // "1937"); check("FromRomanNumeral(\"MMMDCCXLVIII\")", // "3748"); check( "FromRomanNumeral({\"ci\", \"cii\", \"ciii\", \"civ\", \"cv\", \"cvi\", \"cvii\", \"cviii\"})", // "{101,102,103,104,105,106,107,108}"); } @Test public void testFullDefinition() { check("FullDefinition(ArcSinh)", // "Attributes(ArcSinh)={Listable,NumericFunction,Protected}\n" // + "\n" // + "ArcSinh(I/Sqrt(2))=I*1/4*Pi\n" // + "\n" // + "ArcSinh(Undefined)=Undefined\n" // + "\n" // + "ArcSinh(Infinity)=Infinity\n" // + "\n" // + "ArcSinh(I*Infinity)=Infinity\n" // + "\n" // + "ArcSinh(I)=I*1/2*Pi\n" // + "\n" // + "ArcSinh(0)=0\n" // + "\n" // + "ArcSinh(I*1/2)=I*1/6*Pi\n" // + "\n" // + "ArcSinh(I*1/2*Sqrt(3))=I*1/3*Pi\n" // + "\n" // + "ArcSinh(ComplexInfinity)=ComplexInfinity"); check("a(x_):=b(x,y);b[u_,v_]:={{u,v},a}", // ""); check("a(test)", // "{{test,y},a}"); check("FullDefinition(a)", // "a(x_):=b(x,y)\n" // + "\n" // + "b(u_,v_):={{u,v},a}"); } @Test public void testFullForm() { check("N( 1/2+8 ,12)//FullForm", // "8.5`"); check("N( Pi/13^101 ,30)//FullForm", // "9.74700726352830962565070727338`30*^-113"); check("N(Sin(Pi/7),30)//FullForm", // "4.33883739117558120475768332848`30*^-1"); check("Association(A->1,B->2,C->3,D->4) // FullForm", // "Association(Rule(A, 1), Rule(B, 2), Rule(C, 3), Rule(D, 4))"); check("( _. ) // FullForm", // "Optional(Blank())"); check("Optional(Blank())", // "_."); check("( _:2 ) // FullForm", // "Optional(Blank(), 2)"); check("Optional(Blank(),2)", // "_:2"); check("( x_. ) // FullForm", // "Optional(Pattern(x, Blank()))"); check("Optional(Pattern(x, Blank()))", // "x_."); check("( x_:2 ) // FullForm", // "Optional(Pattern(x, Blank()), 2)"); check("Optional(Pattern(x,Blank()),2)", // "x_:2"); check("Hold(Function(#[[1]]*#[[2]])[SignOfFactor(Map(NormalizeSumFactors,u))]) // FullForm", // "Hold(Function(Times(Part(Slot(1), 1), Part(Slot(1), 2)))[signoffactor(Map(normalizesumfactors, u))])"); check("FullForm(a:=b)", "Null"); } @Test public void testFullSimplify() { // https://github.com/axkr/symja_android_library/issues/856 check("FullSimplify((4+3*Sqrt(2)+Sqrt(3)+Sqrt(6))/(2+Sqrt(2)+Sqrt(3)))", // "1+Sqrt(2)"); check("FullSimplify((Cosh(x) - 1)/(Cosh(x) + Sinh(x))-(1 - Exp(-x))^2/2)", // "0"); check("FullSimplify(Sign(z)*Abs(z))", // "z"); check("FullSimplify( Sqrt(9-4*Sqrt(5)))", // "-2+Sqrt(5)"); check("FullSimplify(Gamma(z) / Gamma(z-2))", // "(-2+z)*(-1+z)"); check("FullSimplify( Sqrt(-9+4*Sqrt(5)))", // "I*(-2+Sqrt(5))"); // MMA factorizes this to (-2 + x)*(-1 + x) ? Although the ComplexityFunction returns 9 for both // expressions check("2-3*x+x^2 // FullSimplify", // "2-3*x+x^2"); // MMA doesn't factorize this check("f(2-3*Sin(x)+Sin(x)^2) // FullSimplify", // "f(2-3*Sin(x)+Sin(x)^2)"); check("FullSimplify(x^2,ComplexInfinity)", // "x^2"); // see Logarithms#test0128() Rubi rule 2447 ==> -(Sqrt(-(e/d))/(2*e)) check( "FullSimplify( (d-2*d*Sqrt(-e/d)*x-e*x^2)/(2*d^2*Sqrt(-e/d)+4*d*e*x-2*d*e*Sqrt(-e/d)*x^2) )", // "1/(2*d*Sqrt(-e/d))"); check( "PolynomialQuotientRemainder((d-2*d*Sqrt(-e/d)*x-e*x^2),(2*d^2*Sqrt(-e/d)+4*d*e*x-2*d*e*Sqrt(-e/d)*x^2),x)", // "{1/(2*d*Sqrt(-e/d)),0}"); // check("FullSimplify((1/(d + e*x^2) * (1-((2*x*(d*Sqrt(-(e/d)) + e*x))/(d + e*x^2)))) / " // // + "(-((4*e*x^2*(d*Sqrt(-(e/d)) + e*x))/(d + e*x^2)^2) + (2*e*x)/(d + e*x^2) + // (2*(d*Sqrt(-(e/d)) + e*x))/(d + // e*x^2)))", // // "(d-2*d*Sqrt(-e/d)*x-e*x^2)/(2*d^2*Sqrt(-e/d)+4*d*e*x-2*d*e*Sqrt(-e/d)*x^2)"); check("FullSimplify((1/(d + e*x^2) * (1-((2*x*(d*Sqrt(-(e/d)) + e*x))/(d + e*x^2)))) / " // + "(-((4*e*x^2*(d*Sqrt(-(e/d)) + e*x))/(d + e*x^2)^2) + (2*e*x)/(d + e*x^2) + (2*(d*Sqrt(-(e/d)) + e*x))/(d + e*x^2)))", // "-Sqrt(-e/d)/(2*e)"); check( "FullSimplify(Numerator((1/(d + e*x^2) * (1-((2*x*(d*Sqrt(-(e/d)) + e*x))/(d + e*x^2)))) / " // + "(-((4*e*x^2*(d*Sqrt(-(e/d)) + e*x))/(d + e*x^2)^2) + (2*e*x)/(d + e*x^2) + (2*(d*Sqrt(-(e/d)) + e*x))/(d + e*x^2))))", // "1+(-2*x*(d*Sqrt(-e/d)+e*x))/(d+e*x^2)"); check( "FullSimplify(Denominator((1/(d + e*x^2) * (1-((2*x*(d*Sqrt(-(e/d)) + e*x))/(d + e*x^2)))) / " // + "(-((4*e*x^2*(d*Sqrt(-(e/d)) + e*x))/(d + e*x^2)^2) + (2*e*x)/(d + e*x^2) + (2*(d*Sqrt(-(e/d)) + e*x))/(d + e*x^2))))", // "(2*e*(d+e*x^2))/(-d*Sqrt(-e/d)+2*e*x+e*Sqrt(-e/d)*x^2)"); check("Together( 1+(-2*x*(d*Sqrt(-e/d)+e*x))/(d+e*x^2) )", // "(d-2*d*Sqrt(-e/d)*x-e*x^2)/(d+e*x^2)"); check("Together( (d*(2*d*Sqrt(-e/d)+4*e*x-2*e*Sqrt(-e/d)*x^2))/(d+e*x^2) )", // "(2*d^2*Sqrt(-e/d)+4*d*e*x-2*d*e*Sqrt(-e/d)*x^2)/(d+e*x^2)"); // #github #152 check("FullSimplify(Sqrt(-9-4*Sqrt(5)))", // "I*(2+Sqrt(5))"); // check("FullSimplify( Sqrt(9-4*Sqrt(5)))", // // "-2+Sqrt(5)"); check("FullSimplify(Sqrt(9+4*Sqrt(5)))", // "2+Sqrt(5)"); check("FullSimplify(-Sqrt(9-4*Sqrt(5))+Sqrt(9+4*Sqrt(5)))", // "4"); check("-Sqrt(9-4*Sqrt(5))+Sqrt(9+4*Sqrt(5.0))", // "4.0"); check("FullSimplify(f(x*y,-Sqrt(9-4*Sqrt(5))+Sqrt(9+4*Sqrt(5)),Sqrt(-9-4*Sqrt(5))))", // "f(x*y,4,I*(2+Sqrt(5)))"); check("FullSimplify(Sqrt(2) + Sqrt(3) - Sqrt(5 + 2*Sqrt(6)))", // "0"); check("FullSimplify(Cos(n*ArcCos(x)) == ChebyshevT(n, x))", // "True"); // check("Factor((d^2+2*d*e*x^2+e^2*x^4))",// // "(d+e*x^2)^2"); // check("Together(D( 1-(2*x*(d*Sqrt(-(e/d)) + e*x))/(d + e*x^2),x))",// // "(-2*d^2*Sqrt(-e/d)-4*d*e*x+2*d*e*Sqrt(-e/d)*x^2)/(d^2+2*d*e*x^2+e^2*x^4)"); check("FullSimplify(D( 1-(2*x*(d*Sqrt(-(e/d)) + e*x))/(d + e*x^2),x))", // "2/(-Sqrt(-d/e)-2*x+(e*x^2)/(d*Sqrt(-e/d)))"); check("p = Expand((x + 1)^2 (x + 2)^2 (x + 3)^3)", // "108+432*x+711*x^2+625*x^3+318*x^4+94*x^5+15*x^6+x^7"); check("FullSimplify(p)", // "(1+x)^2*(2+x)^2*(3+x)^3"); check("FullSimplify(Cosh(x)/(b*Cosh(x)+c*Sinh(x)))", // "1/(b+c*Tanh(x))"); check("FullSimplify((b*Cosh(x)+c*Sinh(x))/Cosh(x))", // "b+c*Tanh(x)"); check("Simplify(Cos(n*ArcCos(x)) == ChebyshevT(n, x))", // "-ChebyshevT(n,x)+Cos(n*ArcCos(x))==0"); // FullSimplify uses FunctionExpand and can test the equation: check("FullSimplify(Cos(n*ArcCos(x)) == ChebyshevT(n, x))", // "True"); check("FullSimplify(Cosh(x)+Sinh(x))", // "E^x"); } @Test public void testFullSimplifyIssue856() { // github issue #856 check("FullSimplify( (2 *Sqrt(6) - Sqrt(3)) * (Sqrt(2) + 4))", // "7*Sqrt(6)"); check("FullSimplify( (2 *Sqrt(6) - Sqrt(3)) * (-Sqrt(2) - 4) )", // "-7*Sqrt(6)"); check("FullSimplify( (2 *Sqrt(6) - Sqrt(3)) / (Sqrt(2) - 4) )", // "-Sqrt(3/2)"); } @Test public void testFunction() { EvalEngine.resetModuleCounter4JUnit(); // check("(p + #) & /. p -> q", // // "q+#1&"); // check("fufufu=Function({x},Function({y},Function({z},x+y+z)))", // // "Function({x},Function({y},Function({z},x+y+z)))"); // message: Parameter specification f(x) in Function(f(x),g(a)) should be a symbol or a list of // symbols. check("Function(f(x), g(a))", // "Function(f(x),g(a))"); // Function: Function called with 4 arguments; between 1 and 3 arguments are expected. check("Function(a,b,c,d)", // "Function(a,b,c,d)"); check("g = (#1 + #2) &[3,4]", // "7"); check("(4*# + (2*# &)[a] &)[b]", // "2*a+4*b"); check("fufufu=Function({x},Function({y},Function({z},x+y+z)))", // "Function({x},Function({y},Function({z},x+y+z)))"); check("fufufu(a)", // "Function({y$1},Function({z$1},a+y$1+z$1))"); check("fufufu(y)", // "Function({y$2},Function({z$2},y+y$2+z$2))"); check("fufufu(y)[z]", // "Function({z$3$4},y+z+z$3$4)"); check("fufufu(y)[x][z]", // "x+y+z"); check("Function({x, y}, x^2 + y^3)[a, b]", // "a^2+b^3"); check("f(x, ##, y, ##) &(a, b, c, d)", // "f(x,a,b,c,d,y,a,b,c,d)"); check("f(x, ##2, y, ##3) &(a, b, c, d)", // "f(x,b,c,d,y,c,d)"); check("If(# > 5, #, False) &(2)", // "False"); check("{##} &(a, b, c)", // "{a,b,c}"); check("{##2} &(a, b, c)", // "{b,c}"); check("Table(a(i0, j), ##) & @@ {{i0, 3}, {j, 2}}", // "{{a(1,1),a(1,2)},{a(2,1),a(2,2)},{a(3,1),a(3,2)}}"); check("Map(Function(-#),-z+w)", // "-w+z"); check("f(#1) &(x, y, z)", // "f(x)"); check("17 & /@ {1, 2, 3}", // "{17,17,17}"); check("(p + #) & /. p -> q", // "q+#1&"); check("FullForm(x -> y &)", // "Function(Rule(x, y))"); check("FullForm(x -> (y &))", // "Rule(x, Function(y))"); check("FullForm(Mod(#, 5) == 1 &)", // "Function(Equal(Mod(Slot(1), 5), 1))"); check("FullForm(a == b && c == d &)", // "Function(And(Equal(a, b), Equal(c, d)))"); check("FullForm(Mod(#, 3) == 1 && Mod(#, 5) == 1 &)", // "Function(And(Equal(Mod(Slot(1), 3), 1), Equal(Mod(Slot(1), 5), 1)))"); check("({#1,Plus(##2)}&) @@@(Range/@Range(2,3))", // "{{1,2},{1,5}}"); check("(#[[1]]+#[[2]]&) /@{{1,2},{3,4,5},{6,7}}", // "{3,7,13}"); check("((#+##&) @@#&) /@{{1,2},{2,2,2},{3,4}}", // "{4,8,10}"); check("Function({x,y},x y)[2,3]", // "6"); check("Function(x,2 x)[5]", // "10"); check("(Function@@{{x},x==2})[2]", // "True"); // new lambda operator |-> check("Array(x |-> 1+x^2, 10)", // "{2,5,10,17,26,37,50,65,82,101}"); check("(x |-> {#1, x}) /@ #2 &[n0, {n1, n2, n3, n4, n5}]", // "{{n0,n1},{n0,n2},{n0,n3},{n0,n4},{n0,n5}}"); check("Array(x \\[Function] 1+x^2, 10)", // "{2,5,10,17,26,37,50,65,82,101}"); check("(x \\[Function] {#1, x}) /@ #2 &[n0, {n1, n2, n3, n4, n5}]", // "{{n0,n1},{n0,n2},{n0,n3},{n0,n4},{n0,n5}}"); check("h := Function({x}, Hold(1+x))", // ""); check("h(1 + 1)", // "Hold(1+2)"); check("h := Function({x}, Hold(1+x), HoldAll)", // ""); check("h(1 + 1)", // "Hold(1+1+1)"); } @Test public void testFunctionDomain() { check("FunctionDomain(ArcCoth(2+3*x)*ArcSec(7+2/3*x), x)", // "x<=-12||(-9<=x&&x<-1)||x>-1/3"); check("FunctionDomain(ArcSin(2+3*x), x)", // "-1<=x&&x<=-1/3"); check("FunctionDomain(Sqrt(2+3*x), x)", // "x>=-2/3"); check("FunctionDomain(Sqrt(-2-3*x), x)", // "x<=-2/3"); check("FunctionDomain((x^2+x+1)/(-7+x^2), x)", // "x<-Sqrt(7)||(-Sqrt(7)Sqrt(7)"); check("FunctionDomain((x^2+x+1)/x, x)", // "x<0||x>0"); check("FunctionDomain(1/(x^2), x)", // "x<0||x>0"); check("FunctionDomain(Sqrt(-3-x), x)", // "x<=-3"); check("FunctionDomain(Sqrt(x-3), x)", // "x>=3"); check("FunctionDomain(Sqrt(x+3), x)", // "x>=-3"); check("FunctionDomain((x+3)^-3, x)", // "x<-3||x>-3"); check("FunctionDomain((x+3)^3, x)", // "True"); check("FunctionDomain((2+x)^(-3), x)", // "x<-2||x>-2"); check("FunctionDomain(Gamma(-3*x+2), x)", // "2-3*x∉Integers&&x<2/3"); check("FunctionDomain(ArcCosh(x-1), x)", // "x>=2"); check("FunctionDomain(Tan(3+x^2), x)", // "1/2+(3+x^2)/Pi∉Integers"); check("FunctionDomain(Log(x-1), x)", // "x>1"); check("FunctionDomain(ArcCos(x)*Log(x), x)", // "0=-1"); check("FunctionDomain(Tan(3+x), x)", // "1/2+(3+x)/Pi∉Integers"); check("FunctionDomain(x/(x^4 - 1), x)", // "x<-1||(-11"); check("FunctionDomain(x/(x^4 - 1)+Tan(2+x), x)", // "(1/2+(2+x)/Pi∉Integers&&x<-1)||(1/2+(2+x)/Pi∉Integers&&-1\n" + "1)"); // message FunctionDomain: Unable to find the domain with the available methods. check("FunctionDomain(Log(Tan(x) - 1), x)", // "FunctionDomain(Log(-1+Tan(x)),x)"); } @Test public void testFunctionPeriod() { check("FunctionPeriod(E^Sin(x), x)", // "2*Pi"); check("FunctionPeriod(Sin(x), x)", // "2*Pi"); // TODO implement for multiple variables check("FunctionPeriod(Cos(x) + Sin(y), {x, y})", // "FunctionPeriod(Cos(x)+Sin(y),{x,y})"); } @Test public void testFunctionRange() { // TODO // check("FunctionRange(Sqrt(x^2 - 1)/x, x, y)", // // ""); // check( // "FunctionRange(E^x, x, y)", // // "y>0"); check("FunctionRange(LogIntegral(a), a, b)", // "True"); check("FunctionRange(x^2-1, x, y)", // "y>=-1"); check("FunctionRange(x/(1 + x^2), x, y)", // "-1/2<=y<=1/2"); check("FunctionRange(1/(1 + x^2), x, y)", // "0<=y<=1"); check("FunctionRange(Sqrt(Sin(2*x)),x,y)", // "0<=y<=1"); check("FunctionRange(Sin(x)*Cos(x),x,y)", // "-1<=y<=1"); check("FunctionRange(Sin(x),x,y)", // "-1<=y<=1"); check("FunctionRange(Cos(x),x,y)", // "-1<=y<=1"); } @Test public void testFunctionURL() { assertEquals(ID.LINE_NUMBER_OF_JAVA_CLASS.length, ID.ZTransform + 1); checkRegex("FunctionURL(NIntegrate)", // "^.+L?\\d$" // "https://github.com/axkr/symja_android_library/blob/master/symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/reflection/system/NIntegrate.java#L771" ); } @Test public void testGamma() { check("Gamma(-9223372036854775808/11,-3.141592653589793,3/4)", // "-1.0032310722904763*10^104759677232087062"); check("Gamma(4,3)", // "78/E^3"); check("Gamma(Underflow())", // "Overflow()"); check("Log(Gamma(1.*^20))", // "Overflow()"); check("Gamma(-1.0000)", // "ComplexInfinity"); check("N(Gamma(-42), 100)", // "ComplexInfinity"); check("N(Gamma(15/10, 75/10), 100)", // "0.001609963228272320187037891277384183535570037262441668777093667293610308190983760142167627458859492548"); check("N(Gamma(15/10+2*I, 75/10-1/3*I), 30)", // "-0.0002066609364277930243748741602+I*(-0.00168711069242446915572696537201)"); // Iteration limit check("Gamma(1009,-9223372036854775807/9223372036854775808)", "Hold(Gamma(1009,-9223372036854775807/9223372036854775808))"); check("Gamma(-9223372036854775808/11,0.5)", // "Gamma(-8.38488*10^17,0.5)"); check("Gamma(2147483647)", // "Hold(Gamma(2147483647))"); check("Gamma(a,b,Infinity)", // "Gamma(a,b)"); check("Gamma(4,a,0)", // "-6+Gamma(4,a)"); check("Gamma(42,0,b)", // "33452526613163807108170062053440751665152000000000-Gamma(42,b)"); check("{Gamma(2.2), Gamma(1.5, 7.5), Gamma(1, 1.1, 2.2)}", // "{1.1018,0.00160996,0.222068}"); check("Gamma(2.3 + I)", // "0.719141+I*0.540614"); check("Gamma(2.20000000000000000000000000000000000000000)", // "1.10180249087971273276914198622299648082418"); check("N(Gamma(100.000000000000000000000000000+374.000000000000000000000000000*I), 30)", // "47.4294943677064514689542753376+I*(-32.7488916473624576880974867017)"); check("Gamma(1/2, a*x)", // "Gamma(1/2,a*x)"); check("Gamma(3, a*x)", // "Gamma(3,a*x)"); check("Gamma(0)", // "ComplexInfinity"); check("Gamma(0.0+I*0.0)", // "ComplexInfinity"); check("Table(Gamma(x+I*y), {x,-0.5, 0.5, 1/4}, {y,-0.5, 0.5, 1/4})", // "{{-1.58148+I*0.0548502,-2.75473+I*0.0310004,-3.54491,-2.75473+I*(-0.0310004),-1.58148+I*(-0.0548502)},{-1.31815+I*1.01078,-2.77536+I*1.61484,-4.90167,-2.77536+I*(-1.61484),-1.31815+I*(-1.01078)},{-0.399279+I*1.60339,-0.524105+I*3.76716,ComplexInfinity,-0.524105+I*(-3.76716),-0.399279+I*(-1.60339)},{0.515524+I*1.30733,1.65113+I*1.83788,3.62561,1.65113+I*(-1.83788),0.515524+I*(-1.30733)},{0.818164+I*0.763314,1.38511+I*0.673182,1.77245,1.38511+I*(-0.673182),0.818164+I*(-0.763314)}}"); check("Table(Gamma(x+I ), {x,-10.0, 10.0, 1/2})", // "{5.57498*10^-8+I*5.54232*10^-8,-1.68355*10^-7+I*1.86667*10^-7,-6.12921*10^-7+I*(-4.98482*10^-7),1.4127*10^-6+I*(-1.94169*10^-6),6.01477*10^-6+I*3.87342*10^-6,-0.0000100663+I*0.0000179171,-0.0000519916+I*(-0.0000249726),0.00005758+I*(-0.000144445),0.000388914+I*0.000122817,-0.000229825+I*0.00099647,-0.0024563+I*(-0.000347985),0.00026757+I*(-0.00571041),0.0126295+I*(-0.000716374),0.00450635+I*0.0259644,-0.0498016+I*0.015495,-0.0417366+I*(-0.0863691),0.13391+I*(-0.0962865),0.190711+I*0.174186,-0.171533+I*0.326483,-0.460252+I*(-0.0705685),-0.15495+I*(-0.498016),0.300695+I*(-0.424968),0.498016+I*(-0.15495),0.575315+I*0.0882107,0.652965+I*0.343066,0.774762+I*0.707631,0.962865+I*1.3391,1.22927+I*2.54384,1.5495+I*4.98016,1.75862+I*10.13271,1.21784+I*21.47013,-2.21893+I*47.35583,-15.38094+I*108.5685,-59.55994+I*258.2382,-200.8541+I*636.0298,-645.3778+I*1618.988,-2042.009+I*4251.355,-6459.321+I*11497.03,-20587.42+I*31968.83,-66401.27+I*91265.46,-217255.6+I*267132.0}"); check("Refine(Gamma(n), Element(n,Integers)&&n>=0)", // "(-1+n)!"); check("Gamma(-1)", // "ComplexInfinity"); check("Gamma(Infinity)", // "Infinity"); check("Gamma(-Infinity)", // "Indeterminate"); check("Gamma(I*Infinity)", // "0"); check("Gamma(-I*Infinity)", // "0"); check("Gamma(ComplexInfinity)", // "Indeterminate"); checkNumeric("Gamma(1.5,7.5)", // "0.0016099632282723204"); checkNumeric("LogGamma(1.5)", // "-0.12078223763524548"); checkNumeric("Gamma(0.5+0.5*-0.5, -0.5*-0.5)", // "0.9293237832774184"); check("Table(Gamma(-x+0.5*y, x*y), {x,-0.5, 0.5, 1/4}, {y,-0.5, 0.5, 1/4})", // "{{0.929324,1.18798,1.77245,1.60979+I*(-0.423147),1.59749+I*(-0.372071)}," // + "{1.62343,1.91573,3.62561,2.00338+I*(-0.886162),1.77245+I*(-0.737708)}," // + "{ComplexInfinity,ComplexInfinity,Infinity,7.53394,3.62561}," // + "{-3.54491+I*(-4.93464),-1.04856+I*(-6.70384),ComplexInfinity,2.69605,1.62343}," // + "{-5.44839+I*(-0.614248),-5.56253+I*(-4.27276),ComplexInfinity,2.41664,1.20262}}"); check("Table(Gamma(-x+0.5*I*y, x+I*y), {x,-0.5, 0.5, 1/4}, {y,-0.5, 0.5, 1/4})", // "{{0.454825+I*1.15991,0.929691+I*1.43063,1.77245+I*(-1.68993),0.929691+I*(-1.43063),0.454825+I*(-1.15991)}," // + "{0.193901+I*1.01773,0.624332+I*1.42459,1.51824+I*(-2.10737),0.624332+I*(-1.42459),0.193901+I*(-1.01773)}," // + "{0.113061+I*0.824051,0.642244+I*1.21171,Infinity,0.642244+I*(-1.21171),0.113061+I*(-0.824051)}," // + "{0.12069+I*0.587019,0.604734+I*0.69309,1.20262,0.604734+I*(-0.69309),0.12069+I*(-0.587019)}," // + "{0.114848+I*0.359991,0.391432+I*0.335157,0.590691,0.391432+I*(-0.335157),0.114848+I*(-0.359991)}}"); check("Gamma(-3/4, 0)", // "ComplexInfinity"); check("Gamma(10, -1)", // "133496*E"); check("Gamma(1/2, x)", // "Gamma(1/2,x)"); check("Gamma(8)", // "5040"); check("Gamma(1/2)", // "Sqrt(Pi)"); // check("Gamma(1.0+I)", ""); checkNumeric("Gamma(2.2)", // "1.1018024908797126"); } @Test public void testGammaRegularized() { check("N(GammaRegularized(5, 3,{2,3,5,7}), 50)", // "{-0.13208373813251677697126440853762923150933999928159," // + "0," // + "0.37476995945855965484415039060643335707553920092208," // + "0.64227163664170072066013711492328393408012799819306}"); check("N(GammaRegularized(2, 33/10), 50)", // "0.15859761982533202341609593038851663410395766708586"); checkNumeric("N(GammaRegularized(2 + 3 I, 4 - I))", // "-1.152239855432952+I*(-0.23324343668111)"); check("GammaRegularized(1, 1.5)", // "0.22313"); check("GammaRegularized(2, 2.2)", // "0.35457"); check("GammaRegularized(2, 3.3)", // "0.158598"); check("GammaRegularized(2, 3.3, 3.4)", // "0.0117552"); // TODO improve output Format to E^(-x)-E^(-y) check("GammaRegularized(1,x,y)", // "E^(-x)-1/E^y"); check("GammaRegularized(-42,x,y)", // "0"); // check("GammaRegularized(a,z1,z2)", "GammaRegularized(a,z1)-GammaRegularized(a,z2)"); check("GammaRegularized(1/2, z)", // "Erfc(Sqrt(z))"); check("GammaRegularized(-4, z)", // "0"); check("GammaRegularized(12, 0)", // "1"); check("GammaRegularized(-42, 0)", // "0"); check("GammaRegularized(1, x)", // "E^(-x)"); } @Test public void testGather() { check("Gather({1, 7, 3, 7, 2, 3, 9})", // "{{1},{7,7},{3,3},{2},{9}}"); check("Gather({1/3, 2/6, 1/9})", // "{{1/3,1/3},{1/9}}"); check("Gather({{a, 1}, {b, 1}, {a, 2}, {d, 1}, {b, 3}}, (First(#1) == First(#2)) &)", // "{{{a,1},{a,2}},{{b,1},{b,3}},{{d,1}}}"); check("Gather({1,2,3,2,3,4,5,6,2,3})", // "{{1},{2,2,2},{3,3,3},{4},{5},{6}}"); check("Gather(Range(0, 3, 1/3), Floor(#1) == Floor(#2) &)", // "{{0,1/3,2/3},{1,4/3,5/3},{2,7/3,8/3},{3}}"); } @Test public void testGlaisher() { check("Glaisher // N", // "1.28243"); check("N(Glaisher,50)", // "1.282427129100622636875342568869791727767688927325"); } @Test public void testGatherBy() { check("GatherBy({{1, 2}, {2, 1}, {3, 5}, {5, 1}, {2, 2, 2}}, {})", // "{{{1,2}},{{2,1}},{{3,5}},{{5,1}},{{2,2,2}}}"); check("GatherBy({{1, 3}, {2, 2}, {1, 1}}, Total)", // "{{{1,3},{2,2}},{{1,1}}}"); check("GatherBy({\"xy\", \"abc\", \"ab\"}, StringLength)", // "{{xy,ab},{abc}}"); check("GatherBy({{2, 0}, {1, 5}, {1, 0}}, Last)", // "{{{2,0},{1,0}},{{1,5}}}"); check("GatherBy({{1, 2}, {2, 1}, {3, 5}, {5, 1}, {2, 2, 2}}, {Total, Length})", // "{{{{1,2},{2,1}}},{{{3,5}}},{{{5,1}},{{2,2,2}}}}"); check("rr=Range(10); GatherBy(rr, OddQ)", // x = Range[5000]; First[Timing[GatherBy[x, OddQ]]] "{{1,3,5,7,9},{2,4,6,8,10}}"); check("GatherBy({{a,10},{b,5},{a,7},{b,3},{b,10}}, First)", // "{{{a,10},{a,7}},{{b,5},{b,3},{b,10}}}"); check("Tuples({{a, b}, {1, 2}, {x, y}})", // "{{a,1,x},{a,1,y},{a,2,x},{a,2,y},{b,1,x},{b,1,y},{b,2,x},{b,2,y}}"); check( "GatherBy({{a,1,x},{a,1,y},{a,2,x},{a,2,y},{b,1,x},{b,1,y},{b,2,x},{b,2,y}}, {First,Last})", // "{{{{a,1,x},{a,2,x}},{{a,1,y},{a,2,y}}},{{{b,1,x},{b,2,x}},{{b,1,y},{b,2,y}}}}"); } @Test public void testGCD() { // Long.MIN_VALUE = -9223372036854775808 check("-9223372036854775808/2", // "-4611686018427387904"); check("-9223372036854775808/7", // "-9223372036854775808/7"); check("GCD(-9223372036854775808,-9223372036854775808)", // "9223372036854775808"); // Integer.MIN_VALUE = -2147483648 check("-2147483648/2", // "-1073741824"); check("GCD(-2147483648,-2147483648)", // "2147483648"); check("GCD(0,b)", // "GCD(0,b)"); check("GCD(a,a)", // "GCD(a,a)"); check("GCD(a,b)", // "GCD(a,b)"); check("GCD(3/7,12/22)", // "3/77"); check("GCD(5+3*I, 2-8*I)", // "1+I"); check("GCD(5+3*I, 2+8*I)", // "5+I*3"); check("GCD(1+5*I, 3+2*I)", // "3+I*2"); check("GCD(5+I, 2+3*I)", // "2+I*3"); check("GCD(1,I)", // "1"); check("GCD(I,I)", // "1"); check("GCD(-I,-I)", // "1"); check("GCD(-1/2, 5)", // "1/2"); check("GCD(0,Cos(b*x)[[2]])", // "GCD(0,Cos(b*x)[[2]])"); check("GCD(0, CoshIntegral(b*x))", // "GCD(0,CoshIntegral(b*x))"); check("GCD(x,x)", // "GCD(x,x)"); check("GCD(-2147483648)", // "2147483648"); check("GCD(-2147483648, -2147483648/2)", // "1073741824"); check("GCD(I)", // "1"); check("GCD(-I)", // "1"); check("GCD()", // "0"); check("GCD(10)", // "10"); check("GCD(2, 3, 5)", // "1"); check("GCD(1/3, 2/5, 3/7)", // "1/105"); check("GCD(-3, 9)", // "3"); check("GCD(b, a)", // "GCD(a,b)"); check("GCD(20, 30)", // "10"); check("GCD(-20, 30)", // "10"); check("GCD(20, -30)", // "10"); check("GCD(-20, -30)", // "10"); check("GCD(10, y)", // "GCD(10,y)"); check("GCD(4, {10, 11, 12, 13, 14})", // "{2,1,4,1,2}"); } @Test public void testGeometricMean() { checkNumeric("GeometricMean(13.261197054679151) // N", // "GeometricMean(13.261197054679151)"); checkNumeric("GeometricMean({1, 2.0, 3, 4})", // "2.213363839400643"); check("GeometricMean({Pi,E,2})", // "(2*E*Pi)^(1/3)"); check("GeometricMean({1, 2, 3, 4,5, 6, 7})", // "2^(4/7)*3^(2/7)*35^(1/7)"); check("GeometricMean({})", // "GeometricMean({})"); check("GeometricMean({2, 6, 5, 15, 10, 1})", // "3^(1/3)*Sqrt(10)"); check("GeometricMean({{5, 10}, {2, 1}, {4, 3}, {12, 15}})", // "{2*30^(1/4),2^(1/4)*Sqrt(15)}"); checkNumeric("GeometricMean(N({2, 6, 5, 15, 10, 1}))", // "4.56079359657056"); } @Test public void testGeoDistance() { // distance between Oslo and Berlin check("GeoDistance({59.914, 10.752}, {52.523, 13.412})", // "521.4299[mi]"); check("UnitConvert(GeoDistance({59.914, 10.752}, {52.523, 13.412}),\"km\")", // "839.1601[km]"); check("GeoDistance({37, -109}, {40.113, -88.261})", // "1140.843[mi]"); check("GeoDistance({30, 40}, {-40, 120})", // "7031.637[mi]"); } @Test public void testGet() { if (Config.FILESYSTEM_ENABLED) { // message: Get: Cannot open noopen-file-test.m. check("Get(\"noopen-file-test.m\")", // "True"); String pathToVectorAnalysis = LowercaseTestCase.class.getResource("/symja/VectorAnalysis.m").getFile(); // remove 'file:/' // pathToVectorAnalysis = pathToVectorAnalysis.substring(6); System.out.println(pathToVectorAnalysis); // PatternMatching.getFile(pathToVectorAnalysis, engine) evalString("Get(\"" + pathToVectorAnalysis + "\")"); check("DotProduct({a,b,c},{d,e,f}, Spherical)", // "a*d*Cos(b)*Cos(e)+a*d*Cos(c)*Cos(f)*Sin(b)*Sin(e)+a*d*Sin(b)*Sin(c)*Sin(e)*Sin(f)"); // check("Information(Sin)", ""); // check("Information(DotProduct)", ""); } } @Test public void testGoldenAngle() { // check("IntegerPart[GoldenAngle^100]", // // ""); check("NumericQ(GoldenAngle)", // "True"); check("N(GoldenAngle)", // "2.39996"); check("Attributes(GoldenAngle)", // "{Constant,Protected}"); check("FunctionExpand[GoldenAngle]", // "(3-Sqrt(5))*Pi"); } @Test public void testGoldenRatio() { check("N(GoldenRatio)", // "1.61803"); check("Log(GoldenRatio)", // "ArcCsch(2)"); } @Test public void testGroebnerBasis() { check("GroebnerBasis({x*y-2*y, 2*y^2-x^2}, {y, x})", // "{-2*x^2+x^3,-2*y+x*y,-x^2+2*y^2}"); check("GroebnerBasis({x*y-2*y, 2*y^2-x^2}, {x, y})", // "{-2*y+y^3,-2*y+x*y,x^2-2*y^2}"); check( "GroebnerBasis({-5*x^2+y*z-x-1, 2*x+3*x*y+y^2,x-3*y+x*z-2*z^2},{x,y,z}, MonomialOrder ->DegreeReverseLexicographic)", // "{x-3*y+x*z-2*z^2,2*x+3*x*y+y^2,1+x+5*x^2-y*z,-1+27*y+5*y^2-z-29*y*z+18*z^2+y*z^2-\n" + "20*z^3,6-156*y-20*y^2+6*z+174*y*z+y^2*z-104*z^2+120*z^3,180-20*x-4185*y-559*y^2+\n" + "15*y^3+162*z+4680*y*z-2808*z^2+3240*z^3,4026-20*x-106386*y-17140*y^2+4086*z+\n" + "114129*y*z-70866*z^2+78768*z^3+1560*z^4}"); check("GroebnerBasis({x^2 - 2*y^2, x*y - 3}, {x, y})", // "{-9+2*y^4,3*x-2*y^3}"); check("GroebnerBasis({x + y, x^2 - 1, y^2 - 2*x}, {x, y})", // "{1}"); check("GroebnerBasis({x^2 + y^2 + z^2 - 1, x*y - z + 2, z^2 - 2*x + 3*y}, {x, y, z})", // "{1024-832*z-215*z^2+156*z^3-25*z^4+24*z^5+13*z^6+z^8,-11552+2560*y+2197*z+2764*z^\n" + "2+443*z^3+728*z^4+169*z^5+32*z^6+13*z^7,-34656+5120*x+6591*z+5732*z^2+1329*z^3+\n" + "2184*z^4+507*z^5+96*z^6+39*z^7}"); check("GroebnerBasis({x^2 + y^2 + z^2 - 1, x*y - z + 2}, {x, y, z})", // "{4-y^2+y^4-4*z+z^2+y^2*z^2,-2*x-y+y^3+x*z+y*z^2,2+x*y-z,-1+x^2+y^2+z^2}"); check("GroebnerBasis({x^2 + y^2 + z^2 - 1, x*y - z + 2, z^2 - 3 + x,x - y^2 + 1}, {x, y, z})", // "{1}"); } @Test public void testGudermannian() { check("N(Gudermannian(4/3), 50)", // "1.0553273957593967167251201219876788679534384811898"); check("N(Gudermannian(I*Pi+5), 50)", // "1.584272016863742216280221584803507365335847712497"); check("Gudermannian(6/4*Pi*I)", // "-I*Infinity"); check("Gudermannian(3.75)", // "1.52377"); check("Gudermannian(1.111111)", // "0.934757"); check("Gudermannian(100.0)", // "1.5708"); check("Gudermannian(I*Pi+5.0)", // "1.58427"); } @Test public void testHarmonicMean() { checkNumeric("HarmonicMean({-3.1415,2.987,-1,1})", // "242.94266666666653"); checkNumeric("HarmonicMean({-3.1415,2.987,I,1})", // "1.9997333373775112+I*1.9673414730736105"); check("HarmonicMean({-3.1415,2.987,-1,0,1})", // "0"); check("HarmonicMean({{-3.1415,2.987,-1,0,1}})", // "{-3.1415,2.987,-1,0,1}"); check("HarmonicMean({1, 2, 3, 4,5, 6, 7})", // "980/363"); check("HarmonicMean({a,b,c,d})", // "4/(1/a+1/b+1/c+1/d)"); check("HarmonicMean({{1, 2}, {5, 10}, {5, 2}, {4, 8}})", // "{80/33,160/49}"); } @Test public void testHarmonicNumber() { check("HarmonicNumber(Infinity,1)", // "Infinity"); check("HarmonicNumber(Infinity,5)", // "Zeta(5)"); checkNumeric("HarmonicNumber({-3.1415,2.987,-1,0,1},0.5)", // "{-0.19602750271156133+I*4.277725609252295,2.277519248535999,ComplexInfinity,0.0,1.0000000000000007}"); checkNumeric("HarmonicNumber(-0.5,0.5)", // "-0.8554558653879558"); check("D(HarmonicNumber(x),{x,4})", // "24/x^5+PolyGamma(4,x)"); check("HarmonicNumber(-9223372036854775808/11,0.5)", // "ComplexInfinity"); check("N(HarmonicNumber(1/17, 5), 50)", // "0.25327615206118707521034626118754228313433140885746"); check("HarmonicNumber(0.33000000000000000000) ", // "0.44152364693736352811"); check("n /. FindRoot(HarmonicNumber(n) == 1.5, {n, 5})", // "2.0"); check("HarmonicNumber(400,{-1,-2})", // "{80200,21413400}"); check("HarmonicNumber(0.8)", // "0.862207"); check("HarmonicNumber(130.71)", // "5.45402"); check("HarmonicNumber(0.8,3 )", // "0.940124"); check("HarmonicNumber(E,1.0)", // "1.75002"); check("N(HarmonicNumber(1/17,5))", // "0.253276"); check("N(HarmonicNumber(27,5-I))", // "1.02598+I*0.0251513"); check("HarmonicNumber(n, -1)", // "n/2+n^2/2"); // Iteration limit check("HarmonicNumber(2147483647,2)", // "Hold(HarmonicNumber(2147483647,2))"); check("HarmonicNumber(10007, 3)", // "Hold(HarmonicNumber(10007,3))"); check(" HarmonicNumber(m,-2) ", // "m/6+m^2/2+m^3/3"); check("Table(HarmonicNumber(m,-n), {n, 1, 5, 1})", // "{m/2+m^2/2,m/6+m^2/2+m^3/3,m^2/4+m^3/2+m^4/4,-m/30+m^3/3+m^4/2+m^5/5,-m^2/12+5/\n" + "12*m^4+m^5/2+m^6/6}"); check("HarmonicNumber(z, -2)", // "z/6+z^2/2+z^3/3"); check("HarmonicNumber(10007, -2)", // "334083895140"); check("HarmonicNumber(10007, -1)", // "50075028"); check("HarmonicNumber(-10, -3)", // "2025"); check("HarmonicNumber(10, 3)", // "19164113947/16003008000"); check("HarmonicNumber(10, -3)", // "3025"); check("HarmonicNumber(-10, 3)", // "ComplexInfinity"); if (Config.EXPENSIVE_JUNIT_TESTS) { check("HarmonicNumber(101,1009)", // "BigInteger bit length 206136 exceeded"); check("HarmonicNumber(1009,101)", // "BigInteger bit length 201800 exceeded"); } check("HarmonicNumber(10007)", // "Hold(HarmonicNumber(10007))"); check("HarmonicNumber(-Infinity)", // "ComplexInfinity"); check("HarmonicNumber(Infinity)", // "Infinity"); check("HarmonicNumber(-42)", // "ComplexInfinity"); check("HarmonicNumber(2,-3/2)", // "1+2*Sqrt(2)"); check("Table(HarmonicNumber(n), {n, 8})", // "{1,3/2,11/6,25/12,137/60,49/20,363/140,761/280}"); check("HarmonicNumber(4,r)", // "1+2^(-r)+3^(-r)+4^(-r)"); check("HarmonicNumber(1,r)", // "1"); check("HarmonicNumber(0, r)", // "0"); check("HarmonicNumber(Infinity,2)", // "Pi^2/6"); } @Test public void testHaversine() { check("N(Haversine(1/7), 50)", // "0.0050933697766924586521369314932831270629836495502145"); check("N(Haversine(798+I), 50)", // "-0.27105513255154801719412701505423122282395758411135+I*0.02083546725316235662066240547292017854082982767312"); checkNumeric("Haversine(1.5)", // "0.46463139916614854"); checkNumeric("Haversine(0.5 + 2 * I)", // "-1.1508186664570472+I*0.8694047522371582"); checkNumeric("Haversine(0.5)", // "0.06120871905481362"); checkNumeric("Haversine(1.5+I)", // "0.44542339697277356+I*0.5861286494553962"); check("Haversine(Pi/3)", // "1/4"); check("Haversine(90*Degree)", // "1/2"); check("Haversine({0, Pi/4, Pi/3, Pi/2})", // "{0,1/2*(1-1/Sqrt(2)),1/4,1/2}"); } @Test public void testHead() { check("Head(f(a, b))", // "f"); check("Head(a + b + c)", // "Plus"); check("Head(a / b)", // "Times"); check("Head(45)", // "Integer"); check("Head(x)", // "Symbol"); check("Head(f(x)[y][z])", // "f(x)[y]"); check("Head({3, 4, 5})", // "List"); check("FixedPoint(Head, f(x)[y][z])", // "Symbol"); check("FixedPoint(Head, {3, 4, 5})", // "Symbol"); check("Head(a * b)", // "Times"); check("Head(6)", // "Integer"); check("Head(x)", // "Symbol"); } @Test public void testHeavisideTheta() { check("Derivative(1)[HeavisideTheta]", // "DiracDelta(#1)&"); check("HeavisideTheta(x)", // "HeavisideTheta(x)"); check("D(HeavisideTheta(x), x)", // "DiracDelta(x)"); check("HeavisideTheta(0)", // "HeavisideTheta(0)"); check("HeavisideTheta(42)", // "1"); check("HeavisideTheta(-1)", // "0"); check("HeavisideTheta(-42)", // "0"); check("HeavisideTheta({1.6, 1.6000000000000000000000000})", // "{1,1}"); check("HeavisideTheta({-1, 0, 1})", // "{0,HeavisideTheta(0),1}"); check("HeavisideTheta(1, 2, 3)", // "1"); check("HeavisideTheta(-2, -1, 1, 2)", // "0"); } @Test public void testHold() { check("Hold(1<2<3!=a<2==3) // FullForm", // "Hold(Inequality(1, Less, 2, Less, 3, Unequal, a, Less, 2, Equal, 3))"); check("Hold(3*2)", // "Hold(3*2)"); check("Hold(2+2)", // "Hold(2+2)"); check("lst = Hold(1 + 2, 2*3*4*5, 1/0, Quit())", // "Hold(1+2,2*3*4*5,1/0,Quit())"); check("Apply(List, Map(Hold, lst))", // "{Hold(1+2),Hold(2*3*4*5),Hold(1/0),Hold(Quit())}"); check("expr = Hold({1 + 2, g(3 + 4, 2*3), f(1 + g(2 + 3))})", // "Hold({1+2,g(3+4,2*3),f(1+g(2+3))})"); check("pos = Position(expr, _Plus)", // "{{1,1},{1,2,1},{1,3,1,2,1},{1,3,1}}"); check("val = Extract(expr, pos)", // "{3,7,5,1+g(5)}"); check("ReplacePart(expr, Thread(pos -> val))", // "Hold({3,g(7,2*3),f(1+g(5))})"); check("Hold(6/8)==6/8", // "Hold(6/8)==3/4"); } @Test public void testHoldComplete() { check("HoldComplete(Evaluate(a+a),2+2,Sequence(a,b))", // "HoldComplete(Evaluate(a+a),2+2,Sequence(a,b))"); check("g /: HoldComplete(g(x_)) := x", // ""); check("HoldComplete(g(1))", // "HoldComplete(g(1))"); check("HoldComplete(f(1 + 2)) /. f(x_) :> g(x)", // "HoldComplete(g(1+2))"); check("ReleaseHold(HoldComplete(Sequence(1, 2)))", // "Identity(1,2)"); check("g /: Hold(g(x_)) := x", // ""); check("Hold(g(1))", // "1"); } @Test public void testHoldAllComplete() { check("ClearAll(fump); " // + "SetAttributes(fump, HoldAllComplete);" // + "fump(e_) := (Print(ToString(Unevaluated(e)) <> \" ~~>\\n\" <> ToString(e)); e); " // + "fump((42 + 3)*6)", // "270"); } @Test public void testHoldForm() { check("HoldForm(3*2)", // "3*2"); check("HoldForm(6/8)==6/8", // "6/8==3/4"); } @Test public void testHoldPattern() { check("a + b /. HoldPattern(_ + _) -> 0", // "0"); check("MatchQ(And(x, y, z), Times(p__))", // "True"); check("HoldPattern( 1/(sq(a_)*sq(b_)) ) //FullForm", // "HoldPattern(Power(Times(sq(Pattern(a, Blank())), sq(Pattern(b, Blank()))), -1))"); check(" 1/(sq(a_)*sq(b_)) //FullForm", // "Times(Power(sq(Pattern(a, Blank())), -1), Power(sq(Pattern(b, Blank())), -1))"); check("HoldPattern( Sqrt(2*Pi*x_) )", // "HoldPattern(Sqrt(2*Pi*x_))"); check("MatchQ(And(x, y, z), p__)", // "True"); // because of OneIdentity attribute for Times check("MatchQ(And(x, y, z), Times(p__))", // "True"); check("Times(p__)===And(p__)", // "True"); check("MatchQ(And(x, y, z), HoldPattern(Times(p__)))", // "False"); check("HoldPattern(Times(p__))===HoldPattern(And(p__))", // "False"); check("And(x, y, z)/.HoldPattern(And(a__)) ->List(a)", // "{x,y,z}"); check("And(x, y, z)/.And->List", // "{x,y,z}"); check("And(x, y, z)/.And(a_,b___)->List(a,b)", // "{x,y,z}"); check("a + b /. HoldPattern(_ + _) -> 0", // "0"); check("MatchQ(Log(a, b), HoldPattern(Log(_)/Log(_)))", // "True"); check("Cases({a -> b, c -> d}, HoldPattern(a -> _))", // "{a->b}"); } @Test public void testHorner() { check("Horner(1/Sqrt(5))", // "1/Sqrt(5)"); } @Test public void testHornerForm() { check("HornerForm(x^(1/3) + x + x^(3/2))", // "x^(1/3)+(1+Sqrt(x))*x"); check("HornerForm(1/Sqrt(5))", // "1/Sqrt(5)"); check("HornerForm(#2)", // "#2"); check("Horner(Infinity)", // "Infinity"); check("HornerForm(11*x^3 - 4*x^2 + 7*x + 2)", // "2+x*(7+x*(-4+11*x))"); check("HornerForm(a+b*x+c*x^2,x)", // "a+x*(b+c*x)"); } @Test public void testHurwitzLerchPhi() { check("HurwitzLerchPhi(-1,-1,1)", // "1/4"); check("HurwitzLerchPhi(2,1,1)", // "-I*1/2*Pi"); check("Table(HurwitzLerchPhi(z , 1, 1), {z, -1, 2})", // "{Log(2),1,Infinity,-I*1/2*Pi}"); } @Test public void testHurwitzZeta() { checkNumeric("N(HurwitzZeta(1/3, 8/7), 50)", // "-1.1389367444490991746548674334535727810961919460755"); checkNumeric("HurwitzZeta(2.3000000000000000000000000, 48)", // "0.0050854686158964511510171449"); // https://github.com/mtommila/apfloat/issues/34 // checkNumeric("HurwitzZeta(-9223372036854775808/11,-0.8+I*1.2)", // // "Overflow()"); checkNumeric("HurwitzZeta(2.2,3.1)", // "0.26067453797192913"); check("HurwitzZeta(3,-4)", // "ComplexInfinity"); checkNumeric("HurwitzZeta(-2.0,0.5+I*0.5)", // "I*0.08333333333333333"); check("HurwitzZeta(7,5.0)", // "0.0000184949"); checkNumeric("HurwitzZeta(2147483647,3.141592653589793)", // "0.0"); check("HurwitzZeta(1.5708,1317624576693539401)", // "7.95681*10^-11"); check("HurwitzZeta(3,0.2)", // "125.739"); check("HurwitzZeta(.51, .87)", // "-1.32016"); check("Table(HurwitzZeta(x, 0.5+I*0.5), {x,-2.0,2,0.25})", // "{I*0.0833333,0.0371452+I*0.0888619,0.080604+I*0.0797892,0.125994+I*0.0515943,"// + "0.166667,0.192966+I*(-0.0787252),0.190832+I*(-0.187445),0.138749+I*(-0.327822),"// + "I*(-0.5),-0.300858+I*(-0.702294),-0.972875+I*(-0.930936),-3.02493+I*(-1.17988),"// + "ComplexInfinity,4.69929+I*(-1.70242),2.46351+I*(-1.95199),1.49152+I*(-2.17411),"// + "0.783802+I*(-2.35189)}"); check("Table(HurwitzZeta(x, 0.5), {x,-2.0,2,0.25})", // "{0.0,0.00695768,0.0164748,0.0283452,0.0416667,0.0541783,0.0608885,0.0509849,0.0," // + "-0.153878,-0.604899,-2.34624,ComplexInfinity,6.33397,4.77654,4.63811,4.9348}"); check("D(HurwitzZeta(s, x), x)", // "-s*HurwitzZeta(1+s,x)"); check("HurwitzZeta(20,a) // FunctionExpand", // "PolyGamma(19,a)/121645100408832000"); // http://fungrim.org/entry/6e69fc/ check("HurwitzZeta(6,11)", // "-52107472322919827957/51219253009612800000+Pi^6/945"); check("HurwitzZeta(-4,42)", // "-24607093"); // http://fungrim.org/entry/af23f7/ check("HurwitzZeta(s,1)", // "Zeta(s)"); // http://fungrim.org/entry/b721b4/ check("HurwitzZeta(s,2)", // "-1+Zeta(s)"); // http://fungrim.org/entry/af7d3d/ check("HurwitzZeta(s,1/2)", // "(-1+2^s)*Zeta(s)"); check("HurwitzZeta(3,1/2)", // "7*Zeta(3)"); // http://fungrim.org/entry/951f86/ check("HurwitzZeta(2,3/4)", // "-8*Catalan+Pi^2"); // http://fungrim.org/entry/7dab87/ check("HurwitzZeta(-9, 0)", // "-1/132"); check("HurwitzZeta(-10, 0)", // "0"); check("HurwitzZeta(-11, 0)", // "691/32760"); // http://fungrim.org/entry/532f31/ check("HurwitzZeta(1,a)", // "ComplexInfinity"); // http://fungrim.org/entry/d99808/ check("HurwitzZeta(0,a)", // "1/2-a"); } @Test public void testHyperfactorial() { check("Hyperfactorial(-1/2)", // "Glaisher^(3/2)/(2^(1/24)*E^(1/8))"); check("Hyperfactorial(10)", // "215779412229418562091680268288000000000000000"); check("Hyperfactorial(-7)", // "-4031078400000"); check("Hyperfactorial(-8)", // "3319766398771200000"); } @Test public void testHypergeometric0F1() { check("N(Hypergeometric0F1(1, -2), 50)", // "-0.19654809527046820004079337208793223132588978731089"); check("Hypergeometric0F1(1, -2.00000000000000000000000000000)", // "-0.1965480952704682000407933720879"); check("Hypergeometric0F1(b, 0)", // "1"); check("Hypergeometric0F1(b, Infinity)", // "ComplexInfinity"); check("Hypergeometric0F1(1/2, z)", // "Cosh(2*Sqrt(z))"); check("Hypergeometric0F1(1/2, -a)", // "Cos(2*Sqrt(a))"); check("Hypergeometric0F1(3/2, z)", // "Sinh(2*Sqrt(z))/(2*Sqrt(z))"); check("Hypergeometric0F1(3/2, -a)", // "Sin(2*Sqrt(a))/(2*Sqrt(a))"); check("Hypergeometric0F1({1, 2, 3}, 1.5)", // "{3.16559,1.96279,1.60374}"); check("Hypergeometric0F1(1,-2.0)", // "-0.196548"); checkNumeric("Hypergeometric0F1(1,1.5)", // "3.1655890675997247"); } @Test public void testHypergeometric0F1Regularized() { checkNumeric("Hypergeometric0F1Regularized(0., E)", // "8.522277545659726"); check("Hypergeometric0F1Regularized(b, 0)", // "1/Gamma(b)"); check("N(Hypergeometric0F1Regularized(0, -48), 50)", // "-0.75356407978144308380327864211537660841009027837077"); } @Test public void testHypergeometric1F1() { checkNumeric("Hypergeometric1F1(1,1/2,z)", // "1+E^z*Sqrt(Pi)*Sqrt(z)*Erf(Sqrt(z))"); checkNumeric("Hypergeometric1F1(1,{2,3,4},5.0)", // "{29.482631820515323,11.393052728206126,6.235831636923676}"); check("Hypergeometric1F1(3,b,z)", // "1/2*(-1+b)*(4-b+z+(2-b)*(3-b)*E^z*z^(1-b)*(Gamma(-1+b)-Gamma(-1+b,z))+2*(3-b)*E^z*z^(\n" + "2-b)*(Gamma(-1+b)-Gamma(-1+b,z))+E^z*z^(3-b)*(Gamma(-1+b)-Gamma(-1+b,z)))"); check("Hypergeometric1F1(a,a+1,z)", // "(a*(Gamma(a,0)-Gamma(a,-z)))/(-z)^a"); check("Hypergeometric1F1(1,a+1,z)", // "(a*E^z*(Gamma(a)-Gamma(a,z)))/z^a"); check("Hypergeometric1F1(a-1, a, z)", // "(-1+a)*(-z)^(1-a)*(Gamma(-1+a,0)-Gamma(-1+a,-z))"); check("Hypergeometric1F1(a, a - 1, z)", // "(E^z*(-1+a+z))/(-1+a)"); check("Hypergeometric1F1({0,0,0},a,{{0,0},{0,0},0})", // "{{1,1},{1,1},1}"); checkNumeric("Hypergeometric1F1(-0.5, 1.0 / 3.0, -1)", // "2.269314995817225"); // assertThat(Maja.hypergeo1F1(-0.5, 1.0 / 3.0, -1)).isEqualTo(2.269314995817403); check("N(Hypergeometric1F1(10, 1/3, -1), 50)", // "1.0856469662771144181060999200053894821341819655655"); check("Hypergeometric1F1(10, 1/3, -1.000000000000000000000000000000000000)", // "1.0856469662771144181060999200053894821"); check("Hypergeometric1F1(-2,-1-a,-a)", // "1+(2*a)/(-1-a)+a/(1+a)"); check("Hypergeometric1F1(-3,b,z)", // "1+(-3*z)/b+(3*z^2)/(b*(1+b))-z^3/(b*(1+b)*(2+b))"); check("Hypergeometric1F1(-2,b,z)", // "1+(-2*z)/b+z^2/(b*(1+b))"); // slow // check("Hypergeometric1F1(-9223372036854775808/11,{2,3,4},0.5)", // // "{Hypergeometric1F1(-8.38488*10^17,2.0,0.5),Hypergeometric1F1(-8.38488*10^17,3.0,0.5),Hypergeometric1F1(-8.38488*10^17,4.0,0.5)}"); // TODO check wrong check("Hypergeometric1F1(3,Quantity(1.2,\"m\"),-1+I)", // "Hypergeometric1F1(3,1.2[m],-1+I)"); check("Hypergeometric1F1(2 + I, {2,3,4}, 0.5)", // "{1.61833+I*0.379258,1.391+I*0.228543,1.28402+I*0.161061}"); check("Hypergeometric1F1(1,b,z)", // "(-1+b)*E^z*z^(1-b)*(Gamma(-1+b)-Gamma(-1+b,z))"); check("Hypergeometric1F1(2,b,z)", // "(-1+b)*(1+(2-b)*E^z*z^(1-b)*(Gamma(-1+b)-Gamma(-1+b,z))+E^z*z^(2-b)*(Gamma(-1+b)-Gamma(-\n" + "1+b,z)))"); check("Hypergeometric1F1(-2,-1,0)", // "1"); check("Hypergeometric1F1(-2,-1,z)", // "ComplexInfinity"); check("Hypergeometric1F1(-2,-7,z)", // "1+2/7*z+z^2/42"); check("Hypergeometric1F1(-2,0,z)", // "ComplexInfinity"); check("Hypergeometric1F1(a,a,z)", // "E^z"); check("Hypergeometric1F1(0,1,z)", // "1"); check("Hypergeometric1F1(a,1,z) // FunctionExpand", // "LaguerreL(-a,z)"); check("Hypergeometric1F1(3,1,z)", // "Hypergeometric1F1(3,1,z)"); check("Hypergeometric1F1(-1,b,z)", // "1-z/b"); check("Hypergeometric1F1(-1,2,3.0)", // "-0.5"); check("Hypergeometric1F1(1,2,3.0)", // "6.36185"); } @Test public void testHypergeometric1F1Regularized() { // TODO interrupt long running calculations // check("Hypergeometric1F1Regularized(-9223372036854775808/11,-0.8,-11)", // // ""); check("N(Hypergeometric1F1Regularized(2,-4,2), 50)", // "1891.5983613262464581709894299072020001741607860612"); check("N(Hypergeometric1F1Regularized(1, 0, 1), 30)", // "2.71828182845904523536028747135"); checkNumeric("Hypergeometric1F1Regularized(7, 23, 0.5)", // "1.0370581075059291E-21"); check("Hypergeometric1F1Regularized(a, b, 0)", // "1/Gamma(b)"); check("Hypergeometric1F1Regularized(a, a, z)", // "E^z/Gamma(a)"); } @Test public void testHypergeometric2F1() { // https://dlmf.nist.gov/15.4 check("Hypergeometric2F1(a,b,1/2*a+1/2*b+1/2, 1/2)", // "(Sqrt(Pi)*Gamma(1/2+a/2+b/2))/(Gamma(1/2+a/2)*Gamma(1/2+b/2))"); check("Hypergeometric2F1(1,a,a+1,-1)", // "1/2*a*(PolyGamma(0,1/2+a/2)-PolyGamma(0,a/2))"); check("Hypergeometric2F1(a,b,a-b+1, -1)", // "(Sqrt(Pi)*Gamma(1+a-b))/(2^a*Gamma(1/2+a/2)*Gamma(1+a/2-b))"); check("Hypergeometric2F1(a+1,b,a,z)", // "(-a+a*z-b*z)/(a*(1-z)^b*(-1+z))"); check("Hypergeometric2F1(a,1-a,1/2,z)", // "Cos((-1+2*(1-a))*ArcSin(Sqrt(z)))/Sqrt(1-z)"); check("Hypergeometric2F1(1-a,a,1/2,z)", // "Cos((-1+2*(1-a))*ArcSin(Sqrt(z)))/Sqrt(1-z)"); check("Hypergeometric2F1(a,-a,1/2,z)", // "Cos(2*a*ArcSin(Sqrt(z)))"); check("Hypergeometric2F1(1/2,1,3/2,3)", // "ArcTanh(3)/3"); check("Hypergeometric2F1(1/2,1,3/2,t^2)", // "ArcTanh(t)/t"); check("Hypergeometric2F1(a, a + 1/2, 2*a, z)", // "(1+Sqrt(1-z))^(1-2*a)/(2^(1-2*a)*Sqrt(1-z))"); // https://github.com/mtommila/apfloat/issues/29 checkNumeric("Hypergeometric2F1(-3.0, -1, -2, 1.0)", // "-0.5"); // https://github.com/paulmasson/math/issues/10 - uses ThrowException check("Hypergeometric2F1(0.5,0.333,0.666,1)", // "Hypergeometric2F1(0.333,0.5,0.666,1.0)"); checkNumeric("Hypergeometric2F1(-0.5, 1.0 / 3.0, 4.0 / 3.0, -1)", // "1.1114479705325755"); checkNumeric("Hypergeometric2F1(-0.5, 1.0 / 3.0, -4.0 / 3.0, 0)", // "1.0"); checkNumeric("Hypergeometric2F1(-0.5, 1.0 / 4.0, -4.0 / 3.0, -3)", // "0.6919237698061459"); checkNumeric("Hypergeometric2F1(-0.5, 1.0 / 4.0, -4.0 / 3.0,-1.5)", // "0.8274559676019725"); checkNumeric("Hypergeometric2F1(0.5, 1.0 / 3.0, 4.0 / 3.0, 1)", // "1.4021821053254544"); checkNumeric("Hypergeometric2F1(-5, 1.0 / 3.0, 4.0 / 3.0, 1)", // "0.5006868131868132"); checkNumeric("Hypergeometric2F1(-0.5, 3.0, 1.0, 0.2)", // "0.66383268082025"); checkNumeric("Hypergeometric2F1(2, 2.0, 3.0, 0.95)", // "35.46652127744268"); checkNumeric("Hypergeometric2F1(2, 2.0, 3.01, 0.95)", // "34.8101340764061"); checkNumeric("Hypergeometric2F1(20, 2.0, 3.01, 0.95)", // "5.513090059384318E23"); checkNumeric("Hypergeometric2F1(0.123, 2.0, 3.01, 0.95)", // "1.166719619920925"); checkNumeric("Hypergeometric2F1(-1, 2.0, 3.01, 0.95)", // "0.3687707641196013"); checkNumeric("N(Hypergeometric2F1(-23/10, 1/2 - 1/8 + 23/10 + 1, 1/8 + 1, (12 + 1)/2),50)", // "316.8942332151300302909232080800472001326090876729+I*436.16750112351808402055619284015549992820985322775"); checkNumeric("Hypergeometric2F1(-2.3, 1/2 - 1/8 + 2.3 + 1, 1/8 + 1, (12 + 1)/2)", // "316.89423321513+I*436.1675011235181"); check("D( Hypergeometric2F1(a,b,c,x), {x,-4})", // "D(Hypergeometric2F1(a,b,c,x),{x,-4})"); check("N(Hypergeometric2F1(1/2, 1/3, 2, 1), 50)", // "1.1595952669639283657699920515700208819451652634397"); check("Hypergeometric2F1(1/2, 1/3, 2, 1.000000000000000000000000000000000)", // "1.15959526696392836576999205157002"); // iteration limit of exceeded. // https://github.com/paulmasson/math/issues/29#issuecomment-1120230707 check("Hypergeometric2F1(1, 0.5, 1.5, -0.9999999999999976)", // "0.785398163397448652"); check("Hypergeometric2F1(n,n,2*n+1,1)", // "Gamma(1+2*n)/Gamma(1+n)^2"); check("Hypergeometric2F1(2/3,3/7,10, 1)", // "(362880*Gamma(187/21))/(Gamma(28/3)*Gamma(67/7))"); // message Expand: m^2 and m are incompatible units check("Hypergeometric2F1(-5,Quantity(1.2,\"m\"),c,1)", // "Expand((-1.2[m]+c)*(1+-1.2[m]+c)*(2+-1.2[m]+c)*(3+-1.2[m]+c)*(4+-1.2[m]+c))/(c*(\n" + "1+c)*(2+c)*(3+c)*(4+c))"); // check("Hypergeometric2F1(1317624576693539401,0.333,-3/2,-0.5)", // // "Hypergeometric2F1(0.333,1.31762*10^18,-1.5,-0.5)"); check("Hypergeometric2F1(-1,b,c,1)", // "(-b+c)/c"); check("Hypergeometric2F1(-2,b,c,1)", // "(-b+b^2+c-2*b*c+c^2)/(c*(1+c))"); check("Hypergeometric2F1(3,0,-1,x)", // "1"); check("Hypergeometric2F1(a,3/2,1/2,x)", // "(1-x+2*a*x)/(1-x)^(1+a)"); check("Hypergeometric2F1(3,1,-1,x)", // "ComplexInfinity"); check("Hypergeometric2F1(1/2,I,-10,x)", // "ComplexInfinity"); check("D( Hypergeometric2F1(a,b,c,x), {x,-4})", // "D(Hypergeometric2F1(a,b,c,x),{x,-4})"); check("D( Hypergeometric2F1(a,b,c,x), {x,n})", // "(Hypergeometric2F1(a+n,b+n,c+n,x)*Pochhammer(a,n)*Pochhammer(b,n))/Pochhammer(c,n)"); check("D( Hypergeometric2F1(a,b,c,x), {x,4})", // "(a*(1+a)*(2+a)*(3+a)*b*(1+b)*(2+b)*(3+b)*Hypergeometric2F1(4+a,4+b,4+c,x))/(c*(1+c)*(\n" + // "2+c)*(3+c))"); check("D( Hypergeometric2F1(a,b,c,x), x)", // "(a*b*Hypergeometric2F1(1+a,1+b,1+c,x))/c"); // check("Hypergeometric2F1(-3, 1, 2, z)", // // "(1-(1-z)^4)/(4*z)"); check("Hypergeometric2F1(2,1-I,2-I,I*E^(I*x))", // "Hypergeometric2F1(1-I,2,2-I,I*E^(I*x))"); check("Hypergeometric2F1(3/2, 2, 5/2, z^n) ", // "3/2*(-z^(n/2)+ArcTanh(z^(n/2))-z^n*ArcTanh(z^(n/2)))/(z^(3/2*n)*(-1+z^n))"); check("Hypergeometric2F1(3/2, 2, 5/2, -z) ", // "(-I*3/2*(I*Sqrt(z)-I*ArcTan(Sqrt(z))-I*z*ArcTan(Sqrt(z))))/((-1-z)*z^(3/2))"); check("Hypergeometric2F1(3/2, 2, 5/2, z) ", // "3/2*(-Sqrt(z)+ArcTanh(Sqrt(z))-z*ArcTanh(Sqrt(z)))/((-1+z)*z^(3/2))"); // CatalanNumber: check("Hypergeometric2F1(-9, -10, 2, 1)", // "16796"); // TODO currently unsupported check("Hypergeometric2F1(0.5,0.333,1,1.5708)", // "1.12923+I*(-0.568083)"); check("Hypergeometric2F1(1, b, 2, z)", // "-(-1+(1-z)^b+z)/((-1+b)*(1-z)^b*z)"); check("Hypergeometric2F1(a, b, a, z)", // "(1-z)^(-b)"); check("Hypergeometric2F1(a, b, b-1, z)", // "Hypergeometric2F1(a,b,-1+b,z)"); check("Hypergeometric2F1(a, b, b, z)", // "(1-z)^(-a)"); // check("Hypergeometric2F1(a, b, b+1, z)", // // "(b*Beta(z,b,1-a))/z^b"); check("Hypergeometric2F1(-5, b, c, 1)", // "(-24*b+50*b^2-35*b^3+10*b^4-b^5+24*c-100*b*c+105*b^2*c-40*b^3*c+5*b^4*c+50*c^2-\n" + "105*b*c^2+60*b^2*c^2-10*b^3*c^2+35*c^3-40*b*c^3+10*b^2*c^3+10*c^4-5*b*c^4+c^5)/(c*(\n" + "1+c)*(2+c)*(3+c)*(4+c))"); check("Hypergeometric2F1(-n, b, c, 1)", // "Hypergeometric2F1(b,-n,c,1)"); check("Hypergeometric2F1(2 + I, -I, 3/4, 0.5-0.5*I)", // "-0.972167+I*(-0.181659)"); // Hypergeometric2F1(1 - n, -n, 2, 1) == CatalanNumber(n) check("Hypergeometric2F1(-3, -4, 2, 1)==CatalanNumber(4)", // "True"); check("Hypergeometric2F1(1,2,3/2,x^2/9)", // "3/2*(1/3*Sqrt(1-x^2/9)*Sqrt(x^2)+ArcSin(Sqrt(x^2)/3))/((1-x^2/9)^(3/2)*Sqrt(x^2))"); check("Hypergeometric2F1(-2,b,c,1)", // "(-b+b^2+c-2*b*c+c^2)/(c*(1+c))"); check("Hypergeometric2F1(0.5,0.333,0.666,0.5)", // "1.18566"); checkNumeric("Hypergeometric2F1(0.5,Sin(Pi),0.666,-0.5)", // "1.0"); checkNumeric("Hypergeometric2F1(0.5,0.333,0.666,-0.5)", // "0.9026782488379916"); checkNumeric("Hypergeometric2F1(0.5,0.333,0.666,0.75)", // "1.3975732184289733"); checkNumeric("Hypergeometric2F1(0.5,0.333,0.666,-0.75)", // "0.8677508558430819"); } @Test public void testHypergeometric2F1Regularized() { check("Hypergeometric2F1Regularized(I, -I, .5 + I, 5)", // "-0.91139+I*(-1.76606)"); check("Hypergeometric2F1Regularized(-1, -1, 0, .5)", // "0.5"); check("N(Hypergeometric2F1Regularized(1/3, 1, 3, -7), 50)", // "0.35510204081632653061224489795918367346938775510204"); check("N(Hypergeometric2F1Regularized(1/3, 1, 0, -7), 25)", // "-0.1458333333333333333333333"); checkNumeric("Hypergeometric2F1Regularized(1, 2, -3, 4.5)", // "26.768438320767704"); check("Hypergeometric2F1Regularized(1, 1/3, -1, -0.3000000025555555555522220000)", // "0.0216866352303372915924565340457"); check("Hypergeometric2F1Regularized(7, 2, -0.3, .5)", // "17490.25"); check("Hypergeometric2F1Regularized(a,b,b,x)", // "1/((1-x)^a*Gamma(a))"); check("Hypergeometric2F1Regularized(a,b,c,0)", // "1/Gamma(c)"); } @Test public void testHypergeometricPFQ() { check("HypergeometricPFQ({1, 1}, {1/2, 1}, z)", // "1+E^z*Sqrt(Pi)*Sqrt(z)*Erf(Sqrt(z))"); check("HypergeometricPFQ({0,a1,a2,a3,a4},{b1,b2,b3},z)", // "1"); // message HypergeometricPFQ: general hypergeometric argument currently restricted. check("HypergeometricPFQ({1, 1, 1}, {3/2, 3/2, 3/2}, 10.0)", // "HypergeometricPFQ({1,1,1},{3/2,3/2,3/2},10.0)"); check("HypergeometricPFQ({1, 1}, {3, 3, 3}, 2.)", // "HypergeometricPFQ({1,1},{3,3,3},2.0)"); check("HypergeometricPFQ({I, I, I}, {2, 2 , 2}, -1.0*I)", // "0.870032+I*(-0.00484538)"); check("HypergeometricPFQ({1, 2, 3, 4}, {5, 6, 7}, {0.1, 0.3, 0.5})", // "{1.01164,1.03627,1.06296}"); check("HypergeometricPFQ({1/2, b}, {3/2, b + 1}, z)", // "(b*(Sqrt(Pi)*Sqrt(1/z)*Erfi(Sqrt(z))+(-Gamma(b)+Gamma(b,-z))/(-z)^b))/(-1+2*b)"); check("HypergeometricPFQ({a,b}, {c,d}, 0)", // "1"); check("HypergeometricPFQ({a, b}, {c, b}, z)", // "HypergeometricPFQ({a},{c},z)"); } @Test public void testHypergeometricU() { // TODO throws hypergeometric function pole // https://github.com/mtommila/apfloat/issues/36 check("HypergeometricU(3.0, 1.0, 0.0)", // "HypergeometricU(3.0,1.0,0.0)"); check("HypergeometricU(3, 2, 1.0)", // "0.105479"); check("N(HypergeometricU(3, 2, 1),50)", // "0.10547895651520888848838225094608093588873320977117"); check("D(HypergeometricU(a,b,x), x)", // "-a*HypergeometricU(1+a,1+b,x)"); check("HypergeometricU(2, b, z)", // "(-1+E^z*(2-b+z)*z^(1-b)*Gamma(-1+b,z))/(2-b)"); check("HypergeometricU(a, a+3, z)", // "(1+(a*(1+a))/z^2+(2*a)/z)/z^a"); check("HypergeometricU(3, 2.5, 1.0)", // "0.173724"); check("HypergeometricU(3, 2.5, 0.0)", // "ComplexInfinity"); check("Table( HypergeometricU(3, 2.5, x), {x,-2.0,2,0.25})", // "{0.19001+I*(-0.148415),0.27603+I*(-0.141362),0.39355+I*(-0.107638),0.553199+I*(-0.0227102)," // + "0.76904+I*0.163012,1.05965+I*0.56395,1.44956+I*1.52035,1.97105+I*4.83136,ComplexInfinity," // + "2.45436,0.688641,0.312167,0.173724,0.1086,0.0732253,0.0520871,0.0385635}"); check("Table( HypergeometricU(3, 1.0, x), {x,-2.0,2,0.25})", // "{0.0852414+I*0.212584,0.0312283+I*0.264433,-0.0527303+I*0.306681,-0.171748+I*0.323467,-0.325706+I*0.288932,-0.500123+I*0.162311,-0.642219+I*(-0.119092),-0.575265+I*(-0.649898),HypergeometricU(3.0,1.0,0.0),0.214115,0.105593,0.0644474,0.0436079,0.0314298,0.0236577,0.0183874,0.0146502}"); } @Test public void testI() { check("I*0.0//FullForm", // "Complex(0.0`,0.0`)"); check("I*1.0//FullForm", // "Complex(0.0`,1.0`)"); check("(3+I)*(3-I)", // "10"); } @Test public void testIdentity() { check("Composition(Through, {Identity, Sqrt}) /@ {0, 1.0, 2.0, 3.0, 4.0}", // "{{0,0},{1.0,1.0},{2.0,1.41421},{3.0,1.73205},{4.0,2.0}}"); check("Identity'", // "1&"); check("D(Identity(Sin(x)),x)", // "Cos(x)"); check("Composition(f,g,Identity,h,Identity,g)", // "f@*g@*h@*g"); check("Identity(0)", // "0"); } @Test public void testIf() { check("If(FreeQ(a+b*x,x),1,a+b*x)", // "a+b*x"); check("If(1 == k, itstrue, itsfalse)", // "If(1==k,itstrue,itsfalse)"); check("If(1<2, a, b)", // "a"); check("If(1<2, a)", // "a"); check("If(False, a) //FullForm", // "Null"); check("If(a>b,true)", // "If(a>b,True)"); check("If(a>b,1,0)", // "If(a>b,1,0)"); check("If(a>b,1,0, Indeterminate)", // "Indeterminate"); check("If(TrueQ(a>b),1,0)", // "0"); check("If(TrueQ(a>b),1) // FullForm", // "Null"); } @Test public void testIn001() { check("a=1.0", // "1.0"); check("a=a/2+1/a", // "1.5"); check("In(2)", // "1.41667"); check("In(2)", // "1.41422"); check("Definition(Out)", // "Attributes(Out)={Listable,NHoldFirst,Protected}\n" // + "\n" // + "Out(1)=1.0`\n" // + "\n" // + "Out(2)=1.5`\n" // + "\n" // + "Out(3)=1.4166666666666665`\n" // + "\n" // + "Out(4)=1.4142156862745097`"); check("Definition(In)", // "Attributes(In)={Listable,NHoldFirst,Protected}\n" // + "\n" // + "In(1):=a=1.0`\n" // + "\n" // + "In(2):=a=a/2 + 1/a\n" // + "\n" // + "In(3):=In(2)\n" // + "\n" // + "In(4):=In(2)\n" // + "\n" // + "In(5):=Definition(Out)"); } @Test public void testIn002() { check("a=1.0", // "1.0"); check("b=3/2", // "3/2"); check("a=a/2+b/a", // "2.0"); check("In(3)", // "1.75"); check("Do(In(3), {3})", // ""); check("a-Sqrt(3)", // "2.22045*10^-16"); check("Definition(In)", // "Attributes(In)={Listable,NHoldFirst,Protected}\n" // + "\n" // + "In(1):=a=1.0`\n" // + "\n" // + "In(2):=b=3/2\n" // + "\n" // + "In(3):=a=a/2 + b/a\n" // + "\n" // + "In(4):=In(3)\n" // + "\n" // + "In(5):=Do(In(3),{3})\n" // + "\n" // + "In(6):=-Sqrt(3) + a"); } @Test public void testIm() { check("Im(I*Arg(z) + Log(2) + (1/2)*Log(Im(z)^2 + Re(z)^2))", // "Arg(z)+Im(Log(Im(z)^2+Re(z)^2))/2"); check("Im(I*Re(z)+x+y+Im(t)*I)", // "Im(t+x+y)+Re(z)"); check("Im(Quantity(2,\"m\"))", // "0[m]"); check("Im(Quantity(a,\"m\"))", // "Im(a)[m]"); check("Im(I*x+y)", // "Im(y)+Re(x)"); check("Im(I*x)", // "Re(x)"); check("Im(I*Pi/4)", // "Pi/4"); check("Im(E^(I*Pi/4))", // "1/Sqrt(2)"); check("Im(E^(I*3))", // "Sin(3)"); check("Im(Sin(42)*Cos(43))", // "0"); check("Im(Sin(42))", // "0"); check("Im(I*9*Sin(5))", // "9*Sin(5)"); check("Im(3*(-2)^(3/4))", // "3*2^(1/4)"); check("Im(3*2^(3/4))", // "0"); check("Im(0)", // "0"); check("Im(I)", // "1"); check("Im(Indeterminate)", // "Indeterminate"); check("Im(Infinity)", // "0"); check("Im(-Infinity)", // "0"); check("Im(ComplexInfinity)", // "Indeterminate"); } @Test public void testImportString() { check( "ImportString( \"[\\\"Association\\\",[\\\"Rule\\\",\\\"'x'\\\",\\\"1\\\"],[\\\"Rule\\\",\\\"'y'\\\",\\\"2\\\"],[\\\"Rule\\\",\\\"'z'\\\",\\\"3\\\"]]\", \"ExpressionJSON\") // InputForm", // "<|\"x\"->1,\"y\"->2,\"z\"->3|>"); check( "ImportString(\"[\\\"Graphics3D\\\", [\\\"Line\\\",[\\\"List\\\", [\\\"List\\\",1.0,1.0,-1.0], [\\\"List\\\",2.0,2.0,1.0], [\\\"List\\\",3.0,3.0,-1.0], [\\\"List\\\",4.0,4.0,1.0]] ] ]\", \"ExpressionJSON\")", // "Graphics3D(Line({{1.0,1.0,-1.0},{2.0,2.0,1.0},{3.0,3.0,-1.0},{4.0,4.0,1.0}}))"); check( "ImportString(\"[ \\\"Quantity\\\", 2.45, \\\"'Meters'\\\"]\", \"ExpressionJSON\") // FullForm", // "Quantity(2.45`, \"Meters\")"); check("ImportString(\"\\\"'abc'\\\"\", \"ExpressionJSON\") // FullForm", // "\"abc\""); check("ImportString(\"[\\\"List\\\", 1, 2, 3 ]\", \"ExpressionJSON\")", // "{1,2,3}"); check("ImportString(\"{\\\"id\\\":1,\\\"text\\\":\\\"ñía\\\"}\", \"JSON\") // InputForm", // "{\"id\"->1,\"text\"->\"ñía\"}"); check("ImportString(\"{\\\"id\\\":1,\\\"text\\\":\\\"ñía\\\"}\", \"RawJSON\") // InputForm", // "<|\"id\"->1,\"text\"->\"ñía\"|>"); check("ImportString(\"[1,2,3]\", \"JSON\") // InputForm", // "{1,2,3}"); check("ImportString(\"[1,2,3]\", \"RawJSON\") // InputForm", // "{1,2,3}"); check("ImportString(\"{\\\"x\\\":1, \\\"y\\\":2, \\\"z\\\":3}\", \"JSON\") // InputForm", // "{\"x\"->1,\"y\"->2,\"z\"->3}"); check("ImportString(\"{\\\"x\\\":1, \\\"y\\\":2, \\\"z\\\":3}\", \"RawJSON\") // InputForm", // "<|\"x\"->1,\"y\"->2,\"z\"->3|>"); check("ImportString(\"3,4,6\\na,b,c\", \"Table\")", // "{{3,4,6},{a,b,c}}"); check("ImportString(\"3,4,6\\na,b,c\", \"Text\") // InputForm", // "\"3,4,6\n" + "a,b,c\""); check("ImportString(\"a+a+a\", \"String\")", // "3*a"); } @Test public void testIncrement() { check("a = 2", // "2"); check("a++", // "2"); check("a", // "3"); check("++++a+++++2//Hold//FullForm", // "Hold(Plus(PreIncrement(PreIncrement(Increment(Increment(a)))), 2))"); check("index = {1,2,3,4,5,6}", // "{1,2,3,4,5,6}"); check("index[[2]]++", // "2"); check("index", // "{1,3,3,4,5,6}"); } @Test public void testIndeterminate() { check("Tan(Indeterminate)", // "Indeterminate"); check("{And(True, Indeterminate), And(False, Indeterminate)}", // "{Indeterminate,False}"); check("Indeterminate==Indeterminate", // "Indeterminate==Indeterminate"); check("Indeterminate===Indeterminate", // "True"); check("{Re(Indeterminate), Im(Indeterminate)}", // "{Indeterminate,Indeterminate}"); check("NumberQ(Indeterminate)", // "False"); check("{1,2,3}*Indeterminate", // "{Indeterminate,Indeterminate,Indeterminate}"); check("{1,2,3}+Indeterminate", // "{Indeterminate,Indeterminate,Indeterminate}"); check("Integrate(Indeterminate,x)", // "Indeterminate"); check("D(Indeterminate,x)", // "Indeterminate"); check("DirectedInfinity(Indeterminate)", // "ComplexInfinity"); } @Test public void testInexactNumberQ() { check("InexactNumberQ(a)", // "False"); check("InexactNumberQ(3.0)", // "True"); check("InexactNumberQ(2/3)", // "False"); check("InexactNumberQ(4.0+I)", // "True"); } @Test public void testInfinity() { // 1/2*(2+3*l+l^2-4*(-Infinity)-2*l*(-Infinity)+(-Infinity)^2) check("-2*l*(-Infinity)", // "Infinity*l"); check("(-Infinity)^2", // "Infinity"); check("1/2*(2+3*l+l^2-4*(-Infinity)-2*l*(-Infinity)+(-Infinity)^2)", // "1/2*(Infinity+3*l+Infinity*l+l^2)"); check("1 / Infinity", // "0"); check("Infinity + 100", // "Infinity"); check("Sum(1/x^2, {x, 1, Infinity})", // "Pi^2/6"); check("FullForm(Infinity)", // "DirectedInfinity(1)"); check("(2 + 3.5*I) / Infinity", // "0.0"); check("Infinity + Infinity", // "Infinity"); check("Infinity / Infinity", // "Indeterminate"); } @Test public void testInformation() { // print documentation in console check("Information(Sin)", // ""); } @Test public void testInner() { check("Inner({{1,0},{0,1},Indeterminate},{{1,0},{0,1},SparseArray({0,0})},{-1/2,{1,2,3,a},3})", // "Inner({{1,0},{0,1},Indeterminate},{{1,0},{0,1},SparseArray(Number of elements: 0 Dimensions: {2} Default value: 0)},{-\n" + "1/2,{1,2,3,a},3})"); check("Inner(f,{{}},{5},g)", // "Inner(f,{{}},{5},g)"); check("Inner(f,{{1,0},{0,1},1/Sqrt(5)},{x,-3,3/4},g)", // "g(f({1,0},x),f({0,1},-3),f(1/Sqrt(5),3/4))"); check("Inner(I,{{1,0},{0,1},1/Sqrt(5)},{x,-3,3/4},DirectedInfinity(-3.141592653589793))", // "-Infinity[I[{1,0},x],I[{0,1},-3],I[1/Sqrt(5),3/4]]"); check("Inner(Times,{},{ })", // "0"); check("Inner(f,{},{ })", // "0"); check("Inner(Times,{},{x,y})", // "Inner(Times,{},{x,y})"); check("Inner(Times, {a, b}, {x, y}, Plus)", // "a*x+b*y"); check("Inner(Times, {a, b}, {x, y})", // "a*x+b*y"); check("Inner(Power, {a, b, c}, {x, y, z}, Times)", // "a^x*b^y*c^z"); check("Inner(f, {a, b}, {x, y}, g)", // "g(f(a,x),f(b,y))"); check("Inner(f, {{a, b}, {c, d}}, {x, y}, g)", // "{g(f(a,x),f(b,y)),g(f(c,x),f(d,y))}"); check("Inner(f, {{a, b}, {c, d}}, {{u, v}, {w, x}}, g)", // "{{g(f(a,u),f(b,w)),g(f(a,v),f(b,x))},{g(f(c,u),f(d,w)),g(f(c,v),f(d,x))}}"); check("Inner(f, {x, y}, {{a, b}, {c, d}}, g)", // "{g(f(x,a),f(y,c)),g(f(x,b),f(y,d))}"); check("Inner(s, f(1), f(2), t)", // "t(s(1,2))"); check("Inner(And, {{False, False}, {False, True}}, {{True, False}, {True, True}}, Or)", // "{{False,False},{True,True}}"); check("Inner(f, {{{a, b}}, {{x, y}}}, {{1}, {2}}, g)", // "{{{g(f(a,1),f(b,2))}},{{g(f(x,1),f(y,2))}}}"); } @Test public void testInputForm() { check("InputForm(Sin(0))", // "0"); check("\"a string\" // InputForm", // "\"a string\""); } @Test public void testInsert() { // print: The argument x is not a rule or a list of rules. check("Insert(<||>, x, 1)", // "<||>"); check("Insert(<||>, x->y, 3)", // "Insert(<||>,x->y,3)"); check("Insert({a, b, c, d, e}, x, 3)", // "{a,b,x,c,d,e}"); check("Insert({a, b, c, d, e}, x, -2)", // "{a,b,c,d,x,e}"); // test operator form check("Insert(e, pos)", // "Insert(e,pos)"); check("Insert(e, pos)[x]", // "Insert(e,pos)[x]"); check("Insert(2, -1)[{a, b, c, d, e}]", // "{a,b,c,d,e,2}"); check("Insert(2, -2)[{a, b, c, d, e}]", // "{a,b,c,d,2,e}"); } @Test public void testInteger() { check("123456789012345678901234567890", // "123456789012345678901234567890"); check("Head(5)", // "Integer"); check("{a, b} = {2^10000, 2^10000 + 1}; {a == b, a < b, a <= b}", // "{False,True,True}"); } @Test public void testIntegerDigits() { check("IntegerDigits({123,456,789}, 2, 10)", // "{{0,0,0,1,1,1,1,0,1,1},{0,1,1,1,0,0,1,0,0,0},{1,1,0,0,0,1,0,1,0,1}}"); // Long.MAX_VALUE == 9_223_372_036_854_775_807L // check("IntegerDigits(9223372036854775807,2)", // // "{0,1,1}"); check("IntegerDigits(11,2,3)", // "{0,1,1}"); check("IntegerDigits(11,2,2)", // "{1,1}"); // https://oeis.org/A018900 - Sum of two distinct powers of 2 check("Select(Range(1000), (Count(IntegerDigits(#, 2), 1)==2)&)", // "{3,5,6,9,10,12,17,18,20,24,33,34,36,40,48,65,66,68,72,80,96,129,130,132,136,144,\n" + "160,192,257,258,260,264,272,288,320,384,513,514,516,520,528,544,576,640,768}"); check("IntegerDigits(0)", // "{0}"); check("IntegerDigits(123)", // "{1,2,3}"); check("IntegerDigits(-123)", // "{1,2,3}"); check("IntegerDigits(123, 2)", // "{1,1,1,1,0,1,1}"); check("IntegerDigits(123, 2)", // "{1,1,1,1,0,1,1}"); check("IntegerDigits(123, 2, 10)", // "{0,0,0,1,1,1,1,0,1,1}"); check("IntegerDigits({123,456,789}, 2, 10)", // "{{0,0,0,1,1,1,1,0,1,1},{0,1,1,1,0,0,1,0,0,0},{1,1,0,0,0,1,0,1,0,1}}"); check("IntegerDigits(123, -2)", // "IntegerDigits(123,-2)"); check("IntegerDigits(58127, 2)", // "{1,1,1,0,0,0,1,1,0,0,0,0,1,1,1,1}"); check("IntegerDigits(58127, 16)", // "{14,3,0,15}"); check("IntegerDigits({6,7,2}, 2)", // "{{1,1,0},{1,1,1},{1,0}}"); check("IntegerDigits(7, {2,3,4})", // "{{1,1,1},{2,1},{1,3}}"); check("IntegerDigits(Range(0,7), 2)", // "{{0},{1},{1,0},{1,1},{1,0,0},{1,0,1},{1,1,0},{1,1,1}}"); check("IntegerDigits(Range(0,7), 2, 3)", // "{{0,0,0},{0,0,1},{0,1,0},{0,1,1},{1,0,0},{1,0,1},{1,1,0},{1,1,1}}"); } @Test public void testIntegerExponent() { check("IntegerExponent(1230000)", // "4"); check("IntegerExponent(2^10+2^7, 2)", // "7"); check("IntegerExponent(0, 2)", // "Infinity"); check("IntegerExponent(100,100)", // "1"); check("Table(IntegerExponent(n!), {n, 50})", // "{0,0,0,0,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,9,\n" + "9,9,9,9,10,10,10,10,10,12}"); check("IntegerExponent(2524,2)", // "2"); check("IntegerExponent(-510000)", // "4"); check("IntegerExponent(16, 2)", // "4"); check("IntegerExponent(-510000)", // "4"); check("IntegerExponent(10, b)", // "IntegerExponent(10,b)"); } @Test public void testIntegerLength() { check("IntegerLength(8,1)", // "IntegerLength(8,1)"); check("IntegerLength(123456)", // "6"); check("IntegerLength(10^10000)", // "10001"); check("IntegerLength(-10^1000)", // "1001"); check("IntegerLength(8, 2)", // "4"); check("IntegerLength /@ (10 ^ Range(100)) == Range(2, 101)", // "True"); check("IntegerLength(3, -2)", // "IntegerLength(3,-2)"); check("IntegerLength(0)", // "1"); check("IntegerLength /@ (10 ^ Range(100) - 1) == Range(1, 100)", // "True"); } @Test public void testIntegerPart() { check("IntegerPart(Quantity(-1.1, \"Meters\"))", // "-1[Meters]"); check("IntegerPart(Pi^20)", // "8769956796"); check("IntegerPart(2^128-1)", // "340282366920938463463374607431768211455"); check("IntegerPart(Infinity)", // "Infinity"); check("IntegerPart(-Infinity)", // "-Infinity"); check("IntegerPart(I*Infinity)", // "I*Infinity"); check("IntegerPart(-I*Infinity)", // "-I*Infinity"); check("IntegerPart(Pi)", // "3"); check("IntegerPart(-Pi)", // "-3"); check("IntegerPart(IntegerPart(Pi))", // "3"); check("IntegerPart(-9/4)", // "-2"); check("IntegerPart(2.4)", // "2"); check("IntegerPart(-2.4)", // "-2"); check("IntegerPart({-2.4, -2.5, -3.0})", // "{-2,-2,-3}"); } @Test public void testIntegerPartitions() { // message Maximum AST dimension 2147483647 exceededs check("IntegerPartitions(2147483647)", // "IntegerPartitions(2147483647)"); // TODO improve performance // check("IntegerPartitions(1009,2)", // // "{{1009}}"); check("IntegerPartitions(1009,1)", // "{{1009}}"); check("IntegerPartitions(1009,0)", // "{}"); check("IntegerPartitions(1,7,{-1,-2,3})", // "{{3,-2},{3,3,3,-2,-2,-2,-2}}"); check("IntegerPartitions(50, All, {6, 9, 20})", // "{{20,9,9,6,6},{20,6,6,6,6,6}}"); // https://oeis.org/A214772 - McNugget partitions - Number of partitions of n into parts 6, 9 or // 20. check("Table(Length(IntegerPartitions(i, All, {6, 9, 20})), {i,0, 100, 1})", // "{1,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,2,0,1,1,0,0,2,0,1,2,0,1,2,0,1,2,0,1,3,0,2,2,\n" + "1,1,3,0,2,3,1,2,3,1,2,3,1,2,4,1,3,3,2,2,5,1,3,4,2,3,5,2,3,5,2,3,6,2,4,5,3,3,7,2,\n" + "5,6,3,4,7,3,5,7,3,5,8,3,6,7,4,5,9,3,7,8,5}"); check("IntegerPartitions(50, All, {6, 9, 20})", // "{{20,9,9,6,6},{20,6,6,6,6,6}}"); check("IntegerPartitions(156, {9,10}, {1, 5, 10, 25})", // "{{25,25,25,25,25,10,10,10,1},{25,25,25,25,25,10,10,5,5,1}}"); check("IntegerPartitions(156, 10, {1, 5, 10, 25})", // "{{25,25,25,25,25,10,10,10,1},{25,25,25,25,25,25,5,1},{25,25,25,25,25,10,10,5,5,1}}"); check("IntegerPartitions(4)", // "{{4},{3,1},{2,2},{2,1,1},{1,1,1,1}}"); check("IntegerPartitions(6)", // "{{6},{5,1},{4,2},{4,1,1},{3,3},{3,2,1},{3,1,1,1},{2,2,2},{2,2,1,1},{2,1,1,1,1},{\n" // + "1,1,1,1,1,1}}"); check("IntegerPartitions(6, {3,4})", // "{{4,1,1},{3,2,1},{3,1,1,1},{2,2,2},{2,2,1,1}}"); check("IntegerPartitions(10,2)", // "{{10},{9,1},{8,2},{7,3},{6,4},{5,5}}"); check("IntegerPartitions(10,{2})", // "{{9,1},{8,2},{7,3},{6,4},{5,5}}"); check("IntegerPartitions(0)", // "{{}}"); check("IntegerPartitions(1)", // "{{1}}"); check("IntegerPartitions(-1)", // "{}"); check("IntegerPartitions(.5)", // "IntegerPartitions(0.5)"); check("IntegerPartitions(1/2)", // "{}"); } @Test public void testIntegrateDefinite() { check("Integrate(1/(x^3+1), {x,0,1})", // "Pi/(3*Sqrt(3))+Log(2)/3"); check("Integrate(1/(x^3+1), x)", // "ArcTan((-1+2*x)/Sqrt(3))/Sqrt(3)+Log(1+x)/3-Log(1-x+x^2)/6"); check("Integrate(x^4+x^2+1, {x,1,3})", // "886/15"); check("Integrate(a*x^2 + b*x + c, {x,-2,2})", // "16/3*a+4*c"); check("Integrate((4*x^2-7*x- 12)/((x+2)*(x-3)), {x, -1, 2})", // "12-21/5*Log(4)"); check("Integrate(1/((2 + x^2)*Sqrt(4 + 3*x^2)),x)", // "ArcTanh(x/Sqrt(4+3*x^2))/2"); // same as ArcCosh(Sqrt(3/2)) check("Integrate(1/((2 + x^2)*Sqrt(4 + 3*x^2)), {x, -Infinity, Infinity})", // "ArcTanh(1/Sqrt(3))"); check("Integrate((1 + x^3)*x^(1/3), {x, -1, 1})", // "51/52+27/52*(-1)^(1/3)"); if (Config.PROFILE_MODE) { BuiltinFunctionCalls.printStatistics(); } } @Test public void testIntegrateSurd() { check("Integrate(Surd(x,-1), x)", // "Log(x)"); check("Integrate(CubeRoot(x), x)", // "3/4*x*Surd(x,3)"); check("Integrate(Surd(x,3), x)", // "3/4*x*Surd(x,3)"); check("Integrate(Surd(x,6), x)", // "6/7*x*Surd(x,6)"); check("Integrate(Surd(x,-5), x)", // "5/4*x/Surd(x,5)"); check("Integrate(Surd(x,-3), x)", // "3/2*x/Surd(x,3)"); check("Integrate(x^3*CubeRoot(x), x)", // "3/13*x^4*Surd(x,3)"); check("Integrate((1 + x^3)*CubeRoot(x), {x, -1, 1})", // "6/13"); check("Integrate(x^a*CubeRoot(x)^p, x)", // "(x^(1+a)*Surd(x,3)^p)/(1+a+p/3)"); } @Test public void testIntegrateIssue330() { check("Integrate(x*ArcSin(x) ,x)", // "1/6*x^2*(3*ArcSin(x)+3/2*(x*(Sqrt(1-x^2)*Sqrt(x^2)-ArcSin(Sqrt(x^2))))/(x^2)^(3/\n" // + "2))"); check("Limit(x/Sqrt(1-x^2),x->1)", // "Indeterminate"); check("Integrate(x*(1/2*Pi-ArcSin(x)),x)", // "1/4*x^2*(Pi-2*ArcSin(x))+1/4*(-1+x^2)*(x/Sqrt(1-x^2)-ArcTan(x/Sqrt(1-x^2))+(-x^2*ArcTan(x/Sqrt(\n" + "1-x^2)))/(1-x^2))"); } @Test public void testIntegrateIssue851() { check("Integrate(x^n*Haversine(m*x^p),x)", // "(x^(1+n)*(2*p*(m^2*x^(2*p))^((1+n)/p)+(1+n)*(I*m*x^p)^((1+n)/p)*Gamma((1+n)/p,-I*m*x^p)+(\n" // + "1+n)*(-I*m*x^p)^((1+n)/p)*Gamma((1+n)/p,I*m*x^p)))/(4*(1+n)*p*(m^2*x^(2*p))^((1+n)/p))"); check("Integrate(x^n*ArcSin(m*x^p),x)", // "(x^(1+n)*ArcSin(m*x^p))/(1+n)+(-m*p*x^(1+n+p)*Hypergeometric2F1(1/2,(1+n+p)/(2*p),\n" + "1+(1+n+p)/(2*p),m^2*x^(2*p)))/((1+n)*(1+n+p))"); check("Integrate(x^n*ArcSinh(m*x^p),x)", // "(x^(1+n)*ArcSinh(m*x^p))/(1+n)+(-m*p*x^(1+n+p)*Hypergeometric2F1(1/2,(1+n+p)/(2*p),\n" + "1+(1+n+p)/(2*p),-m^2*x^(2*p)))/((1+n)*(1+n+p))"); check("Integrate(PolyGamma(m*x),x)", // "LogGamma(m*x)/m"); check("Integrate(LogisticSigmoid(m*x),x)", // "-Log(1-LogisticSigmoid(m*x))/m"); check("Integrate(Haversine(m*x),x)", // "x/2-Sin(m*x)/(2*m)"); check("Integrate(x^n*Haversine(m*x),x)", // "1/4*x^n*((2*x)/(1+n)+(x*Gamma(1+n,-I*m*x))/(-I*m*x)^(1+n)+(x*Gamma(1+n,I*m*x))/(I*m*x)^(\n"// + "1+n))"); check("Integrate(InverseHaversine(m*x),x)", // "(Sqrt(m*x*(1-m*x))+(-1+2*m*x)*ArcSin(Sqrt(m*x)))/m"); check("Integrate(x^n*InverseHaversine(m*x),x)", // "(2*x^(1+n)*((3+2*n)*ArcSin(Sqrt(m*x))-Sqrt(m*x)*Hypergeometric2F1(1/2,3/2+n,5/2+n,m*x)))/((\n"// + "1+n)*(3+2*n))"); check("Integrate(InverseErf(m*x),x)", // "-1/(E^InverseErf(m*x)^2*m*Sqrt(Pi))"); check("Integrate(InverseErfc(m*x),x)", // "1/(E^InverseErfc(m*x)^2*m*Sqrt(Pi))"); check("Integrate(EllipticE(m*x),x)", // "2/3*((1+m*x)*EllipticE(m*x)+(-1+m*x)*EllipticK(m*x))/m"); check("Integrate(EllipticK(m*x),x)", // "(2*(EllipticE(m*x)+(-1+m*x)*EllipticK(m*x)))/m"); check("Integrate(x*EllipticE(m*x),x)", // "1/4*Pi*x^2*HypergeometricPFQ({-1/2,1/2,2},{1,3},m*x)"); check("Integrate(x*EllipticK(m*x),x)", // "1/4*Pi*x^2*HypergeometricPFQ({1/2,1/2,2},{1,3},m*x)"); check("Integrate(x^n*EllipticE(m*x),x)", // "(Pi*x^(1+n)*HypergeometricPFQ({-1/2,1/2,1+n},{1,2+n},m*x))/(2+2*n)"); check("Integrate(x^n*EllipticK(m*x),x)", // "(Pi*x^(1+n)*HypergeometricPFQ({1/2,1/2,1+n},{1,2+n},m*x))/(2+2*n)"); check("Integrate(x^n*CubeRoot(m*x),x)", // "(x^(1+n)*Surd(m*x,3))/(4/3+n)"); check("Integrate(Surd(m*x,7),x)", // "7/8*x*Surd(m*x,7)"); check("Integrate(x^n*Surd(m*x,7),x)", // "(x^(1+n)*Surd(m*x,7))/(8/7+n)"); check("Integrate(x^n*ArcCot(11*Sin(s)*x),x)", // "(x^(1+n)*ArcCot(11*x*Sin(s)))/(1+n)+(11*x^(2+n)*Hypergeometric2F1(1,1/2*(2+n),1/\n"// + "2*(4+n),-121*x^2*Sin(s)^2)*Sin(s))/(2+3*n+n^2)"); check("Integrate(ArcSin(x),x)", // "Sqrt(1-x^2)+x*ArcSin(x)"); check("Integrate(x^(-3)*ArcSin(x),x)", // "(-x*Sqrt(1-x^2)-ArcSin(x))/(2*x^2)"); check("Integrate(x*ArcSin(x),{x,0,1})", // "Pi/8"); check("Integrate(x*ArcSin(x),x)", // "1/6*x^2*(3*ArcSin(x)+3/2*(x*(Sqrt(1-x^2)*Sqrt(x^2)-ArcSin(Sqrt(x^2))))/(x^2)^(3/\n" // + "2))"); check("Integrate(x^n*ArcSin(m*x),x)", // "(x^(1+n)*ArcSin(m*x))/(1+n)+(-m*x^(2+n)*Hypergeometric2F1(1/2,1/2*(2+n),1/2*(4+n),m^\n" // + "2*x^2))/(2+3*n+n^2)"); check("Integrate(x^n*ArcTanh(m*x),x)", // "(x^(1+n)*ArcTanh(m*x))/(1+n)+(-m*x^(2+n)*Hypergeometric2F1(1,1/2*(2+n),1/2*(4+n),m^\n" + "2*x^2))/(2+3*n+n^2)"); check("Integrate(x*ArcTanh(3*x),{x,0,1})", // "1/6*(1/9*(9-3*ArcTanh(3))+3*ArcTanh(3))"); } @Test public void testIntegrate() { check("Integrate(Cos(x^3), x)", // "(-x*Gamma(1/3,-I*x^3))/(6*(-I*x^3)^(1/3))+(-x*Gamma(1/3,I*x^3))/(6*(I*x^3)^(1/3))"); check("Integrate(Round(1.235512+1.23787m, 0.01),m)", // "100000/123787*Rubi`subst[Integrate(Round(m,1/100),m),m,154439/125000+123787/\n" + "100000*m]"); check("Integrate(Tan(x),Cos(x))", // "Integrate(Tan(x),Cos(x))"); check("Integrate(Piecewise({{1/(2 x^2), Abs(x) > 1} },4),x)", // "Piecewise({{-1/(2*x),Abs(x)>1}},4*x)"); check("Integrate(Piecewise({{x^2, x <= 0}, {x, x > 0}}),x)", // "Piecewise({{x^3/3,x<=0},{x^2/2,x>0}},0)"); check("Integrate((Sinh(x)-x)/(x^2*Sinh(x)),x)", // "-1/x-Integrate(Csch(x)/x,x)"); check("Refine(Integrate(Abs(E+Pi*x^(-8)),x), Element(x,Reals))", // "-Pi/(7*x^7)+E*x"); check("Refine(Integrate(Abs(Pi+42*x^6),x), Element(x,Reals))", // "Pi*x+6*x^7"); check("Refine(Integrate(Abs(E+Pi*x^(-1)),x), Element(x,Reals))", // "Piecewise({{E*x+Pi*Log(x),x<=-Pi/E},{-E*x+2*Pi*(-2+I*Pi+Log(Pi))-Pi*Log(x),-Pi/E3)", // // ""); // see github #128 // check("Apart(a/((8/3*a*b^(2/3)-16/9*b)^2*(4/3*a*b^(2/3)+16/9*b)))", // // "a/(a^3-4/3*a*b^(2/3)+16/27*b)"); check("Integrate(a/(a^3-4/3*a*b^(2/3)+16/27*b),a)", // "-1/(3*a-2*b^(1/3))+Log(3*a-2*b^(1/3))/(3*b^(1/3))-Log(3*a+4*b^(1/3))/(3*b^(1/3))"); check( "Simplify(D(-1/(3*a-2*b^(1/3))+Log(3*a-2*b^(1/3))/(3*b^(1/3))-Log(3*a+4*b^(1/3))/(3*b^(1/3)),a))", // "(27*a)/(27*a^3-36*a*b^(2/3)+16*b)"); // "3/(3*a-2*b^(1/3))^2+1/(3*a*b^(1/3)-2*b^(2/3))-1/(3*a*b^(1/3)+4*b^(2/3))"); // expensive JUnit test // check("Integrate(((a+b)/(a^(1/3)+b^(1/3))-(a*b)^(1/3))/(a^(1/3)-b^(1/3))^2,a)", // // "a+3/2*a^(2/3)*b^(1/3)+6*a^(1/3)*b^(2/3)+(-3*b^(4/3))/(a^(1/3)-b^(1/3))-3/2*a^(1/\n" + // "3)*(a*b)^(1/3)-6*b^(1/3)*(a*b)^(1/3)+(3*b*(a*b)^(1/3))/(a^(1/3)*(a^(1/3)-b^(1/3)))+\n" + // "3*b*Log(a^(1/3)-b^(1/3))+(-9*b^(2/3)*(a*b)^(1/3)*Log(a^(1/3)-b^(1/3)))/a^(1/3)-3*b*Log(a^(\n" // + // "1/3)+b^(1/3))+3*b*Log(a-a^(2/3)*b^(1/3)-a^(1/3)*b^(2/3)+b)"); // see github #120 check("Integrate(Ln(x)^2, {x,0,2})", // "4-4*Log(2)+2*Log(2)^2"); check("Integrate(Ln(x)^2, {x,0,2}) // N", // "2.18832"); check("NIntegrate(Ln(x)^2, {x,0,2}) // N", // "2.1857"); // see github #116 // should give (2*ArcTan((1 + 2*x)/Sqrt(3)))/Sqrt(3) check(" Integrate(1/(x^2+x+1),x) ", // "(2*ArcTan((1+2*x)/Sqrt(3)))/Sqrt(3)"); // see github #109 check("Int(1/Sqrt(9*x^4+1),{x,0,999})//N", // "1.07012"); check("Integrate(x^n,x)", // "x^(1+n)/(1+n)"); check("Integrate(x^n,{x,0,1})", // "ConditionalExpression(1/(1+n),n>-1)"); // https://github.com/RuleBasedIntegration/Rubi/issues/12 check("Integrate(Tan(Log(x)),x)", // "-I*x+I*2*x*Hypergeometric2F1(-I*1/2,1,1-I*1/2,-x^(I*2))"); check("Integrate(5*E^(3*x),{x,2,a})", // "1/3*(-5*E^6+5*E^(3*a))"); check("Integrate(Sqrt(9-x^2),x)", // "1/2*x*Sqrt(9-x^2)+9/2*ArcSin(x/3)"); check("Integrate(Sqrt(9-x^2),{x,0,3})", // "9/4*Pi"); check("Integrate({Sin(x),Cos(x)},x)", // "{-Cos(x),Sin(x)}"); check("Integrate({Sin(x),Cos(x)},{x,a,b})", // "{Cos(a)-Cos(b),-Sin(a)+Sin(b)}"); check("Integrate(2*x,x)", "x^2"); check("Integrate(Tan(x) ^ 5, x)", // "-Log(Cos(x))-Tan(x)^2/2+Tan(x)^4/4"); check("Integrate(x*Sin(x),{x,1.0,2*Pi})", // "-6.58435"); // check("Integrate(x/(1+x+x^7),x)", ""); check("Integrate(1/y(x)^2,y(x))", // "-1/y(x)"); check("Integrate(f(x,y),x)", // "Integrate(f(x,y),x)"); check("Integrate(f(x,x),x)", // "Integrate(f(x,x),x)"); if (Config.PROFILE_MODE) { BuiltinFunctionCalls.printStatistics(); } } @Test public void testInterpolation() { // print message: InterpolatingFunction: Input value {10} lies outside the range of data in the // interpolating // function. Extrapolation will be used. check("ipf=Interpolation({{0, 0}, {0.1, .3}, {0.5, .6}, {1, -.2}, {2, 3}}); ipf(10) ", // "6311.0"); check("ipf= Interpolation({{0, 0}, {0.1, .3}, {0.5, .6}, {1, -.2}, {2, 3}}); ipf(3/4) ", // "0.26864"); check("ipf=Interpolation({{0, 0}, {0.1, .3}, {0.5, .6}, {1, -.2}, {2, 3}}); ipf(0.75) ", // "0.26864"); check("ipf=Interpolation({{0,17},{1,3},{2,5},{3,4},{4,3},{5,0},{6,23}}); ipf(19/4) ", // "-19/32"); check("ipf=Interpolation({{0, 0}, {1, 1}, {2, 3}, {3, 4}, {4, 3}, {5, 0}}); ipf(5/2) ", // "59/16"); check("Interpolation({{0, 0}, {1, 1}, {2, 3}, {3, 4}, {4, 3}, {5, 0}})", // "InterpolatingFunction[Piecewise({{InterpolatingPolynomial({{0,0},{1,1},{2,3},{3,4}},#1),#1<2},{InterpolatingPolynomial({{\n" + "1,1},{2,3},{3,4},{4,3}},#1),2<=#1&<3},{InterpolatingPolynomial({{2,3},{3,4},{\n" + "4,3},{5,0}},#1),#1>=3}})&]"); check( "ipf=Interpolation({{0, 0}, {1, 1}, {2, 3}, {3, 4}, {4, 3}, {5, 0}});{ipf(2.5),ipf(3.0),ipf(3.5)}", // "{3.6875,4.0,3.75}"); } @Test public void testInterpolatingFunction() { check("ipf=Interpolation({{0, 0}, {0.1, .3}, {0.5, .6}, {1, -.2}, {2, 3}}); ipf(0.75) ", // "0.26864"); check("ipf=Interpolation({{0,17},{1,3},{2,5},{3,4},{4,3},{5,0},{6,23}}); ipf(19/4) ", // "-19/32"); check("ipf=Interpolation({{0, 0}, {1, 1}, {2, 3}, {3, 4}, {4, 3}, {5, 0}}); ipf(5/2) ", // "59/16"); check("Interpolation({{0, 0}, {1, 1}, {2, 3}, {3, 4}, {4, 3}, {5, 0}})", // "InterpolatingFunction[Piecewise({{InterpolatingPolynomial({{0,0},{1,1},{2,3},{3,4}},#1),#1<2},{InterpolatingPolynomial({{\n" + "1,1},{2,3},{3,4},{4,3}},#1),2<=#1&<3},{InterpolatingPolynomial({{2,3},{3,4},{\n" + "4,3},{5,0}},#1),#1>=3}})&]"); check( "ipf=Interpolation({{0, 0}, {1, 1}, {2, 3}, {3, 4}, {4, 3}, {5, 0}});{ipf(2.5),ipf(3.0),ipf(3.5)}", // "{3.6875,4.0,3.75}"); } @Test public void testInterpolatingPolynomial() { check("InterpolatingPolynomial( {{0.1,0.3}, {0.5,0.6}, {1,-0.2}, {2.0,3.0}},x)", // "0.3+(0.75+(-2.61111+3.05848*(-1+x))*(-0.5+x))*(-0.1+x)"); check("InterpolatingPolynomial( {{0.1,0.3}, {0.5,0.6}, {1,-0.2}, {2.0,3.0}},0.75)", // "0.238944"); check("InterpolatingPolynomial( {{0.0,0.0},{0.1,0.3}, {0.5,0.6}, {1,-0.2}, {2.0,3.0}},0.75)", // "0.26864"); check("InterpolatingPolynomial({1.0,4.0},x)", // "1.0+3.0*(-1+x)"); check("InterpolatingPolynomial({1,4},x)", // "1+3*(-1+x)"); check("InterpolatingPolynomial({1,4,9},x)", // "1+(-1+x)*(1+x)"); check("InterpolatingPolynomial({1,4,9,16},x)", // "1+(-1+x)*(1+x)"); check("InterpolatingPolynomial({1,2},x)", // "x"); check("InterpolatingPolynomial({{-1, 4}, {0, 2}, {1, 6}}, x)", // "4+(1+x)*(-2+3*x)"); check("Expand((3*x-2)*(x+1)+4)", // "2+x+3*x^2"); check("InterpolatingPolynomial({{0, 1}, {a, 0}, {b, 0}, {c, 0}}, x)", // "1+x*(-1/a+(1/(a*b)+(b-x)/(a*b*c))*(-a+x))"); check("InterpolatingPolynomial({1,2,3,5,8,5},x)", // "1+(1+(1/6+(-1/24+1/20*(5-x))*(-4+x))*(-3+x)*(-2+x))*(-1+x)"); check("((x-1)*((x-3)*(x-2)*((x-4)*(-1/20*x+5/24)+1/6)+1)+1) /. x -> Range(6)", // "{1,2,3,5,8,5}"); } @Test public void testInterquartileRange() { // https://en.wikipedia.org/wiki/Interquartile_range check("InterquartileRange({7,7,31,31,47,75,87,115,116,119,119,155,177})", // "88"); check("InterquartileRange({1, 3, 4, 2, 5, 6})", // "3"); check("InterquartileRange(BernoulliDistribution(x))", // "Piecewise({{1,1/4Equal)", // "True"); check("IntersectingQ(f(b, a, b,d), f(c,c,c,d))", // "True"); check("IntersectingQ(f(b, a, b,d), f(e,g))", // "False"); // same as ContainsAny check("IntersectingQ({b, a, b}, {a, b, c})", // "True"); check("IntersectingQ({b, a, b,d}, {c,c,c,d})", // "True"); check("IntersectingQ({d,f,e}, {a, b, c})", // "False"); check("IntersectingQ({ }, {a, b, c})", // "False"); check("IntersectingQ(1, {1,2,3})", // "IntersectingQ(1,{1,2,3})"); check("IntersectingQ({1,2,3}, 4)", // "IntersectingQ({1,2,3},4)"); check("IntersectingQ({1.0,2.0}, {1,2,3})", // "False"); check("IntersectingQ({1.0,2.0}, {1,2,3}, SameTest->Equal)", // "True"); } @Test public void testInterrupt() { check("Print(test1); Interrupt(); Print(test2)", // "$Aborted"); } @Test public void testInverseBetaRegularized() { check("InverseBetaRegularized(10, 12.0, 0.5)", // "InverseBetaRegularized(10.0,12.0,0.5)"); check("InverseBetaRegularized(0.1, 12.0, 0.5)", // "0.891295"); check("InverseBetaRegularized(0.8, 1, 2)", // "0.552786"); check("Table(InverseBetaRegularized(s, 2, 3), {s, 0, 1,0.1})", // "{0.0,0.142559,0.212317,0.272384,0.329167,0.385728,0.4445,0.508405,0.582454,0.679539,1.0}"); check("InverseBetaRegularized(0,42,b)", // "0"); check("InverseBetaRegularized(1,47.11,b)", // "1"); check("InverseBetaRegularized(z,0,a,b)", // "z"); check("InverseBetaRegularized(0,z,a,b)", // "InverseBetaRegularized(z,a,b)"); } @Test public void testInverseCDF() { // https://github.com/axkr/symja_android_library/issues/147 check("InverseCDF(StudentTDistribution(24), 0.95)", // "1.71088"); check("InverseCDF(BetaDistribution(2,3), 0.1)", // "0.142559"); check("InverseCDF(BetaDistribution(2,3), 0.9)", // "0.679539"); check("InverseCDF(CauchyDistribution(a, b), x)", // "ConditionalExpression(Piecewise({{a+b*Tan(Pi*(-1/2+x)),0E^((-I*Pi+Log(a0)-Log(a1))/(-p+q))}}"); check("Solve(c*x*a^x==12,x)", // "{{x->ProductLog((12*Log(a))/c)/Log(a)}}"); check("InverseFunction(#*a^# &)", // "ProductLog(#1*Log(a))/Log(a)&"); check("InverseFunction(c*#*a^# &)", // "ProductLog((#1*Log(a))/c)/Log(a)&"); check("InverseFunction(#^p &)", // "#1^(1/p)&"); check("InverseFunction(Composition(f, g, h))[x]", // "InverseFunction(h)[InverseFunction(g)[InverseFunction(f)[x]]]"); check("Sin @* InverseFunction(Tan)", // "Sin@*ArcTan"); check("D(InverseFunction(Sin)[x],x)", // "1/Sqrt(1-x^2)"); check("D(InverseFunction(f)[x],x)", // "1/f'(InverseFunction(f)[x])"); check("D(InverseFunction(f(g))[x],x)", // "1/f(g)'[InverseFunction(f(g))[x]]"); check("InverseFunction((a*#)/(c*#) &)", // "InverseFunction((a*#1)/(c*#1)&)"); check("InverseFunction((a*#)/(c*# + d) &)", // "(#1*d)/(a*(1+(-#1*c)/a))&"); check("InverseFunction((a*# + b)/(c*# + d) &)", // "(-b+#1*d)/(a-#1*c)&"); check("InverseFunction((a * # + b)&)", // "(#1-b)/a&"); check("InverseFunction(Abs)", // "-#1&"); check("InverseFunction(Sin)", // "ArcSin"); check("f = 2 # & @*Cases(_Symbol)", // "(2*#1&)@*Cases(_Symbol)"); check("f({a, \"b\", c, d, \"e\", 5})", // "{2*a,2*c,2*d}"); } @Test public void testInverseGammaRegularized() { check("InverseGammaRegularized(a, Infinity, z)", // "InverseGammaRegularized(a,-z)"); check("InverseGammaRegularized(42,0)", // "Infinity"); check("InverseGammaRegularized(10,1)", // "0"); } @Test public void testInverseGudermannian() { check("N(InverseGudermannian(4/3), 50)", // "2.126176090782269391936236271172156185450325122338"); check("N(InverseGudermannian(4/3-2/3*I), 50)", // "1.0709631602353002334250501606064505306184199829854+I*(-1.253841344203559414899366482437511230389585771795)"); check("InverseGudermannian(3.75)", // "-0.649839+I*3.14159"); check("InverseGudermannian(1.111111)", // "1.45253"); check("InverseGudermannian(100.0)", // "-0.55783"); check("InverseGudermannian(I*Pi+5.0)", // "-0.0829127+I*1.54624"); check("InverseGudermannian({1.5, 3.75, 5.5, 7.25})", // "{3.34068,-0.649839+I*3.14159,-0.878248,1.1663}"); } @Test public void testInverseHaversine() { check("N(InverseHaversine(1/7), 50)", // "0.77519337331036130720409371118247342579981743402299"); check("N(InverseHaversine(798+I), 50)", // "3.1403387355052352207114821042916462562377389087353+I*8.067776883665043131189388013520931297785865736445"); checkNumeric("InverseHaversine(0.5)", // "1.5707963267948968"); checkNumeric("InverseHaversine(1 + 2.5 * I)", // "1.764589463349828+I*2.3309746530493123"); check("InverseHaversine(1/4)", // "Pi/3"); checkNumeric("InverseHaversine(0.7)", // "1.9823131728623846"); // Java double machine precision // check("ArcSin(1.3038404810405)", // "1.5707963267948966+I*(-0.7610396837317912)"); // apfloat/apcomplex precision // TODO use ExprParser#getReal() if apfloat problems are fixed // check("ArcSin(1.3038404810405297)", // "1.5707963267948966+I*(-7.610396837318266e-1)"); checkNumeric("N(ArcSin(-2),30)", // "-1.57079632679489661923132169163+I*1.3169578969248167086250463473"); checkNumeric("N(ArcSin(2),30)", // "1.5707963267948966192313216916+I*(-1.3169578969248167086250463473)"); checkNumeric("ArcSin(-2.0)", // "-1.5707963267948966+I*1.3169578969248164"); checkNumeric("ArcSin(2.0)", // "1.5707963267948966+I*(-1.3169578969248166)"); checkNumeric("ArcSin(1.3038404810405297)", // "1.570796326794896+I*(-0.7610396837318266)"); checkNumeric("InverseHaversine(1.7)", // "3.141592653589793+I*(-1.5220793674636532)"); } @Test public void testJaccardDissimilarity() { check("JaccardDissimilarity({1, 0, 1, 1, 0}, {1, 1, 0, 1, 1})", // "3/5"); check("JaccardDissimilarity({True, False, True}, {True, True, False})", // "2/3"); check("JaccardDissimilarity({1, 1, 1, 1}, {1, 1, 1, 1})", // "0"); check("JaccardDissimilarity({0, 0, 0, 0}, {1, 1, 1, 1})", // "1"); } @Test public void testJacobiSymbol() { check("JacobiSymbol(12345, 331)", // "-1"); check("JacobiSymbol(98, 331)", // "-1"); check("JacobiSymbol(10^10+1, Prime(1000))", // "1"); check("JacobiSymbol(10^11+1, Prime(2000))", // "-1"); check("JacobiSymbol(10, 5)", // "0"); check("Table(f(n, m), {n, 0, 10}, {m, 1, n, 2})", // "{{},{f(1,1)},{f(2,1)},{f(3,1),f(3,3)},{f(4,1),f(4,3)},{f(5,1),f(5,3),f(5,5)},{f(\n" + "6,1),f(6,3),f(6,5)},{f(7,1),f(7,3),f(7,5),f(7,7)},{f(8,1),f(8,3),f(8,5),f(8,7)},{f(\n" + "9,1),f(9,3),f(9,5),f(9,7),f(9,9)},{f(10,1),f(10,3),f(10,5),f(10,7),f(10,9)}}"); check("Table(JacobiSymbol(n, m), {n, 0, 10}, {m, 1, n, 2})", // "{{},{1},{1},{1,0},{1,1},{1,-1,0},{1,0,1},{1,1,-1,0},{1,-1,-1,1},{1,0,1,1,0},{1,1,\n" + "0,-1,1}}"); check("JacobiSymbol(1001, 9907)", // "-1"); check("JacobiSymbol({2, 3, 5, 7, 11}, 3)", // "{-1,0,-1,1,-1}"); check("JacobiSymbol(3, {1, 3, 5, 7})", // "{1,0,-1,-1}"); check("JacobiSymbol(7, 6)", // "1"); // check("JacobiSymbol(n, 1)", "n"); check("JacobiSymbol(-3, {1, 3, 5, 7})", // "{JacobiSymbol(-3,1),JacobiSymbol(-3,3),JacobiSymbol(-3,5),JacobiSymbol(-3,7)}"); } @Test public void testJavaForm() { EvalEngine.resetModuleCounter4JUnit(); check("JavaForm(Sqrt(x), Complex)", // "(x).sqrt()"); check("JavaForm(1/(x+y), Complex)", // "(x.add(y)).reciprocal()"); check("JavaForm(1/Sqrt(x), Complex)", // "(x).reciprocal().sqrt()"); check("JavaForm(x^(-1/2), Complex)", // "(x).reciprocal().sqrt()"); check("JavaForm((x+1)^2+(x+1)^3+x*y*10*I, Complex)", // "Complex f1(Complex x, Complex y) {\n" // + "Complex v1 = Complex.valueOf(1.0).add(x);\n" + "return (v1).pow(Complex.valueOf(2.0)).add((v1).pow(Complex.valueOf(3.0)).add(Complex.valueOf(0.0, 10.0).multiply(x.multiply(y))));\n" + "}\n" + ""); check("JavaForm((x+1)^2+(x+1)^3, Float)", // "double f2(double x) {\n" // + "double v1 = 1+x;\n" + "return Math.pow(v1,2)+Math.pow(v1,3);\n" + "}\n" + ""); check("JavaForm(f(123456789123456789))", // "$(f,ZZ(123456789123456789L))"); check("JavaForm(E^3-Cos(Pi^2/x), Prefix->True)", // "F.Subtract(F.Exp(F.C3),F.Cos(F.Times(F.Sqr(F.Pi),F.Power(F.x,F.CN1))))"); check("JavaForm(E^3-Cos(Pi^2/x), Float->True)", // "(20.085536923187664)-Math.cos((9.869604401089358)/x)"); check("JavaForm(E^3-Cos(Pi^2/x), Float)", // "(20.085536923187664)-Math.cos((9.869604401089358)/x)"); check("JavaForm(Hold(D(sin(x)*cos(x),x)), prefix->True)", // "F.D(F.Times(F.Sin(F.x),F.Cos(F.x)),F.x)"); check("JavaForm(Hold(D(sin(x)*cos(x),x)))", // "D(Times(Sin(x),Cos(x)),x)"); check("JavaForm(D(sin(x)*cos(x),x), prefix->True)", // "F.Subtract(F.Sqr(F.Cos(F.x)),F.Sqr(F.Sin(F.x)))"); check("JavaForm(D(sin(x)*cos(x),x))", // "Subtract(Sqr(Cos(x)),Sqr(Sin(x)))"); check("JavaForm(I/2*E^((-I)*x)-I/2*E^(I*x), Prefix->True)", // "F.Plus(F.Times(F.CC(0L,1L,1L,2L),F.Exp(F.Times(F.CNI,F.x))),F.Times(F.CC(0L,1L,-1L,2L),F.Exp(F.Times(F.CI,F.x))))"); check("JavaForm(I/2*E^((-I)*x)-I/2*E^(I*x))", // "Plus(Times(CC(0L,1L,1L,2L),Exp(Times(CNI,x))),Times(CC(0L,1L,-1L,2L),Exp(Times(CI,x))))"); check("JavaForm(a+b+x^2+I+7+3/4+x+y, Prefix->True)", // "F.Plus(F.CC(31L,4L,1L,1L),F.a,F.b,F.x,F.Sqr(F.x),F.y)"); check("JavaForm(a+b+x^2+I+7+3/4+x+y)", // "Plus(CC(31L,4L,1L,1L),a,b,x,Sqr(x),y)"); check("JavaForm((x+y)^-1, Prefix->True)", // "F.Power(F.Plus(F.x,F.y),F.CN1)"); check("JavaForm((x+y)^-1, Float)", // "1.0/(x+y)"); } @Test public void testJSForm() { EvalEngine.resetModuleCounter4JUnit(); // check("JSForm(Ramp(x))", // // "((x>=0) ? x : ( 0 ))"); check("JSForm( {Identity( x ),Log( y )} )", // "[x,Math.log(y)]"); check("JSForm(Sign(x)*Abs(x)^(1/3))", // "Math.cbrt(Math.abs(x))*Math.sign(x)"); check("JSForm(Clip(x))", // "\n" // + " (function() {\n" // + "if (x<-1) { return -1;}\n" // + "if (x>1) { return 1;}\n" // + " return x;})()\n"); check("JSForm(Clip(x, {-2, 4}))", // "\n" + " (function() {\n" + "if (x<-2) { return -2;}\n" + "if (x>4) { return 4;}\n" + " return x;})()\n" + ""); check("JSForm(E^3-Cos(Pi^2/x))", // "(20.085536923187664)-Math.cos((9.869604401089358)/x)"); check("Piecewise({{x, 0 < x < 1}, {x^3, 1 < x < 2}}) // JSForm", // "\n" // + " (function() {\n" // + "if (0= 0&&x<1},{Cos(x-1), x >= 1}}) )", // "\n" + " (function() {\n" + "if (x<0) { return Math.pow(x,2);}\n" + "if (x>=0&&x<1) { return x;}\n" + "if (x>=1) { return Math.cos(1-x);}\n" + " return 0;})()\n" + ""); check("JSForm(ConditionalExpression(Log(1- q), 0 <=q<=1))", // "((0<=q && q<=1) ? (Math.log(1-q)) : ( Number.NaN ))"); check("JSForm(x < 10 && y > 1)", // "x<10&&y>1"); check("JSForm(a{-1,2}), {a,0,10}))", // // // "var board = JXG.JSXGraph.initBoard('jxgbox', // {axis:true,showCopyright:false,boundingbox:[-0.8641592653589794,2.7,7.147344572538565,-1.7]});\n" // + "board.suspendUpdate();\n" // + "var a = // board.create('slider',[[-0.0630088815692249,2.2600000000000002],[6.346194188748811,2.2600000000000002],[0,0,10]],{name:'a'});\n" // + "\n" // + "function $f1(x) { try { return [mul(cos(add(1,mul(a.Value(),x))),sin(x))];} catch(e) { // return Number.NaN;} }\n" // + "board.create('functiongraph',[$f1, 0, (6.283185307179586)],{strokecolor:'#5e81b5'});\n" // + "\n" + "\n" + "board.unsuspendUpdate();\n" + ""); // Mathcell syntax / generate TeX for MathJAX check("JSForm(Manipulate(Factor(x^n + 1), {n, 1, 5, 1}))", // "var parent = document.currentScript.parentNode;\n" // + "var id = generateId();\n" // + "parent.id = id;\n" // + "MathCell( id, [ { type: 'slider', min: 1.0, max: 5.0, step: 1.0, name: 'n', label: 'n' }\n" // + " ] );\n" // + "\n" // + "parent.update = function( id ) {\n" // + "\n" // + "var n = getVariable(id, 'n');\n" // + "\n" // + "\n" // + "var expressions = [ '1 + x',\n" // + "'1 + {x}^{2}',\n" // + "'\\\\\\\\left( 1 + x\\\\\\\\right) \\\\\\\\cdot \\\\\\\\left( 1 - x + {x}^{2}\\\\\\\\right) ',\n" // + "'1 + {x}^{4}',\n" // + "'\\\\\\\\left( 1 + x\\\\\\\\right) \\\\\\\\cdot \\\\\\\\left( 1 - x + {x}^{2} - {x}^{3} + {x}^{4}\\\\\\\\right) ' ];\n" // + "\n" // + " var data = '\\\\\\\\[' + expressions[Math.trunc((n-1.0)/1.0)] + '\\\\\\\\]';\n" // + "\n" // + " data = data.replace( /\\\\\\\\/g, '\' );\n" // + "\n" // + " var config = {type: 'text', center: true };\n" // + "\n" // + " evaluate( id, data, config );\n" // + "\n" // + " MathJax.Hub.Queue( [ 'Typeset', MathJax.Hub, id ] );\n" // + "\n" // + "}\n" // + "parent.update( id );\n" // + ""); // JSXGraph.org syntax // @Ignore Deactivate, because of change to Graphics output // check("JSForm(ListPlot(Prime(Range(25))))", // // "var board = JXG.JSXGraph.initBoard('jxgbox', // {axis:true,boundingbox:[-1.85,102.3,27.85,-3.3]});\n" // + "board.suspendUpdate();\n" + "\n" // + "board.create('point', [function() {return 1;},function() {return 2;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + // // "board.create('point', [function() {return 2;},function() {return 3;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 3;},function() {return 5;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 4;},function() {return 7;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 5;},function() {return 11;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 6;},function() {return 13;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 7;},function() {return 17;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + // // "board.create('point', [function() {return 8;},function() {return 19;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 9;},function() {return 23;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 10;},function() {return 29;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 11;},function() {return 31;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 12;},function() {return 37;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 13;},function() {return 41;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 14;},function() {return 43;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 15;},function() {return 47;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 16;},function() {return 53;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 17;},function() {return 59;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 18;},function() {return 61;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 19;},function() {return 67;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 20;},function() {return 71;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 21;},function() {return 73;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 22;},function() {return 79;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 23;},function() {return 83;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 24;},function() {return 89;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "board.create('point', [function() {return 25;},function() {return 97;}], {color:'#5e81b5' // ,name:'', face:'o', size: 2 } );\n" // + "\n" + "\n" + "board.unsuspendUpdate();\n" + ""); check("JSForm((x+y)^-1)", // "1.0/(x+y)"); } @Test public void testJoin() { check("Join(<|a->0,b:>1|>,SparseArray({0,0}))", // "Join(<|a->0,b:>1|>,SparseArray(Number of elements: 0 Dimensions: {2} Default value: 0))"); check("s=SparseArray({{1,0,1},{1,2,0}})", // "SparseArray(Number of elements: 4 Dimensions: {2,3} Default value: 0)"); check("Join(s,{{1,0,1,3},{1,2,0,4}})", // "{{1,0,1},{1,2,0},{1,0,1,3},{1,2,0,4}}"); check("Join(s,s)// MatrixForm", // "{{1,0,1},\n" + // " {1,2,0},\n" + // " {1,0,1},\n" + // " {1,2,0}}"); check("Join(s,s,s) // MatrixForm", // "{{1,0,1},\n" + // " {1,2,0},\n" + // " {1,0,1},\n" + // " {1,2,0},\n" + // " {1,0,1},\n" + // " {1,2,0}}"); check("Join(<|A->1,B->2,C->3,D->4|>,<|A->1,B->2,C->3,D->4|>)", // "<|A->1,B->2,C->3,D->4|>"); check("Join(<|a -> b|>, <|c -> d, a -> e|>)", // "<|a->e,c->d|>"); // http://oeis.org/A001597 - Perfect powers: m^k where m > 0 and k >= 2. // check("Join({1}, Select(Range(1770), GCD@@FactorInteger(#)[[All, 2]]>1&))", // "{1,4,8,9,16,25,27,32,36,49,64,81,100,121,125,128,144,169,196,216,225,243,256,289,\n" + "324,343,361,400,441,484,512,529,576,625,676,729,784,841,900,961,1000,1024,1089,\n" + "1156,1225,1296,1331,1369,1444,1521,1600,1681,1728,1764}"); check("Join({a, b}, {c, d, e})", // "{a,b,c,d,e}"); check("Join({{a, b}, {c, d}}, {{1, 2}, {3, 4}})", // "{{a,b},{c,d},{1,2},{3,4}}"); check("Join(a + b, c + d, e + f)", // "a+b+c+d+e+f"); check("Join(a + b, c * d)", // "Join(a+b,c*d)"); check("Join(x + y, z)", // "Join(x+y,z)"); check("Join(x + y, y * z, a)", // "Join(x+y,y*z,a)"); check("Join(x, y + z, y * z)", // "Join(x,y+z,y*z)"); check("Join(x, y)", // "Join(x,y)"); check("Join({a,b}, {x,y,z})", // "{a,b,x,y,z}"); check("Join({{a, b}, {x, y}}, {{1, 2}, {3, 4}})", // "{{a,b},{x,y},{1,2},{3,4}}"); } @Test public void testKhinchin() { check("Khinchin // N", // "2.68545"); check("N(Khinchin,50)", // "2.6854520010653064453097148354817956938203822939944"); } @Test public void testKleinInvariantJ() { // check("KleinInvariantJ(-1.5707963267948966)", // "KleinInvariantJ(-1.5707963267948966)"); check("KleinInvariantJ( (1 + I*3*Sqrt(3))/2 )", // "-64000/9"); check("KleinInvariantJ( (1 + I*Sqrt(163))/2 )", // "-151931373056000"); check("KleinInvariantJ(I*Infinity)", // "Infinity"); check("KleinInvariantJ(E^(2*Pi*(I/3)))", // "0"); check("KleinInvariantJ(I)", // "1"); check("KleinInvariantJ(I-42)", // "1"); check("KleinInvariantJ(I+42)", // "1"); check("KleinInvariantJ(1 + 2.0*I) // Chop", // "166.375"); check("Table(KleinInvariantJ(x+I)//Chop, {x,-2.0, 2.0, 1/4})", // "{1.0,0.387321+I*(-0.100372),-0.051849,0.387321+I*0.100372,1.0,0.387321+I*(-0.100372),-0.051849," // + "0.387321+I*0.100372,1.0,0.387321+I*(-0.100372),-0.051849,0.387321+I*0.100372,1.0," // + "0.387321+I*(-0.100372),-0.051849,0.387321+I*0.100372,1.0}"); } @Test public void testValues() { check("Values(<|a :> 1 + 1, b -> Nothing|>, Hold)", // "{Hold(1+1),Hold(Nothing)}"); check("Values(<|a -> x, b -> y|>)", // "{x,y}"); check("Values({a -> x, b -> y})", // "{x,y}"); check("Values({<|a -> x, b -> y|>, {c -> z, {}}})", // "{{x,y},{z,{}}}"); check("Values({c -> z, b -> y, a -> x})", // "{z,y,x}"); check("Values(a->x)", // "x"); check("Values({a -> x, a -> y, {a -> z, <|b -> t|>, <||>, {}}})", // "{x,y,{z,{t},{},{}}}"); check("Values({a -> x, a -> y, <|a -> z, {b -> t}, <||>, {}|>})", // "{x,y,{z,t}}"); check("Values(<|a -> x, a -> y, <|a -> z, <|b -> t|>, <||>, {}|>|>)", // "{z,t}"); check("Values(<|a -> x, a -> y, {a -> z, {b -> t}, <||>, {}}|>)", // "{z,t}"); check("Values({a -> x, <|a -> y, b|>})", // "{x,Values(Association(a->y,b))}"); check("Values(k:>v,f)", // "f(v)"); check("Values(<|ahey->avalue, bkey->bvalue, ckey->cvalue|>)", // "{avalue,bvalue,cvalue}"); check("Values(<|a :> 1 + 1, b -> Nothing|>, Hold)", // "{Hold(1+1),Hold(Nothing)}"); check("Values( <|a -> 4, b -> 2, c -> 1, d -> 5|> )", // "{4,2,1,5}"); check("Values({ahey->avalue, bkey->bvalue, ckey->cvalue})", // "{avalue,bvalue,cvalue}"); check("Values({<|a -> 1, b -> 2|>, {w -> 3, {}}})", // "{{1,2},{3,{}}}"); } @Test public void testKolmogorovSmirnovTest() { check("data1 = {\n" + " 0.53236606, -1.36750258, -1.47239199, -0.12517888, -1.24040594, 1.90357309,\n" + " -0.54429527, 2.22084140, -1.17209146, -0.68824211, -1.75068914, 0.48505896,\n" + " 2.75342248, -0.90675303, -1.05971929, 0.49922388, -1.23214498, 0.79284888,\n" + " 0.85309580, 0.17903487, 0.39894754, -0.52744720, 0.08516943, -1.93817962,\n" + " 0.25042913, -0.56311389, -1.08608388, 0.11912253, 2.87961007, -0.72674865,\n" + " 1.11510699, 0.39970074, 0.50060532, -0.82531807, 0.14715616, -0.96133601,\n" + " -0.95699473, -0.71471097, -0.50443258, 0.31690224, 0.04325009, 0.85316056,\n" + " 0.83602606, 1.46678847, 0.46891827, 0.69968175, 0.97864326, 0.66985742,\n" + "-0.20922486, -0.15265994}", // "{0.532366,-1.3675,-1.47239,-0.125179,-1.24041,1.90357,-0.544295,2.22084,-1.17209<>", // 80); check("KolmogorovSmirnovTest(SparseArray(data1))", // "0.744855"); check("KolmogorovSmirnovTest(data1)", // "0.744855"); check("KolmogorovSmirnovTest(data1, NormalDistribution(), \"TestData\")", // "{0.0930213,0.744855}"); check("data2 = {\n" + " 0.95791391, 0.16203847, 0.56622013, 0.39252941, 0.99126354, 0.65639108,\n" + " 0.07903248, 0.84124582, 0.76718719, 0.80756577, 0.12263981, 0.84733360,\n" + " 0.85190907, 0.77896244, 0.84915723, 0.78225903, 0.95788055, 0.01849366,\n" + " 0.21000365, 0.97951772, 0.60078520, 0.80534223, 0.77144013, 0.28495121,\n" + "0.41300867, 0.51547517, 0.78775718, 0.07564151, 0.82871088, 0.83988694}", // "{0.957914,0.162038,0.56622,0.392529,0.991264,0.656391,0.0790325,0.841246,0.76718<>", // 80); check("KolmogorovSmirnovTest(data1, data2)", // "0.000438682"); check("KolmogorovSmirnovTest(data1, data2, \"TestData\")", // "{0.46,0.000438682}"); } @Test public void testKroneckerDelta() { check("KroneckerDelta(2 - I, 2. - I)", // "1"); check("KroneckerDelta(n,0)", // "KroneckerDelta(0,n)"); check("KroneckerDelta( )", // "1"); check("KroneckerDelta(0)", // "1"); check("KroneckerDelta(1)", // "0"); check("KroneckerDelta(42)", // "0"); check("KroneckerDelta(42, 42.0, 42)", // "1"); check("KroneckerDelta(0,1)", // "0"); check("KroneckerDelta(2,2)", // "1"); check("KroneckerDelta(2,2.0)", // "1"); check("KroneckerDelta(1,1,1,2)", // "0"); check("Table(KroneckerDelta(n), {n, -2, 2})", // "{0,0,1,0,0}"); check("Array(KroneckerDelta, {3, 3})", // "{{1,0,0},{0,1,0},{0,0,1}}"); check("Table((KroneckerDelta(i - j + 1) + KroneckerDelta(i - j + 2))*i*j^2, {i, 5}, {j, 5})", // "{{0,4,9,0,0},{0,0,18,32,0},{0,0,0,48,75},{0,0,0,0,100},{0,0,0,0,0}}"); } @Test public void testLambertW() { check("LambertW(x)", // "ProductLog(x)"); } @Test public void testInverseLaplaceTransform() { // check( // "InverseLaplaceTransform(1/(s^3+4*s^2+s),s,t)", // // ""); check("InverseLaplaceTransform(1/(s^3+2*s^2+s),s,t)", // "1-1/E^t-t/E^t"); check("InverseLaplaceTransform(f(x)*s,s,t)", // "f(x)*DiracDelta'(t)"); check("InverseLaplaceTransform(f(x),s,t)", // "DiracDelta(t)*f(x)"); check("InverseLaplaceTransform(1/s,s,t)", // "1"); check("InverseLaplaceTransform(1/s^5,s,t)", // "t^4/24"); check("InverseLaplaceTransform(1/(s^2 +a^2),s,t)", // "Sin(a*t)/a"); check("InverseLaplaceTransform(s/(s^2 +a^2),s,t)", // "Cos(a*t)"); check("InverseLaplaceTransform(1/(1+s),s,t)", // "E^(-t)"); check("InverseLaplaceTransform(1/(s^2-4),s,t)", // "(-1+E^(4*t))/(4*E^(2*t))"); // test partial fraction decomposition: check("InverseLaplaceTransform(Together(3/(s-1)+(2*s)/(s^2+4)),s,t)", // "3*E^t+2*Cos(2*t)"); check("InverseLaplaceTransform(3/(s-1)+(2*s)/(s^2+4),s,t)", // "3*E^t+2*Cos(2*t)"); } @Test public void testInverseWeierstrassP() { // check("InverseWeierstrassP(2.0,{1,2})", // // "-0.715096"); // check("Table[InverseWeierstrassP[x, {1, 2}], {x, 2.0, 6.0}]", // ""); } @Test public void testInverseLaplaceTransformNumeric() { // check("InverseLaplaceTransform(Erf(s)/Sqrt(s), s, 2.3)", // // ""); check("InverseLaplaceTransform(s/(s + 2)^2, s, 2.3)", // "-0.0362221"); } @Test public void testLaplaceTransform() { // numerical calculation only supported for unary functions check("LaplaceTransform(1/(x + y + 1), {x, y}, {5.4, 4.5})", // "LaplaceTransform(1/(1+x+y),{x,y},{5.4,4.5})"); check("LaplaceTransform(Erf(t)/Sqrt(t), t, 14.2)", // "0.0185749"); check("LaplaceTransform(Erf(t), t, 14.2)", // "0.00554208"); check("LaplaceTransform(Tanh(t),t,s)", // "1/2*(-2/s-PolyGamma(0,s/4)+PolyGamma(0,1/4*(2+s)))"); check("LaplaceTransform(E^2,t,-3+s)", // "E^2/(-3+s)"); check("LaplaceTransform(c*t^2, t, s)", // "(2*c)/s^3"); check("LaplaceTransform((t^3+t^4)*t^2, t, s)", // "720/s^7+120/s^6"); check("LaplaceTransform(t^2*Exp(2+3*t), t, s)", // "(2*E^2)/(-3+s)^3"); check("LaplaceTransform(Exp(2+3*t)/t, t, s)", // "E^2*LaplaceTransform(1/t,t,-3+s)"); check("LaplaceTransform(y'(t),t,s)", // "s*LaplaceTransform(y(t),t,s)-y(0)"); check("LaplaceTransform(y''(t),t,s)", // "s^2*LaplaceTransform(y(t),t,s)-s*y(0)-y'(0)"); check("LaplaceTransform(t, t, t)", // "LaplaceTransform(t,t,t)"); check("LaplaceTransform(t, t, s)", // "1/s^2"); check("LaplaceTransform(t, s, t)", // "1"); check("LaplaceTransform(s, t, t)", // "LaplaceTransform(s,t,t)"); check("LaplaceTransform(E^(-t), t, s)", // "1/(1+s)"); check("LaplaceTransform(t^4*Sin(t), t, s)", // "(384*s^4)/(1+s^2)^5+(-288*s^2)/(1+s^2)^4+24/(1+s^2)^3"); check("LaplaceTransform(t^(1/2), t, s)", // "Sqrt(Pi)/(2*s^(3/2))"); check("LaplaceTransform(t^(1/3), t, s)", // "Gamma(4/3)/s^(4/3)"); check("LaplaceTransform(t^a, t, s)", // "Gamma(1+a)/s^(1+a)"); // issue #941 check("LaplaceTransform(Cos(t), t, s)", // "s/(1+s^2)"); check("LaplaceTransform(Cos(a*b*t), t, s)", // "s/(a^2*b^2+s^2)"); check("LaplaceTransform(Sin(t), t, s)", // "1/(1+s^2)"); check("LaplaceTransform(Sin(a*b*t), t, s)", // "(a*b)/(a^2*b^2+s^2)"); check("LaplaceTransform(Sin(t), t, t)", // "LaplaceTransform(Sin(t),t,t)"); check("LaplaceTransform(Sinh(t), t, s)", // "c/(-1+s^2)"); check("LaplaceTransform(Cosh(t), t, s)", // "s/(-1+s^2)"); check("LaplaceTransform(Log(t), t, s)", // "-(EulerGamma+Log(s))/s"); check("LaplaceTransform(Log(t)^2, t, s)", // "(6*EulerGamma^2+Pi^2+6*Log(s)*(2*EulerGamma+Log(s)))/(6*s)"); check("LaplaceTransform(Erf(t), t, s)", // "(E^(s^2/4)*Erfc(s/2))/s"); check("LaplaceTransform(Erf(t^(1/2)), t, s)", // "1/(s*Sqrt(1+s))"); check("LaplaceTransform(Sin(t)*Exp(t), t, s)", // "1/(1+(1-s)^2)"); } @Test public void testLast() { check("Last(SparseArray({1,2,3,4})) // Normal ", // "4"); check("Last(SparseArray({{1,2},{3,4}})) // Normal ", // "{3,4}"); check("Last(<||>)", // "Last(<||>)"); check("Last({})", // "Last({})"); check("Last({{1,2},{1,2},{1,2},{1,2}})", // "{1,2}"); check("Last(<|1 :> a, 2 -> b, 3 :> c|>)", // "c"); check("Last({}, x)", // "x"); check("Last({a, b, c})", // "c"); check("Last(a + b + c)", // "c"); check("Last(a)", // "Last(a)"); } @Test public void testLCM() { check("LCM(4+I, 1+16*I)", // "65+I*12"); check("QuotientRemainder(1+16*I,1)", // "{1+I*16,0}"); check("QuotientRemainder(5,3-I)", // "{2,-1+I*2}"); check("LCM(5,3-I)", // "5+I*5"); check("LCM(5,2+I)", // "5"); check("LCM(-4 + 5*I, 2 + 3*I)", // "23+I*2"); check("LCM(-5-I, -2-I)", // "9+I*7"); check("LCM(-3,7)", // "21"); check("LCM(0,b)", // "0"); check("LCM(a,a)", // "LCM(a,a)"); check("LCM(a,b)", // "LCM(a,b)"); check("LCM(1/2,2)", // "2"); check("LCM(2/3,4/9)", // "4/3"); check("LCM(1/3,2/5,3/7)", // "6"); check("LCM(2^32 / 3, 2^34 / 7)", // "17179869184"); check("GCD(4+I, 1+16*I)", // "1"); check("LCM(2^32 +I, 1+ 2^34 * I)", // "73786976294838206465+I*12884901888"); check("LCM(5+I, 2+3*I)", // "5+I"); check("LCM(6+ 9*I, 2 + 3*I)", // "6+I*9"); check("LCM(3/7,12/22)", // "6"); check("LCM(-3/7,12/22)", // "6"); check("LCM(3/7,-12/22)", // "6"); check("LCM(-3/7,-12/22)", // "6"); check("LCM(-1/2)", // "1/2"); // System.out.println(Integer.MIN_VALUE); =>-2147483648 check("LCM(-2147483648)", // "2147483648"); check("LCM(I)", // "1"); check("LCM(-I)", // "1"); check("LCM(-2)", // "2"); check("LCM(10)", // "10"); check("LCM(-2147483648, -2147483648/2)", // "2147483648"); check("LCM(2, 3, 5)", // "30"); check("LCM(-3, 7)", // "21"); check("LCM(4)", // "4"); check("LCM(2, {3, 5, 7})", // "{6,10,14}"); check("LCM(0,0)", // "0"); check("LCM(0,10)", // "0"); check("LCM(10,0)", // "0"); check("LCM(a)", // "LCM(a)"); check("LCM(a,-a)", // "LCM(-a,a)"); check("LCM(15, 20)", // "60"); check("LCM(20, 30, 40, 50)", // "600"); check("LCM(-36,45)", // "180"); check("LCM(36,-45)", // "180"); check("LCM(-36,-45)", // "180"); check("LCM(2,3,4,5)", // "60"); check("Sum(LCM(3, k), {k, 100})", // "11784"); // check("LCM(1/3, 2/5, 3/7)", ""); } @Test public void testLeafCount() { check("LeafCount(1 + x + y^a)", // "6"); check("LeafCount(f(x, y))", // "3"); check("LeafCount({1 / 3, 1 + I})", // "7"); check("LeafCount(Sqrt(2))", // "5"); check("LeafCount(100!)", // "1"); check("LeafCount(f(1, 2)[x, y])", // "5"); check("LeafCount(10+I)", // "3"); } @Test public void testLength() { check("Length(\"test\")", // "0"); check("Length(<||>)", // "0"); check("Length(<|a->c,b->d|>)", // "2"); check("Length({{1,2},{1,2},{1,2},{1,2}}[[2]])", // "2"); check("Length(aa)", // "0"); check("Length(Sqrt(aa))", // "2"); check("Length({1, 2, 3})", // "3"); check("Length(Exp(x))", // "2"); check("FullForm(Exp(x))", // "Power(E, x)"); check("Length(a)", // "0"); check("Length(1/3)", // "0"); check("FullForm(1/3)", // "Rational(1,3)"); check("Length(a + b + c + d)", // "4"); check("Length(3 + I)", // "0"); check("Map(Length, {{a, b}, {a, b, c}, {x}})", // "{2,3,1}"); } @Test public void testLengthWhile() { check("LengthWhile({1, 1, 2, 3, 5, 8, 13, 21}, # < 10 &)", // "6"); check("LengthWhile({10, 1, 2, 3, 5, 8, 13, 21}, # < 10 &)", // "0"); check("LengthWhile({1, 2, 3, 10, 5, 8, 42, 11}, # < 10 &)", // "3"); check("LengthWhile({a, Pi, 3, 2, {1, 2, 3}, {a, b}, 10}, Head(#1) =!= List &)", // "4"); check("LengthWhile({E, 8, a, b, 20, 1.4}, If(NumericQ(#1), True, #1) &)", // "2"); check("LengthWhile(h(1, 1, 2, 3, a, 8, 13, b, c, d), IntegerQ)", // "4"); } @Test public void testLerchPhi() { check("LerchPhi(0,1,a)", // "1/Sqrt(a^2)"); check("LerchPhi(z,s,-2)", // "z^2*(1/(2^s*z^2)+1/z+PolyLog(s,z))"); check("LerchPhi(-1,1,0)", // "-Log(2)"); } @Test public void testEqualTo() { check("Select({0, 0., 0.1, 0.001}, EqualTo(0))", // "{0,0.0}"); } @Test public void testUnequalTo() { check("Select({0, 0., 0.1, 0.001}, UnequalTo(0))", // "{0.1,0.001}"); } @Test public void testGreaterThan() { check("GreaterThan(42)[2]", // "False"); check("GreaterThan(y)[x]", // "x>y"); } @Test public void testGreaterEqualThan() { check("GreaterEqualThan(42)[2]", // "False"); check("GreaterEqualThan(y)[x]", // "x>=y"); check(" Select({0, 5, 10, 15}, GreaterEqualThan(10))", // "{10,15}"); check(" Select({0, 5, 10, 15}, GreaterEqual(#,10)&)", // "{10,15}"); } @Test public void testLessThan() { check("LessThan(42)[2]", // "True"); check("LessThan(y)[x]", // "x1,\" \"->8,\"a\"->1,\"b\"->1,\"c\"->1,\"d\"->1,\"e\"->3,\"f\"->1,\"g\"->1,\"h\"->2,\"i\"->1,\"j\"->1,\"k\"->1,\"l\"->1,\"m\"->1,\"n\"->1,\"o\"->4,\"p\"->1,\"q\"->1,\"r\"->2,\"s\"->1,\"t\"->1,\"u\"->2,\"v\"->1,\"w\"->1,\"x\"->1,\"y\"->1,\"z\"->1|>"); } @Test public void testLetterQ() { check("LetterQ(\"a\")", // "True"); check("LetterQ(\"2\")", // "False"); check("LetterQ(\"äü\")", // "True"); } @Test public void testLevel() { check("Level(x, -1)", // "{}"); check("Level(x, 0)", // "{}"); check("Level(x, 1)", // "{}"); check("demo=x+Cos(Pi/3*Sqrt(2+1/x))+Sin(Pi/6*Sqrt(x))", // "x+Cos(1/3*Pi*Sqrt(2+1/x))+Sin(1/6*Pi*Sqrt(x))"); check("Level(demo, 1)", // "{x,Cos(1/3*Pi*Sqrt(2+1/x)),Sin(1/6*Pi*Sqrt(x))}"); check("Level(demo, 2)", // "{x,1/3*Pi*Sqrt(2+1/x),Cos(1/3*Pi*Sqrt(2+1/x)),1/6*Pi*Sqrt(x),Sin(1/6*Pi*Sqrt(x))}"); check("Level(demo, {2})", // "{1/3*Pi*Sqrt(2+1/x),1/6*Pi*Sqrt(x)}"); check("Level(demo, {25})", // "{}"); check("Level(demo, {2,4})", // "{1/3,Pi,2+1/x,1/2,Sqrt(2+1/x),1/3*Pi*Sqrt(2+1/x),1/6,Pi,x,1/2,Sqrt(x),1/6*Pi*Sqrt(x)}"); check("Level(demo, {0,4})", // "{x,1/3,Pi,2+1/x,1/2,Sqrt(2+1/x),1/3*Pi*Sqrt(2+1/x),Cos(1/3*Pi*Sqrt(2+1/x)),1/6,Pi,x,\n" + "1/2,Sqrt(x),1/6*Pi*Sqrt(x),Sin(1/6*Pi*Sqrt(x)),x+Cos(1/3*Pi*Sqrt(2+1/x))+Sin(1/6*Pi*Sqrt(x))}"); check("Level(demo, {-1})", // "{x,1/3,Pi,2,x,-1,1/2,1/6,Pi,x,1/2}"); check("Level(demo, {-4})", // "{Sqrt(2+1/x),Sin(1/6*Pi*Sqrt(x))}"); check("Level(demo, {-25})", // "{}"); check("Level(demo, -4)", // "{Sqrt(2+1/x),1/3*Pi*Sqrt(2+1/x),Cos(1/3*Pi*Sqrt(2+1/x)),Sin(1/6*Pi*Sqrt(x))}"); check("Level(demo, -1)", // "{x,1/3,Pi,2,x,-1,1/x,2+1/x,1/2,Sqrt(2+1/x),1/3*Pi*Sqrt(2+1/x),Cos(1/3*Pi*Sqrt(2+1/x)),\n" + "1/6,Pi,x,1/2,Sqrt(x),1/6*Pi*Sqrt(x),Sin(1/6*Pi*Sqrt(x))}"); check("Level(demo, Infinity)", // "{x,1/3,Pi,2,x,-1,1/x,2+1/x,1/2,Sqrt(2+1/x),1/3*Pi*Sqrt(2+1/x),Cos(1/3*Pi*Sqrt(2+1/x)),\n" + "1/6,Pi,x,1/2,Sqrt(x),1/6*Pi*Sqrt(x),Sin(1/6*Pi*Sqrt(x))}"); check("Level(demo, {1, -3})", // "{2+1/x,Sqrt(2+1/x),1/3*Pi*Sqrt(2+1/x),Cos(1/3*Pi*Sqrt(2+1/x)),1/6*Pi*Sqrt(x),Sin(\n" + "1/6*Pi*Sqrt(x))}"); check("Level(demo, {-4, 2})", // "{x,1/6*Pi*Sqrt(x),Sin(1/6*Pi*Sqrt(x))}"); check("Level(demo, {0, -1})", // "{x,1/3,Pi,2,x,-1,1/x,2+1/x,1/2,Sqrt(2+1/x),1/3*Pi*Sqrt(2+1/x),Cos(1/3*Pi*Sqrt(2+1/x)),\n" + "1/6,Pi,x,1/2,Sqrt(x),1/6*Pi*Sqrt(x),Sin(1/6*Pi*Sqrt(x)),x+Cos(1/3*Pi*Sqrt(2+1/x))+Sin(\n" + "1/6*Pi*Sqrt(x))}"); check("Level(demo, {-Infinity, Infinity})", // "{x,1/3,Pi,2,x,-1,1/x,2+1/x,1/2,Sqrt(2+1/x),1/3*Pi*Sqrt(2+1/x),Cos(1/3*Pi*Sqrt(2+1/x)),\n" + "1/6,Pi,x,1/2,Sqrt(x),1/6*Pi*Sqrt(x),Sin(1/6*Pi*Sqrt(x)),x+Cos(1/3*Pi*Sqrt(2+1/x))+Sin(\n" + "1/6*Pi*Sqrt(x))}"); check("Level(demo, {3, -6})", // "{}"); check("Level(demo, {-3, -1})", // "{x,1/3,Pi,2,x,-1,1/x,2+1/x,1/2,1/6,Pi,x,1/2,Sqrt(x),1/6*Pi*Sqrt(x)}"); check("Level(a + f(x, y^n), {-1})", // "{a,x,y,n}"); check("Level(a + b ^ 3 * f(2*x ^ 2), {-1}, g)", // "g(a,b,3,2,x,2)"); check("Level(a + b ^ 3 * f(2*x ^ 2), {-1})", // "{a,b,3,2,x,2}"); check("Level({{{{a}}}}, 3)", // "{{a},{{a}},{{{a}}}}"); check("Level({{{{a}}}}, -4)", // "{{{{a}}}}"); check("Level({{{{a}}}}, -5)", // "{}"); check("Level(h0(h1(h2(h3(a)))), {0, -1})", // "{a,h3(a),h2(h3(a)),h1(h2(h3(a))),h0(h1(h2(h3(a))))}"); check("Level({{{{a}}}}, 3, Heads -> True)", // "{List,List,List,{a},{{a}},{{{a}}}}"); check("Level(x^2 + y^3, 3, Heads -> True)", // "{Plus,Power,x,2,x^2,Power,y,3,y^3}"); check("Level(a ^ 2 + 2 * b, {-1}, Heads -> True)", // "{Plus,Power,a,2,Times,2,b}"); check("Level(f(g(h))[x], {-1}, Heads -> True)", // "{f,g,h,x}"); // TODO // check("Level(f(g(h))[x], {-2, -1}, Heads -> True)", // "{f,g,h,g(h),x,f(g(h))[x]}"); check("Level(a + f(x, y^n), {-1})", // "{a,x,y,n}"); check("Level(a + f(x, y^n0), 2)", // "{a,x,y^n0,f(x,y^n0)}"); check("Level(a + f(x, y^n0), {0, Infinity})", // "{a,x,y,n0,y^n0,f(x,y^n0),a+f(x,y^n0)}"); check("Level({{{{a}}}}, 1)", // "{{{{a}}}}"); check("Level({{{{a}}}}, 2)", // "{{{a}},{{{a}}}}"); check("Level({{{{a}}}}, 3)", // "{{a},{{a}},{{{a}}}}"); check("Level({{{{a}}}}, 4)", // "{a,{a},{{a}},{{{a}}}}"); check("Level({{{{a}}}}, 5)", // "{a,{a},{{a}},{{{a}}}}"); check("Level({{{{a}}}}, -1)", // "{a,{a},{{a}},{{{a}}}}"); check("Level({{{{a}}}}, -2)", // "{{a},{{a}},{{{a}}}}"); check("Level({{{{a}}}}, -3)", // "{{{a}},{{{a}}}}"); check("Level({{{{a}}}}, -4)", // "{{{{a}}}}"); check("Level({{{{a}}}}, -5)", // "{}"); check("Level({{{{a}}}}, {2, 3})", // "{{a},{{a}}}"); check("Level({{{{a}}}}, {0, -1})", // "{a,{a},{{a}},{{{a}}},{{{{a}}}}}"); check("Level(h0(h1(h2(h3(a)))), {0, -1})", // "{a,h3(a),h2(h3(a)),h1(h2(h3(a))),h0(h1(h2(h3(a))))}"); check("Level({{{{a}}}}, 3, Heads -> True)", // "{List,List,List,{a},{{a}},{{{a}}}}"); check("Level(x^2 + y^3, 3, Heads -> True)", // "{Plus,Power,x,2,x^2,Power,y,3,y^3}"); check("Level(h1(h2(h3(x))), -1)", // "{x,h3(x),h2(h3(x))}"); check("Level(h1(h2(h3(x))), {0, -1})", // "{x,h3(x),h2(h3(x)),h1(h2(h3(x)))}"); check("Level(f(f(g(a), a), a, h(a), f), 2)", // "{g(a),a,f(g(a),a),a,a,h(a),f}"); check("Level(f(f(g(a), a), a, h(a), f), {2})", // "{g(a),a,a}"); check("Level(f(f(g(a), a), a, h(a), f), {-1})", // "{a,a,a,a,f}"); check("Level(f(f(g(a), a), a, h(a), f), {-2})", // "{g(a),h(a)}"); check("x = F(G(a, K(d)), H(b, L(e)), J(c, M(P(f, g))))", // "F(G(a,K(d)),H(b,L(e)),J(c,M(P(f,g))))"); check("Table(Level(x, {k}), {k, 0, 5})", // "{{F(G(a,K(d)),H(b,L(e)),J(c,M(P(f,g))))},"// + "{G(a,K(d)),H(b,L(e)),J(c,M(P(f,g)))},"// + "{a,K(d),b,L(e),c,M(P(f,g))},"// + "{d,e,P(f,g)},"// + "{f,g},"// + "{}}"); check("Table(Level(x, {-k}), {k, 1, 5})", // "{{a,d,b,e,c,f,g},"// + "{K(d),L(e),P(f,g)},"// + "{G(a,K(d)),H(b,L(e)),M(P(f,g))},"// + "{J(c,M(P(f,g)))}," // + "{F(G(a,K(d)),H(b,L(e)),J(c,M(P(f,g))))}}"); } @Test public void testLevelQ() { check("LevelQ(2)", // "True"); check("LevelQ({2, 4})", // "True"); check("LevelQ(Infinity)", // "True"); check("LevelQ(a + b)", // "False"); } // @Test // public void testJacobianMatrix() { // check("JacobianMatrix({Rr, Ttheta, Zz}, Cylindrical)", ""); // } @Test public void testLimit() { check("Limit(7-2*x+4*x^2,x->Infinity)", // "Infinity"); check("Limit(Sqrt(7-2*x+4*x^2),x->Infinity)", // "Infinity"); check("Limit(1+2*x+Sqrt(7-2*x+4*x^2),x->Infinity)", // "Infinity"); check("Limit((-6+6*x)/(1+2*x+Sqrt(7-2*x+4*x^2)),x->Infinity)", // "3/2"); check("Limit(1-Sqrt(7-2*x+4*x^2)+2*x,x->Infinity)", // "3/2"); // issue #931 check("Limit((-1/E^x+E^x)/(E^x+E^(-x)),x -> Infinity)", // "1"); check("Limit((-1+Sqrt(x))/Sqrt(-1+x), x -> Infinity)", // "1"); check("Limit(x^2*Sin(1/x)^3,x->0)", // "0"); check("Limit(x*Sin(1/x)^3,x->0)", // "0"); check("Limit(Sin(1/x)^3,x->0)", // "Indeterminate"); check("Limit(Abs(Sin(1/x)),x->0)", // "Indeterminate"); check("Limit(x*Sin(1/x),x->0)", // "0"); check("Limit(x^2*Sin(1/x),x->0)", // "0"); // github #230 check("Limit((Sqrt(((t+4)*(t-2)^4))/((3*t)-6)^2),t->2) ", // "Sqrt(2/3)/3"); check("Limit((((t+4)*(t-2)^4) /((3*t)-6)^4),t->2) ", // "2/27"); check("Limit((((t+4)*(t-2)^4) /((3*t)-6) ),t->2) ", // "0"); check("Limit(Sqrt(((t+4)*(t-2)^4)) ,t->2) ", // "0"); check("Limit(Tan(9/7)^x,x->-Infinity)", // "0"); check("Limit(Sin(1/7)^x,x->-Infinity)", // "Infinity"); check("Limit(a^x,x->-Infinity)", // "ConditionalExpression(0,Log(a)>0)"); check("Limit(f(a)^x,x->-Infinity)", // "Limit(f(a)^x,x->-Infinity)"); check("Limit(Tan(9/7)^x,x->Infinity)", // "Infinity"); check("Limit(Sin(1/7)^x,x->Infinity)", // "0"); check("Limit(a^x,x->Infinity)", // "ConditionalExpression(Infinity,Log(a)>0)"); check("Limit((a+b+2)^x,x->Infinity)", // "ConditionalExpression(Infinity,Log(2+a+b)>0)"); check("Limit((a+f[b]+2)^x,x->Infinity)", // "Limit((2+a+f(b))^x,x->Infinity)"); check("Limit(f(a)^x,x->Infinity)", // "Limit(f(a)^x,x->Infinity)"); check("Limit(Gamma(1/t),t->Infinity)", // "Infinity"); check("Limit(ArcTanh(x/Sqrt(4+3*x^2)) ,x->-Infinity)", // "-ArcTanh(1/Sqrt(3))"); check("Limit(ArcTanh(x/Sqrt(4+3*x^2)) ,x->Infinity)", // "ArcTanh(1/Sqrt(3))"); check("Limit(x/Sqrt(4+3*x^2) ,x->Infinity)", // "1/Sqrt(3)"); check("Limit(x/Sqrt(4+3*x^2) ,x->-Infinity)", // "-1/Sqrt(3)"); check("Limit((-x^2+1)/(x+2),x->Infinity)", // "-Infinity"); check("Limit(Exp(2*x),x->-Infinity)", // "0"); check("Limit((1+1/x)^x,x->Infinity)", // "E"); check("Limit((1+2/x)^x,x->Infinity)", // "E^2"); check("Limit((1+1/x)^(2*x),x->Infinity)", // "E^2"); check("Limit((1+a*(1/x))^(b*x),x->(-Infinity))", // "E^(a*b)"); check("Limit(-2*x,x->Infinity)", // "-Infinity"); check("Limit((x^2+1)/(-x^3+1),x->Infinity)", // "0"); check("Limit(1/x,x->0)", // "Indeterminate"); check("Limit((Sin(x)-Tan(x))/(x^3),x->0)", // "-1/2"); check("Limit((1+x)^(1/x),x->0)", // "E"); check("Limit((x/(k+x))^x,x->Infinity)", // "E^(-k)"); check("Limit(((a+x)/(b+x))^(c+x),x->Infinity)", // "E^(a-b)"); check("Limit(((a+x)/(b+x))^(c+x),x->-Infinity)", // "E^(a-b)"); check("Limit(((a+x)/(x))^(c+x),x->Infinity)", // "E^a"); check("Limit(x^(a/x), x->Infinity)", // "ConditionalExpression(1,a∈Reals)"); check("Limit(x^(4/x), x->Infinity)", // "1"); // TODO github #175 // check("Limit(((a^(1/x)+b^(1/x))/2)^x, x->Infinity)", // // "Sqr(a)*Sqrt(b)"); check("Limit(Erf(x/Sqrt(2)),x->Infinity,Direction->Reals)", // "1"); check("Limit(Erf(x/Sqrt(2)),x->-Infinity,Direction->Reals)", // "-1"); check("Limit((Cosh(t)-1)/t^2,t->0)", // "1/2"); check("Limit(Gamma(1/t)*Cos(Sin(1/t)),t->0)", // "Indeterminate"); check("Limit(Gamma(1/t),t->Infinity)", // "Infinity"); check("Limit(Gamma(1/t),t->-Infinity)", // "-Infinity"); check("Limit(Gamma(z,t),t->Infinity)", // "0"); check("Limit(Gamma(z,t),t->0)", // "Gamma(z)"); check("limit((1 - cos(x))/x^2, x->0)", // "1/2"); check("limit((1 + 1/n)^n, n->infinity)", // "E"); check("Limit((sin(x) - x)/x^3,x->0)", // "-1/6"); check("Limit(Sqrt(x^2 - 1)/x, x->-Infinity)", // "-1"); check("Limit(x/Sqrt(x^2 - 1), x->-Infinity)", // "-1"); // gitlab #107 check("Limit(x^2-1/x-2, x->0)", // "Indeterminate"); check("Limit((x^2) /(3*x), x->Infinity)", // "Infinity"); check("Limit(x^(-2/3),x->0 , Direction->-1)", // "Infinity"); check("Limit(x^(-2/3),x->0 , Direction->1)", // "Limit(1/x^(2/3),x->0,Direction->1)"); check("Limit(x^(-2/3),x->0)", // "Indeterminate"); check("Limit(x^(-16/7),x->0 , Direction->-1)", // "Infinity"); check("Limit(x^(-16/7),x->0 , Direction->1)", // "Limit(1/x^(16/7),x->0,Direction->1)"); check("Limit(x^(-16/7),x->0)", // "Indeterminate"); check("Limit(x^(-37/4),x->0 , Direction->-1)", // "Infinity"); check("Limit(x^(-37/4),x->0 , Direction->1)", // "Limit(1/x^(37/4),x->0,Direction->1)"); check("Limit(x^(-37/4),x->0)", // "Indeterminate"); check("Limit((x^2-1)/(x-1)^2, x->1)", // "Indeterminate"); check("Limit((3*x^2-6)^(-1/3), x->-Infinity)", // "0"); check("Limit(Cosh(x) , x->3)", // "Cosh(3)"); check("Limit(x^3-4*x^2+6, x->-Infinity)", // "-Infinity"); check("Limit(42, x->Infinity)", // "42"); check("Limit(x^2-x^4, x->Infinity)", // "-Infinity"); check("Limit((4*x^3-3*x+2)/(2*x^3+2*x-1), x->Infinity)", // "2"); check("Limit((x^2-3*x+2)/(x^3+2*x-1), x->Infinity)", // "0"); check("Limit(Sqrt(3*x-2), x->-Infinity) // FullForm", // "DirectedInfinity(Complex(0,1))"); check("Limit((x-1)^2/(x^2-1), x->1)", // "0"); check("Limit((x-1)/(x^2-1), x->1)", // "1/2"); check("Limit((x^2-4)/(x-2), x->2)", // "4"); check("Limit((x^3-1)/(x^2-1), x->1)", // "3/2"); // github #120 check("Limit( x*Log(x) , x->0)", // "0"); check("Limit(Log(x),x->0)", // "-Infinity"); check("Limit(Log(x)^2,x->0)", // "Infinity"); check("Limit(2*x-2*x*Log(x)+x*Log(x)^2, x->0)", // "0"); check("Limit(E^(-x)*Sqrt(x), x -> Infinity)", // "0"); // adjust LimitRules.m if these 2 tests fails // check("FullForm(x*(Sqrt(2*Pi*x)/(x!))^(1/x) )", // // "Times(Power(Power(Times(2, Pi), Rational(1,2)), Power(x, -1)), x, Power(Times(Power(x, // Rational(1,2)), // Power(Factorial(x), -1)), Power(x, -1)))"); // check("Limit(x*(Sqrt(2*Pi*x)/(x!))^(1/x), x->Infinity)", // // "E"); // check("Limit(x/((x!)^(1/x)), x->Infinity)", // // "E"); // github #115 check("Limit(Sqrt(-4+2*x^2)/(4+3*x),x->Infinity)", // "Sqrt(2)/3"); check("Limit((4+3*x)/Sqrt(-4+2*x^2),x->Infinity)", // "3/Sqrt(2)"); check("Limit((4+3*x)^2/(-4+2*x^2),x->Infinity)", // "9/2"); check("Limit(x^(13+n),x->0)", // "ConditionalExpression(0,n>-13)"); // check("Limit(x^(13+n)/a,x->0)", // // ""); check("Limit(E^(3*x), x->a)", // "E^(3*a)"); check("Limit((1+k/x)^x, x->Infinity)", // "E^k"); check("Limit((1-1/x)^x, x->Infinity)", // "1/E"); // check("Limit((1 + Sinh(x))/E^x, x ->Infinity)", "Infinity*Limit(E^(-x),x->Infinity)"); // issue #184 check("N(Limit(tan(x),x->pi/2))", // "Indeterminate"); check("Limit(Tan(x), x->Pi/2)", // "Indeterminate"); check("Limit(Tan(x), x->Pi/2, Direction->1)", // "Infinity"); check("Limit(Tan(x), x->Pi/2, Direction->-1)", // "-Infinity"); check("Limit(Tan(x+3*Pi), x->Pi/2)", // "Indeterminate"); check("Limit(Tan(x+3*Pi), x->Pi/2, Direction->1)", // "Infinity"); check("Limit(Tan(x+3*Pi), x->Pi/2, Direction->-1)", // "-Infinity"); check("Limit(Cot(x), x->0)", // "Indeterminate"); check("Limit(Cot(x), x->0, Direction->1)", // "-Infinity"); check("Limit(Cot(x), x->0, Direction->-1)", // "Infinity"); check("Limit(Cot(x+Pi), x->0)", // "Indeterminate"); check("Limit(Cot(x+Pi), x->0, Direction->1)", // "-Infinity"); check("Limit(Cot(x+Pi), x->0, Direction->-1)", // "Infinity"); check("Limit(Log(x^y), x->0)", // "ConditionalExpression(-Infinity,y>0)"); check("Limit(Log(y*x, b), x->1)", // "Log(b)/Log(y)"); check("Limit(Log(y*x), x->0)", // "-Infinity"); check("Limit(Log(x), x->Infinity)", // "Infinity"); check("Limit(Log(x), x->-Infinity)", // "Infinity"); check("Limit((y*x)/Abs(x), x->0)", // "Indeterminate"); check("Limit((y*x)/Abs(x), x->0, Direction->1)", // "-y"); check("Limit(x/Abs(x), x->0)", // "Indeterminate"); check("Limit(x/Abs(x), x->0, Direction->-1)", // "1"); check("Limit(x/Abs(x), x->0, Direction->1)", // "-1"); check("Limit(Log(x), x -> 0)", // "-Infinity"); check("Limit(x^x, x -> 0)", // "1"); check("Limit(1/x, x -> Infinity, Direction->1)", // "0"); check("Limit(1/x, x -> Infinity, Direction->-1)", // "0"); check("Limit(1/x, x -> 0, Direction->1)", // "-Infinity"); check("Limit(1/x, x -> 0, Direction->-1)", // "Infinity"); // print additional message. Messages are typically suppressed in Limit() steps. check("1/0", // "ComplexInfinity"); // check("Limit((4 - x), x -> 4)", "0"); check("Limit(1/(4 - x), x -> 4)", // "Indeterminate"); check("Limit(1/(x - 4), x -> 4)", // "Indeterminate"); check("Infinity-1", // "Infinity"); check("Limit(a+b+2*x,x->-Infinity)", // "-Infinity"); check("Limit(a+b+2*x,x->Infinity)", // "Infinity"); check("Limit(E^(-x)*Sqrt(x), x -> Infinity)", // "0"); check("Limit(Sin(x)/x,x->0)", // "1"); check("Limit(x*Sin(1/x),x->Infinity)", // "1"); check("Limit(-x,x->Infinity)", // "-Infinity"); check("Limit((1 + x/n)^n, n -> Infinity)", // "E^x"); check("Limit((x^2 - 2*x - 8)/(x - 4), x -> 4)", // "6"); check("Limit((x^3-1)/(2*x^3-3*x),x->Infinity)", // "1/2"); check("Limit((x^3-1)/(2*x^3+3*x),x->Infinity)", // "1/2"); check("Limit((2*x^3-3*x),x->Infinity)", // "Infinity"); check("Limit((2*x^3+3*x),x->Infinity)", // "Infinity"); check("Limit(E^x, x->Infinity)", // "Infinity"); check("Limit(E^x, x->-Infinity)", // "0"); check("Limit(a^x, x->0)", // "1"); check("Limit(c*(x^(-10)), x->Infinity)", // "0"); } @Test public void testLimitIssue536() { // avoid endless recursion: check("Limit(Sqrt((4+x)/(4-x))-Pi/2,x->4)", // "Indeterminate"); // TODO get -4*Pi check( "Limit((-4+x)*(Sqrt((4+x)/(4-x))-ArcTan(Sqrt((4+x)/(4-x)))+(-(4+x)*ArcTan(Sqrt((4+x)/(4-x))))/(4-x)), x->4)", // "Indeterminate"); // Issue 536 check("Integrate(Sqrt((4+x)/(4-x)), x) ", // "(-4+x)*(Sqrt((4+x)/(4-x))-ArcTan(Sqrt((4+x)/(4-x)))+(-(4+x)*ArcTan(Sqrt((4+x)/(4-x))))/(\n"// + "4-x))"); check("Limit(ArcTan(Sqrt((4 + x)/(4 - x))),x->4)", // "Pi/2"); check("Limit(Sqrt((4 + x)/(4 - x)),x->4,Direction->1)", // "Infinity"); check("Limit(Sqrt((4 + x)/(4 - x)),x->4,Direction->-1)", // "I*Infinity"); check("Limit(Sqrt((4 + x)/(4 - x)),x->4,Direction->\"FromBelow\")", // "Infinity"); check("Limit(Sqrt((4 + x)/(4 - x)),x->4,Direction->\"FromAbove\")", // "I*Infinity"); check("Limit(ArcTan(Sqrt((4 + x)/(4 - x))),x->4,Direction->1)", // "Pi/2"); check("Limit(ArcTan(Sqrt((4 + x)/(4 - x))),x->4,Direction->-1)", // "Pi/2"); } @Test public void testLinearModelFit() { check("LinearModelFit({-0.8, -0.2, 0.8, 2.2}, x, x)", // "-2.0+x"); // print message: LinearModelFit: The first argument is not a vector or matrix. check("LinearModelFit({{0, 1, 2}, {1, 0}, {3, 2}, {5, 4}},x,x)", // "LinearModelFit({{0,1,2},{1,0},{3,2},{5,4}},x,x)"); // print message: LinearModelFit: Design matrix different from variable currently not supported // in LinearModelFit. check("LinearModelFit(0^ {{1,0}, {0,1}},{{1,2,3,a}},RegularExpression(1))", // "LinearModelFit({{0,Indeterminate},{Indeterminate,0}},{{1,2,3,a}},RegularExpression(\n" + "1))"); check("LinearModelFit({ { 1, 3 }, { 2, 5 }, { 3, 7 }, { 4, 14 }, { 5, 11 } },x,x)", // "0.5+2.5*x"); check("LinearModelFit({{0, 1}, {1, 0}, {3, 2}, {5, 4}},x,x)", // "0.186441+0.694915*x"); } @Test public void testLinearRecurrence() { check("LinearRecurrence({0, 1, 1}, {1, 1, 1}, 0)", // "LinearRecurrence({0,1,1},{1,1,1},0)"); check("LinearRecurrence({0, 1, 1}, {1, 1, 1}, 1)", // "{1}"); check("LinearRecurrence({0, 1, 1}, {1, 1, 1}, 2)", // "{1,1}"); check("LinearRecurrence({0, 1, 1}, {1, 1, 1}, 3)", // "{1,1,1}"); check("LinearRecurrence({0, 1, 1}, {1, 1, 1}, 10)", // "{1,1,1,2,2,3,4,5,7,9}"); check("$IterationLimit=20000;LinearRecurrence({3, 2, 1, 4}, {1, -36, 9, 80}, 499) // Last", // "4392405770581123238293018208945275262282481636368897269404822983707775767943275\\\n" // + "2397074324032453155999783186143730463033184880119799313454266330175795103523924\\\n" // + "8744360339410536645316069379253837818025841264555121500544037499343216200306170\\\n" // + "3398323176113333063330229192911709396080150894"); check("$IterationLimit=500", // "500"); // message Maximum AST dimension 20511 exceeded check("LinearRecurrence({x,-3,-1/2},{{1,0},{0,1},0},101)", // "LinearRecurrence({x,-3,-1/2},{{1,0},{0,1},0},101)"); // iter limit check("LinearRecurrence({-1,-2,3},{x,-3,-1/2},1009)", // "Hold(LinearRecurrence({-1,-2,3},{x,-3,-1/2},1009))"); check("LinearRecurrence({a, b}, {1, 1}, 5)", // "{1,1,a+b,a^2+b+a*b,a^3+2*a*b+a^2*b+b^2}"); check("LinearRecurrence({-3, 1}, {7, 2}, 10)", // "{7,2,1,-1,4,-13,43,-142,469,-1549}"); // Fibonacci sequence check("LinearRecurrence({1, 1}, {1, 1}, 10)", // "{1,1,2,3,5,8,13,21,34,55}"); check("LinearRecurrence({1, 1}, {1, 1}, {8})", // "21"); check("LinearRecurrence({a,b}, {c,d}, 5)", // "{c,d,b*c+a*d,a*b*c+a^2*d+b*d,a^2*b*c+b^2*c+a^3*d+2*a*b*d}"); check("LinearRecurrence({1, 1}, {{1, 2}, {2, 1}}, 10)", // "{{1,2},{2,1},{3,3},{5,4},{8,7},{13,11},{21,18},{34,29},{55,47},{89,76}}"); // A001608 Perrin sequence // https://oeis.org/A001608 check("LinearRecurrence({0, 1, 1}, {3, 0, 2}, 50)", // "{3,0,2,3,2,5,5,7,10,12,17,22,29,39,51,68,90,119,158,209,277,367,486,644,853,1130,\n" + "1497,1983,2627,3480,4610,6107,8090,10717,14197,18807,24914,33004,43721,57918,\n" + "76725,101639,134643,178364,236282,313007,414646,549289,727653,963935}"); // A016064 Shortest legs of Heronian triangles (sides are consecutive integers, area is an // integer). // https://oeis.org/A016064 check("LinearRecurrence({5, -5, 1}, {1, 3, 13}, 26)", // "{1,3,13,51,193,723,2701,10083,37633,140451,524173,1956243,7300801,27246963,\n" + "101687053,379501251,1416317953,5285770563,19726764301,73621286643,274758382273,\n" + "1025412242451,3826890587533,14282150107683,53301709843201,198924689265123}"); // A251599 Centers of rows of the triangular array formed by the natural numbers. // https://oeis.org/A251599 check("LinearRecurrence({1, 0, 2, -2, 0, -1, 1}, {1, 2, 3, 5, 8, 9, 13}, 60)", // "{1,2,3,5,8,9,13,18,19,25,32,33,41,50,51,61,72,73,85,98,99,113,128,129,145,162,\n" + "163,181,200,201,221,242,243,265,288,289,313,338,339,365,392,393,421,450,451,481,\n" + "512,513,545,578,579,613,648,649,685,722,723,761,800,801}"); // A050250 Number of nonzero palindromes less than 10^n. // https://oeis.org/A050250 check("LinearRecurrence({1, 10, -10}, {9, 18, 108}, 30)", // "{9,18,108,198,1098,1998,10998,19998,109998,199998,1099998,1999998,10999998,\n" + "19999998,109999998,199999998,1099999998,1999999998,10999999998,19999999998,\n" + "109999999998,199999999998,1099999999998,1999999999998,10999999999998,\n" + "19999999999998,109999999999998,199999999999998,1099999999999998,1999999999999998}"); } @Test public void testLiouvilleLambda() { check("LiouvilleLambda(3^5)", // "-1"); check("LiouvilleLambda(2*3^5)", // "1"); check("LiouvilleLambda(50!)", // "1"); check("LiouvilleLambda({1,2,3,4,5,6,20})", // "{1,-1,-1,1,-1,1,-1}"); } @Test public void testList() { check("{a,b,c}(x) // FullForm", // "List(a, b, c)[x]"); // prints error check("{1,2}+{4,5,6}", // "{1,2}+{4,5,6}"); } @Test public void testListable() { check("SetAttributes(f, Listable)", // ""); check("f({1, 2, 3}, {4, 5, 6})", // "{f(1,4),f(2,5),f(3,6)}"); check("f({1, 2, 3}, 4)", // "{f(1,4),f(2,4),f(3,4)}"); check("{{1, 2}, {3, 4}} + {5, 6}", // "{{6,7},{9,10}}"); } @Test public void testListConvolve() { check("ListConvolve({x, y}, {a, b, c, d, e, f})", // "{b*x+a*y,c*x+b*y,d*x+c*y,e*x+d*y,f*x+e*y}"); check("Reverse({{u, v}, {w, x}})", // "{{w,x},{u,v}}"); check("ListConvolve({{u, v}, {w, x}}, {{a,b,c,p}, {d,e,f,q}, {g, h, i,r}})", // "{{e*u+d*v+b*w+a*x,f*u+e*v+c*w+b*x,q*u+f*v+p*w+c*x},{h*u+g*v+e*w+d*x,i*u+h*v+f*w+e*x,r*u+i*v+q*w+f*x}}"); } @Test public void testListCorrelate() { check("ListCorrelate({x, y}, {a, b, c, d, e, f})", // "{a*x+b*y,b*x+c*y,c*x+d*y,d*x+e*y,e*x+f*y}"); check("ListCorrelate({{u, v}, {w, x}}, {{a,b,c,p}, {d,e,f,q}, {g, h, i,r}})", // "{{a*u+b*v+d*w+e*x,b*u+c*v+e*w+f*x,c*u+p*v+f*w+q*x}," // + "{d*u+e*v+g*w+h*x,e*u+f*v+h*w+i*x,f*u+q*v+i*w+r*x}}"); check("ListCorrelate({{1, 0, 1}, {0, -4, 0}, {1, 0, 1}}, Array(Subscript(a, #) &, {4, 4}))", // "{{2*Subscript(a,1)-4*Subscript(a,2)+2*Subscript(a,3),2*Subscript(a,1)-4*Subscript(a,\n"// + "2)+2*Subscript(a,3)},{2*Subscript(a,2)-4*Subscript(a,3)+2*Subscript(a,4),2*Subscript(a,\n"// + "2)-4*Subscript(a,3)+2*Subscript(a,4)}}"); check("ListCorrelate({{1, 1}, {1, 1}}, {{a, b, c}, {d, e, f}, {g, h, i}})", // "{{a+b+d+e,b+c+e+f},{d+e+g+h,e+f+h+i}}"); check("ListCorrelate(N(Differences(Range(10)^2)), N(1/Range(20)))", // "{20.82897,16.07103,13.44037,11.65061,10.3224,9.28594,8.44948,7.75767,7.17457,6.67562,6.24334,5.86489}"); } @Test public void testListQ() { check("ListQ({1, 2, 3})", // "True"); check("ListQ({{1, 2}, {3, 4}})", // "True"); check("ListQ(x)", // "False"); } @Test public void testLog() { checkNumeric("Log(-1.4)", // "0.3364722366212129+I*3.141592653589793"); check("N(Log({2, E, 10}, 5/2),50)", // "{1.3219280948873623478703194294893901758648313930245," // + "0.91629073187415506518352721176801107145010121990826," // + "0.39794000867203760957252221055101394646362023707578}"); check("N(Log({2, E, 10}, -5/2),50)", // "{1.3219280948873623478703194294893901758648313930245+I*4.5323601418271938096276829457166668101718614677237," // + "0.9162907318741550651835272117680110714501012199082+I*3.1415926535897932384626433832795028841971693993751," // + "0.3979400086720376095725222105510139464636202370757+I*1.3643763538418413474857836254313557702101274837239}"); check("Log((-1)^(1/8))", // "I*1/8*Pi"); // check("Log(-(-1)^(1/8))", // // "-I*1/3*Pi"); check("Log(1/2-I*1/2*Sqrt(3))", // "-I*1/3*Pi"); check("Log(Overflow())", // "Overflow()"); check("Log(Underflow())", // "Underflow()"); check("Log(1000, 10)", // "1/3"); check("Log(9) / Log(27)", // "Log(9)/Log(27)"); check("Log(27) / Log(9)", // "Log(27)/Log(9)"); check("Log(Interval({1/3, E}))", // "Interval({-Log(3),1})"); check("Log(Interval({0, 3}))", // "Interval({-Infinity,Log(3)})"); check("Log(Interval({-1, 3}))", // "Log(Interval({-1,3}))"); // github #134 check("Log(10,1)", // "0"); check("Log(0,0)", // "Indeterminate"); check("Log(E^(7+13*I))", // "7+I*13-I*4*Pi"); check("Log(E^(27*I))", // "I*27-I*8*Pi"); check("Log(10*E) // Simplify", // "1+Log(10)"); check("Log(10*E*x*y) // FunctionExpand", // "1+Log(10)+Log(x*y)"); check("Log( )", // "Log()"); check("Log(2/3)", // "-Log(3/2)"); check("Log(3/2)", // "Log(3/2)"); check("Log(-3/2)", // "I*Pi+Log(3/2)"); check("Log(-2/3)", // "I*Pi-Log(3/2)"); check("Log(0, 0)", /// "Indeterminate"); check("Log(0, x)", /// "0"); check("Log(2, 0)", // "-Infinity"); check("Log(3/4, 0)", // "Infinity"); check("Log(-2, 0)", // "(-Infinity)/(I*Pi+Log(2))"); check("Exp(Log(x))", // "x"); check("Refine(Log(Exp(x)),Element(x, Reals))", // "x"); check("Log({0, 1, E, E * E, E ^ 3, E ^ x})", // "{-Infinity,0,1,2,3,Log(E^x)}"); check("Log(0.)", // "Indeterminate"); check("Log(1000) / Log(10)", // "3"); check("Log(1.4)", // "0.336472"); checkNumeric("Log(Exp(1.4))", // "1.3999999999999997"); check("Log(-1)", // "I*Pi"); check("Log(-2)", // "I*Pi+Log(2)"); // test alias check("Ln(E)", // "1"); check("ln(-E)", // "1+I*Pi"); check("Log(a, b)", // "Log(b)/Log(a)"); check("Log(Pi^E)", // "E*Log(Pi)"); check("Log(E^10)", // "10"); check("Log(E)", // "1"); check("Log(-E)", // "1+I*Pi"); check("D(Log(a, x),x)", // "1/(x*Log(a))"); checkNumeric("Log(1000.)", // "6.907755278982137"); checkNumeric("Log(2.5 + I)", // "0.9905007344332917+I*0.3805063771123649"); checkNumeric("Log({2.1, 3.1, 4.1})", // "{0.7419373447293773,1.1314021114911006,1.410986973710262}"); check("Log(2, 16)", // "4"); check("Log(10, 1000)", // "3"); check("Log(10, 10)", // "1"); check("Log(0)", // "-Infinity"); check("Log(1)", // "0"); check("Log(-x)", // "Log(-x)"); check("Log(-1)", // "I*Pi"); check("Log(I)", // "I*1/2*Pi"); check("Log(-I)", // "-I*1/2*Pi"); check("Log(GoldenRatio)", // "ArcCsch(2)"); check("Log(Infinity)", // "Infinity"); check("Log(-Infinity)", // "Infinity"); check("Log(I*Infinity)", // "Infinity"); check("Log(-I*Infinity)", // "Infinity"); check("Log(ComplexInfinity)", // "Infinity"); check("Table(Im(Log(x + I*y)), {x, -2, 2}, {y, -2, 2}) //N ", // "{{-2.35619,-2.67795,3.14159,2.67795,2.35619}," // + "{-2.03444,-2.35619,3.14159,2.35619,2.03444}," // + "{-1.5708,-1.5708,0.0,1.5708,1.5708}," // + "{-1.10715,-0.785398,0.0,0.785398,1.10715}," // + "{-0.785398,-0.463648,0.0,0.463648,0.785398}}"); } @Test public void testLog10() { check("Log10(Log10(Log(Log(Log(Log10(Log10(a)))))))", // "Log(Log(Log(Log(Log(Log(Log(a)/Log(10))/Log(10)))))/Log(10))/Log(10)"); check("Log10(Log10(Log(Log(Log(Log10(Log10( )))))))", // "Log(Log(Log(Log(Log(Log(Log10())/Log(10)))))/Log(10))/Log(10)"); check("Log10(1000)", // "3"); checkNumeric("Log10({2., 5.})", // "{0.30102999566398114,0.6989700043360186}"); check("Log10(E ^ 3)", // "3/Log(10)"); check("Log10(x)", // "Log(x)/Log(10)"); } @Test public void testLog2() { check("Log(2, 0)", // "-Infinity"); check("Log2(0)", // "-Infinity"); check("Log2(4 ^ 8)", // "16"); checkNumeric("Log2(5.6)", // "2.4854268271702415"); check("Log2(E ^ 2) ", // "2/Log(2)"); check("Log2(x)", // "Log(x)/Log(2)"); } @Test public void testLogGamma() { check("N(LogGamma(22/10), 50)", // "0.096947466790638776492015185854629186237721721052839"); check("Table(LogGamma(x), {x,0.0, 8.0, 0.25})", // "{Infinity,1.28802,0.572365,0.203281,0.0,-0.0982718,-0.120782,-0.0844011,0.0,0.124872,0.284683,0.475215,0.693147,0.935802," // + "1.20097,1.48682,1.79176,2.11446,2.45374,2.80857,3.17805,3.56138,3.95781,4.36672,4.78749,5.2196,5.66256,6.11592,6.57925," // + "7.05219,7.53436,8.02546,8.52516}"); checkNumeric("LogGamma(2.5 + 3*I)", // "-1.4709546103488411+I*2.822615638260799"); checkNumeric("LogGamma({2.0+ 3*I, 3+ 3.0*I, 4.0+ 3*I, 5.0+ 3*I, 6.0+ 3*I})", // "{-2.0928517530927335+I*2.302396543466868,-0.8103770743619652+I*3.2851902667141966,0.6348088045861172+I*4.070588430111645," // + "2.2442467170202174+I*4.714089538904929,4.007426979328298+I*5.254509039175513}"); check("LogGamma(-11/2)", // "LogGamma(-11/2)"); check("LogGamma(1/2)", // "Log(Pi)/2"); check("LogGamma(11/2)", // "Log(945/32*Sqrt(Pi))"); check("LogGamma(43/2)", // "Log(13113070457687988603440625/2097152*Sqrt(Pi))"); check("LogGamma(7.7)", // "7.92654"); check("LogGamma(-I*Infinity)", // "ComplexInfinity"); check("LogGamma(6)", // "Log(120)"); check("LogGamma(1)", // "0"); check("LogGamma(0)", // "Infinity"); check("LogGamma(-6)", // "Infinity"); } @Test public void testLogIntegral() { check("LogIntegral(-4.0)", // "-0.158346+I*4.30335"); check("Attributes(LogIntegral)", // "{Listable,NumericFunction,Protected}"); check("LogIntegral(20.0)", // "9.9053"); check("LogIntegral(Infinity)", // "Infinity"); check("LogIntegral(ComplexInfinity)", // "ComplexInfinity"); check("Table(LogIntegral(x), {x,-4.0, 4.0, 1/4})", // "{-0.158346+I*4.30335,-0.129418+I*4.23625,-0.101495+I*4.16812,-0.0747069+I*4.09891,-0.0492077+I*4.02858," // + "-0.0251827+I*3.95708,-0.00285625+I*3.88437,0.0174962+I*3.8104,0.0355323+I*3.73515,0.0508192+I*3.65864," // + "0.0628003+I*3.58092,0.0707443+I*3.50217,0.0736679+I*3.42273,0.0702127+I*3.34336,0.0584548+I*3.26567," // + "0.0356721+I*3.19357,0.0,-0.118662,-0.378671,-0.93693,-Infinity,-0.686488,0.125065,0.645476,1.04516," // + "1.37776,1.66729,1.92665,2.16359,2.38314,2.58877,2.78296,2.96759}"); check("Table(LogIntegral(x), {x, -3.0, 3.0, 0.25})", // "{-0.0492077+I*4.02858,-0.0251827+I*3.95708,-0.00285625+I*3.88437,0.0174962+I*3.8104,0.0355323+I*3.73515," // + "0.0508192+I*3.65864,0.0628003+I*3.58092,0.0707443+I*3.50217,0.0736679+I*3.42273,0.0702127+I*3.34336," // + "0.0584548+I*3.26567,0.0356721+I*3.19357,0.0,-0.118662,-0.378671,-0.93693,-Infinity,-0.686488,0.125065," // + "0.645476,1.04516,1.37776,1.66729,1.92665,2.16359}"); check("Table(LogIntegral(x), {x,-2.0, 20.0, 2/3})", // "{0.0355323+I*3.73515,0.0685993+I*3.52852,0.067332+I*3.31716,0.0,-0.693308,-0.358914,1.04516,1.843,2.45309," // + "2.96759,3.42296,3.83761,4.22222,4.58359,4.92632,5.25372,5.56822,5.87169,6.1656,6.4511,6.72916,7.00055," // + "7.26593,7.52587,7.78083,8.03122,8.27742,8.51972,8.7584,8.99371,9.22587,9.45508,9.6815,9.9053}"); // } @Test public void testLogisticSigmoid() { checkNumeric("LogisticSigmoid(0.8)", // "0.6899744811276125"); checkNumeric("N(LogisticSigmoid(1/9),50)", // "0.52774923505451317879089698533394369096217714446845"); checkNumeric("LogisticSigmoid(1.0000000000000000000000)", // "0.73105857863000487925115"); checkNumeric("N(LogisticSigmoid(1 + 9 I))", // "1.4298207928844138+I*0.32606870958127954"); check("LogisticSigmoid(I*Pi)", // "LogisticSigmoid(I*Pi)"); check("D(LogisticSigmoid(x),x)", // "(1-LogisticSigmoid(x))*LogisticSigmoid(x)"); check("LogisticSigmoid(Infinity)", // "1"); check("LogisticSigmoid(-Infinity)", // "0"); check("LogisticSigmoid(0)", // "1/2"); checkNumeric("LogisticSigmoid(0.5)", // "0.6224593312018546"); checkNumeric("LogisticSigmoid(0.5 + 2.3*I)", // "1.0647505893884985+I*0.8081774171575825"); checkNumeric("LogisticSigmoid({-0.2, 0.1, 0.3})", // "{0.4501660026875221,0.52497918747894,0.5744425168116589}"); checkNumeric("LogisticSigmoid(0.5 + 2.3*I)", // "1.0647505893884985+I*0.8081774171575825"); } @Test public void testLucasL() { check("LucasL(11,{x,0,0,<|a->0,b:>1|>})", // "{11*x+55*x^3+77*x^5+44*x^7+11*x^9+x^11,0,0,<|a->0,b:>LucasL(11,1)|>}"); // check("LucasL(19,<|s1->0,s2:>1|>)", // // "<|s1->0,s2:>LucasL(19,1)|>"); // slow // message Polynomial degree 101 exceeded check("LucasL(151,1/1317624576693539401)", // "LucasL(151,1/1317624576693539401)"); check("LucasL(Quantity(1.2,\"m\"),2.718281828459045)", // "LucasL(1.2[m],2.71828)"); check("LucasL(1+I/2)//N", // "0.0653384+I*0.755095"); check("LucasL(1,0)", // "0"); check("LucasL(0,0)", // "2"); check("LucasL(-1, x)", // "-x"); check("LucasL(-10, x)", // "2+25*x^2+50*x^4+35*x^6+10*x^8+x^10"); check("LucasL(-11, x)", // "-11*x-55*x^3-77*x^5-44*x^7-11*x^9-x^11"); check("LucasL(50, x)", // "2+625*x^2+32500*x^4+672750*x^6+7400250*x^8+50075025*x^10+227613750*x^12+\n" + "736618125*x^14+1767883500*x^16+3241119750*x^18+4639918800*x^20+5272635000*x^22+\n" + "4814145000*x^24+3562467300*x^26+2148789800*x^28+1059575660*x^30+427248250*x^32+\n" + "140512125*x^34+37469900*x^36+8021650*x^38+1357510*x^40+177375*x^42+17250*x^44+\n" + "1175*x^46+50*x^48+x^50"); check("Table(LucasL(n, x), {n, 5})", // "{x,2+x^2,3*x+x^3,2+4*x^2+x^4,5*x+5*x^3+x^5}"); check("LucasL(-11)", // "-199"); check("LucasL(-12)", // "322"); check("Table(LucasL(n), {n, 20})", // "{1,3,4,7,11,18,29,47,76,123,199,322,521,843,1364,2207,3571,5778,9349,15127}"); check("LucasL(1000)", // "9719417773590817520798198207932647373779787915534568508272808108477251881844481\\\n" + "5269080619149045968297679578305403209347401163036907660573971740862463751801641\\\n" + "201490284097309096322681531675707666695323797578127"); } @Test public void testMachineNumberQ() { check("MachineNumberQ(3.14159265358979324)", // "False"); check("MachineNumberQ(2.71828182845904524 + 3.14159265358979324*I)", // "False"); check("MachineNumberQ(1.5 + 3.14159265358979324*I)", // "False"); check("MachineNumberQ(1.5 + 2.3*I)", // "True"); check("MachineNumberQ(1.5 + 5 *I)", // "True"); } @Test public void testMangoldtLambda() { check("MangoldtLambda(3^5)", // "Log(3)"); check("MangoldtLambda({1,2,3,4,5,6,7,8,9})", // "{0,Log(2),Log(3),Log(2),Log(5),0,Log(7),Log(2),Log(3)}"); check("{MangoldtLambda(Prime(10^5)^10), MangoldtLambda(2*Prime(10^5)^10)}", // "{Log(1299709),0}"); } @Test public void testManhattanDistance() { check("ManhattanDistance({-1, -1}, {1.0, 1})", // "4.0"); check("ManhattanDistance({-1, -1}, {1, 1})", // "4"); } @Test public void testMantissaExponent() { // message - MantissaExponent: The value (3.0+I*2.0) is not a real number. check("MantissaExponent(3+2*I, 2)", // "MantissaExponent(3+I*2,2)"); check("MantissaExponent(125.24)", // "{0.12524,3}"); check("MantissaExponent(125., 2)", // "{0.976562,7}"); check("MantissaExponent(10, b)", // "MantissaExponent(10,b)"); check("MantissaExponent(E, Pi)", // "{E/Pi,1}"); check("MantissaExponent(Pi, Pi)", // "{1/Pi,2}"); check("MantissaExponent(5/2 + 3, Pi)", // "{11/2*1/Pi^2,2}"); check("MantissaExponent(17, E)", // "{17/E^3,3}"); check("MantissaExponent(17.0, E)", // "{0.84638,3}"); check("MantissaExponent(Exp(Pi), 2)", // "{E^Pi/32,5}"); check("MantissaExponent(0.0000124)", // "{0.124,-4}"); check("MantissaExponent(0.0000124, 2)", // "{0.812646,-16}"); check("MantissaExponent(0)", // "{0,0}"); check("MantissaExponent(N(Pi, 21))", // "{0.314159265358979323846,1}"); check("MantissaExponent(N(Pi, 20))", // "{0.31415926535897932384,1}"); check("MantissaExponent(3.4*10^30)", // "{0.34,31}"); } @Test public void testMap() { // Map: Options expected (instead of y_) beyond position Map(1/Sqrt(5),{},I,y_) in `3`. An // option must be a rule or a list of rules. check("Map(1/Sqrt(5),ByteArray[{}],I,y_)", // "Map(1/Sqrt(5),{},I,y_)"); check("s=SparseArray({1 -> 1, 2 -> 2, 100 -> 100})", // "SparseArray(Number of elements: 3 Dimensions: {100} Default value: 0)"); check("t=Map(f,s)", // "SparseArray(Number of elements: 3 Dimensions: {100} Default value: f(0))"); check("ArrayRules(t)", // "{{1}->f(1),{2}->f(2),{100}->f(100),{_}->f(0)}"); check("t[[2]]", // "f(2)"); check("Map(#2,1/Sqrt(5),2,Heads->True)", // "#2[Power][#2[5],#2[-1/2]]"); check("Map(f, {{{{a}}}}, -2)", // "{f({f({f({a})})})}"); check("Map(List,Join({1,2,3},4-{1,2,3}))", // "{{1},{2},{3},{3},{2},{1}}"); check("Map(f, {{{{{a}}}}}, 2)", // "{f({f({{{a}}})})}"); check("Map(f, {{{{{a}}}}}, {2})", // "{{f({{{a}}})}}"); check("Map(f, {{{{{a}}}}}, {0,2})", // "f({f({f({{{a}}})})})"); check("Map(f, {{{{{a}}}}}, Infinity)", // "{f({f({f({f({f(a)})})})})}"); check("Map(f, {{{{{a}}}}}, {0, Infinity})", // "f({f({f({f({f({f(a)})})})})})"); check("Map(f, {{{{{a}}}}}, 3)", // "{f({f({f({{a}})})})}"); check("Map(f, {{{{{a}}}}}, Infinity)", // "{f({f({f({f({f(a)})})})})}"); check("Map(f, {{{{{a}}}}}, {0, Infinity})", // "f({f({f({f({f({f(a)})})})})})"); check("Map(f, {{{{{a}}}}}, {2, -3})", // "{{f({f({{a}})})}}"); check("Map(f, h0(h1(h2(h3(h4(a))))), {2, -3})", // "h0(h1(f(h2(f(h3(h4(a)))))))"); check("Map(f, {{{{a}}}}, 2, Heads -> True)", // "f(List)[f(f(List)[f({{a}})])]"); check("Map(f, {a, b, c})", // "{f(a),f(b),f(c)}"); check("Map(f, {a, b, c}, Heads -> True)", // "f(List)[f(a),f(b),f(c)]"); check("f /@ {1, 2, 3}", // "{f(1),f(2),f(3)}"); check("#^2& /@ {1, 2, 3, 4}", // "{1,4,9,16}"); check("Map(f, {{a, b}, {c, d, e}}, {2})", // "{{f(a),f(b)},{f(c),f(d),f(e)}}"); check("Map(f, a + b + c, Heads->True)", // "f(Plus)[f(a),f(b),f(c)]"); check("Map(f, expr, a+b, Heads->True)", // "Map(f,expr,a+b,Heads->True)"); check("Map(f, {{{{a}}}}, -1)", // "{f({f({f({f(a)})})})}"); check("Map(f, {{{{a}}}}, -2)", // "{f({f({f({a})})})}"); check("Map(f, {{{{a}}}}, -3)", // "{f({f({{a}})})}"); check("Map(f, {{{{a}}}}, -4)", // "{f({{{a}}})}"); check("Map(f, {{{{a}}}}, -5)", // "{{{{a}}}}"); check("Map(f, {{{{a}}}}, -6)", // "{{{{a}}}}"); check("Map(Print, {a, b, c})", // "{Null,Null,Null}"); check("Map(x, {a, {{b, c}, d, {e, {f, g}}}}, {-1})", // "{x(a),{{x(b),x(c)},x(d),{x(e),{x(f),x(g)}}}}"); check("Map(x, {a, {{b, c}, d, {e, {f, g}}}}, {-2})", // "{a,{x({b,c}),d,{e,x({f,g})}}}"); } @Test public void testMapAt() { check("MapAt(f, {{a, b, c}, {d, e}}, {All, 2})", // "{{a,f(b),c},{d,f(e)}}"); check("MapAt(f, <|\"a\" -> 1, \"b\" -> 2, \"c\" -> 3, \"d\" -> 4, \"e\" -> 5|>, Key(\"b\"))", // "<|a->1,b->f(2),c->3,d->4,e->5|>"); check("MapAt(f, <|\"a\" -> 1, \"b\" -> 2, \"c\" -> 3, \"d\" -> 4, \"e\" -> 5|>, \"b\")", // "<|a->1,b->f(2),c->3,d->4,e->5|>"); check("MapAt(f, <|\"a\" -> 1, \"b\" -> 2, \"c\" -> 3, \"d\" -> 4, \"e\" -> 5|>, 3)", // "<|a->1,b->2,c->f(3),d->4,e->5|>"); check("MapAt(f, <|\"a\" -> 1, \"b\" -> 2, \"c\" -> 3, \"d\" -> 4, \"e\" -> 5|>, -3)", // "<|a->1,b->2,c->f(3),d->4,e->5|>"); check("MapAt(f, {{a, b, c}, {d, e}}, {2, 1})", // "{{a,b,c},{f(d),e}}"); check("MapAt(f, {a, b, c, d}, {{1}, {4}})", // "{f(a),b,c,f(d)}"); check("MapAt(f,3)[x]", // "MapAt(f,3)[x]"); check("MapAt(f,3)[{a, b, c, d}]", // "{a,b,f(c),d}"); check("MapAt(f, a+b+c+d, 2)", // "a+c+d+f(b)"); check("MapAt(f, {a, b, c, d}, 0)", // "f(List)[a,b,c,d]"); check("MapAt(f, {a, b, c, d}, -2)", // "{a,b,f(c),d}"); check("MapAt(f, {a, b, c, d}, -5)", // "f(List)[a,b,c,d]"); check("MapAt(f, {a, b, c, d}, -4)", // "{f(a),b,c,d}"); // print message: check("MapAt(f, {a, b, c, d}, -6)", // "MapAt(f,{a,b,c,d},-6)"); check("MapAt(f, {a, b, c, d, e}, -6)", // "f(List)[a,b,c,d,e]"); check("MapAt(f, {a, b, c, d}, 2)", // "{a,f(b),c,d}"); } @Test public void testMapIndexed() { // Associations are not supported check("MapIndexed(f, <|\"a\" -> 1, a -> 2, 1 -> 1|>)", // "MapIndexed(f,<|a->1,a->2,1->1|>)"); check("MapIndexed(f, a(b(c, d, e), l(g(h, j), k)), {-Infinity, Infinity})", // "f(a(f(b(f(c,{1,1}),f(d,{1,2}),f(e,{1,3})),{1}),f(l(f(g(f(h,{2,1,1}),f(j,{2,1,2})),{\n" + "2,1}),f(k,{2,2})),{2})),{})"); // f[a[f[b[f[c, {1, 1}], f[d, {1, 2}], f[e, {1, 3}]], {1}], f[l[f[g[f[h, {2, 1, 1}], f[j, {2, 1, // 2}]], {2, 1}], f[k, {2, 2}]], {2}]], {}] // // a(f(b(f(c,{1,1}),f(d,{1,2}),f(e,{1,3})),{1}),f(l(f(g(f(h,{2,1,1}),f(j,{2,1,2})),{ // 2,1}),f(k,{2,2})),{2})) check("MapIndexed(f, a(b(c, d, e), l(g(h, j), k)), Infinity)", // "a(f(b(f(c,{1,1}),f(d,{1,2}),f(e,{1,3})),{1}),f(l(f(g(f(h,{2,1,1}),f(j,{2,1,2})),{\n" + "2,1}),f(k,{2,2})),{2}))"); check("MapIndexed(f, a(b(c, d, e), l(g(h, j), k)), {-2, Infinity})", // "a(f(b(f(c,{1,1}),f(d,{1,2}),f(e,{1,3})),{1}),l(f(g(f(h,{2,1,1}),f(j,{2,1,2})),{2,\n" + "1}),f(k,{2,2})))"); check("MapIndexed(f, a(b(c, d, e), l(g(h, j), k)), {2, -2})", // "a(b(c,d,e),l(f(g(h,j),{2,1}),k))"); check("MapIndexed(f, a(b(c, d, e), l(g(h, j), k)), 2)", // "a(f(b(f(c,{1,1}),f(d,{1,2}),f(e,{1,3})),{1}),f(l(f(g(h,j),{2,1}),f(k,{2,2})),{2}))"); check("MapIndexed(f, a(b(c, d, e), l(g(h, j), k)), -2)", // "a(f(b(c,d,e),{1}),f(l(f(g(h,j),{2,1}),k),{2}))"); check("MapIndexed(f, SparseArray(3 -> a, 5))", // "{f(0,{1}),f(0,{2}),f(a,{3}),f(0,{4}),f(0,{5})}"); check("MapIndexed(f)[x]", // "x"); check("MapIndexed(f, {{{{a, b}}}}, -3)", // "{f({f({{a,b}},{1,1})},{1})}"); check("MapIndexed(f, {{{{a, b},{c, d}}}}, -2)", // "{f({f({f({a,b},{1,1,1}),f({c,d},{1,1,2})},{1,1})},{1})}"); check("MapIndexed(f, {{{{a}}}}, -5)", // "{{{{a}}}}"); check("MapIndexed(f, {{{{a}}}}, -4)", // "{f({{{a}}},{1})}"); check("MapIndexed(f, {{{{a}}}}, -3)", // "{f({f({{a}},{1,1})},{1})}"); check("MapIndexed(f, {{{{a}}}}, -2)", // "{f({f({f({a},{1,1,1})},{1,1})},{1})}"); check("MapIndexed(f, {{{{a}}}}, -1)", // "{f({f({f({f(a,{1,1,1,1})},{1,1,1})},{1,1})},{1})}"); check("MapIndexed(f, {{a}, {c}}, {2})", // "{{f(a,{1,1})},{f(c,{2,1})}}"); check("MapIndexed(f, {a, b})", // "{f(a,{1}),f(b,{2})}"); check("MapIndexed(f, {{a, b}, {c, d, e}})", // "{f({a,b},{1}),f({c,d,e},{2})}"); check("MapIndexed(f, {}, 1)", // "{}"); check("MapIndexed(f, {a, b}, 1)", // "{f(a,{1}),f(b,{2})}"); check("MapIndexed(f, {a, b}, 0)", // "{a,b}"); check("MapIndexed(f, {}, 0)", // "{}"); check("MapIndexed(f, {{{{a, b}, {c, d}}}, {{{u, v}, {s, t}}}}, 2)", // "{f({f({{a,b},{c,d}},{1,1})},{1}),f({f({{u,v},{s,t}},{2,1})},{2})}"); check("MapIndexed(f, {{{{a, b}, {c, d}}}, {{{u, v}, {s, t}}}}, 3)", // "{f({f({f({a,b},{1,1,1}),f({c,d},{1,1,2})},{1,1})},{1}),f({f({f({u,v},{2,1,1}),f({s,t},{\n" + "2,1,2})},{2,1})},{2})}"); check("MapIndexed(f, {{{{a, b}, {c, d}}}, {{{u, v}, {s, t}}}}, 4)", // "{f({f({f({f(a,{1,1,1,1}),f(b,{1,1,1,2})},{1,1,1}),f({f(c,{1,1,2,1}),f(d,{1,1,2,2})},{\n" + "1,1,2})},{1,1})},{1}),f({f({f({f(u,{2,1,1,1}),f(v,{2,1,1,2})},{2,1,1}),f({f(s,{2,\n" + "1,2,1}),f(t,{2,1,2,2})},{2,1,2})},{2,1})},{2})}"); check("MapIndexed(f, {{{a, b}, {c, d}}, {{u, v}, {s, t}}}, 2)", // "{f({f({a,b},{1,1}),f({c,d},{1,2})},{1}),f({f({u,v},{2,1}),f({s,t},{2,2})},{2})}"); check("MapIndexed(f, {{a, b, c}, {x, y, z}})", // "{f({a,b,c},{1}),f({x,y,z},{2})}"); check("MapIndexed(First(#2) + f(#1) &, {a, b, c, d})", // "{1+f(a),2+f(b),3+f(c),4+f(d)}"); check("MapIndexed(f, {{a, b}, {c, d, e}}, {1})", // "{f({a,b},{1}),f({c,d,e},{2})}"); check("MapIndexed(f, {{a, b}, {c, d, e}}, {2})", // "{{f(a,{1,1}),f(b,{1,2})},{f(c,{2,1}),f(d,{2,2}),f(e,{2,3})}}"); check("MapIndexed(f, {{a, b}, {c, d, e}}, {3})", // "{{a,b},{c,d,e}}"); } @Test public void testMapThread() { check("MapThread(f, {{{a, b}, {c, d}}}, 3)", // "MapThread(f,{{{a,b},{c,d}}},3)"); check("MapThread(f)[ {{a, b, c}, {x, y, z}}]", // "{f(a,x),f(b,y),f(c,z)}"); check("MapThread(f, {}, 1)", // "{}"); check("MapThread(f, {a, b}, 1)", // "MapThread(f,{a,b},1)"); check("MapThread(f, {a, b}, 0)", // "f(a,b)"); check("MapThread(f, {}, 0)", // "f()"); check("MapThread(f, {{{{a, b}, {c, d}}}, {{{u, v}, {s, t}}}}, 2)", // "{{f({a,b},{u,v}),f({c,d},{s,t})}}"); check("MapThread(f, {{{{a, b}, {c, d}}}, {{{u, v}, {s, t}}}}, 3)", // "{{{f(a,u),f(b,v)},{f(c,s),f(d,t)}}}"); check("MapThread(f, {{{{a, b}, {c, d}}}, {{{u, v}, {s, t}}}}, 4)", // "MapThread(f,{{{{a,b},{c,d}}},{{{u,v},{s,t}}}},4)"); check("MapThread(f, {{{a, b}, {c, d}}, {{u, v}, {s, t}}}, 2)", // "{{f(a,u),f(b,v)},{f(c,s),f(d,t)}}"); check("MapThread(f, {{a, b, c}, {x, y, z}})", // "{f(a,x),f(b,y),f(c,z)}"); check("MapThread(f, {{a, b, c}, {1, 2, 3}})", // "{f(a,1),f(b,2),f(c,3)}"); } @Test public void testMatchingDissimilarity() { check("MatchingDissimilarity({1, 0, 1, 1, 0, 1, 1}, {0, 1, 1, 0, 0, 0, 1})", // "4/7"); check("MatchingDissimilarity({1, 0, 1, 1, 0}, {1, 1, 0, 1, 1})", // "3/5"); check("MatchingDissimilarity({True, False, True}, {True, True, False})", // "2/3"); check("MatchingDissimilarity({1, 1, 1, 1}, {1, 1, 1, 1})", // "0"); check("MatchingDissimilarity({0, 0, 0, 0}, {1, 1, 1, 1})", // "1"); } @Test public void testMatchQ() { check("MatchQ(<|a -> 1|>, <|key_ -> val_|>)", // "True"); check("MatchQ(22/7, _Rational)", // "True"); check("MatchQ(42, _Complex)", // "False"); check("MatchQ(42, _Rational)", // "False"); check("MatchQ(1.1+2.3*I, _Complex)", // "True"); check("MatchQ(_Integer)[123]", // "True"); check("MatchQ({1, 2, 3}[[]], _List)", // "True"); check("MatchQ({f(a, b), f(a, c), f(a, d)}, {f(_, x_) ..})", // "False"); check("MatchQ({f(a, b), f(a, c), f(a, d)}, {f(x_, _) ..})", // "True"); check("MatchQ({\"U\",\"V\"}, {_String ..})", // "True"); check("MatchQ({a,b,c}, {___Symbol})", // "True"); check("MatchQ({a,2,c}, {___Symbol})", // "False"); check("MatchQ({a,b,c}, _)", // "True"); check("MatchQ({a,b,c}, {_})", // "False"); check("MatchQ({a,b,c}, __)", // "True"); check("MatchQ({a,b,c}, x__)", // "True"); check("MatchQ({ }, __)", // "True"); check("MatchQ(Plus(a,b,c), Plus(__))", // "True"); check("MatchQ({4,6,8}, x_/;Length(x)>4)", // "False"); // Print error message check("MatchQ({4,6,8}, {x___}/;Length(x)>4)", // "False"); check("MatchQ({4,6,8}, {x___}/;Plus(x)>10)", // "True"); check("MatchQ({1,2,3}, _List)", // "True"); check("MatchQ({1,2,3}, _?NumberQ)", // "False"); check("MatchQ({1,2,3}, {__?NumberQ})", // "True"); check( "MatchQ({x*(Sqrt(2*Pi*x)/(x!))^(1/x),x->Infinity}, {x_*(Sqrt(2*Pi*x_)/(x_!))^(1/x_), x_->Infinity})", // "True"); // TODO check("MatchQ({a}, {a, ___})", // "True"); check("MatchQ(2*x, c1_Integer*a_Symbol)", // "True"); check("MatchQ(a + b, x_Symbol + x_Symbol)", // "False"); check("MatchQ({2^a, a}, {2^x_Symbol, x_Symbol})", // "True"); check("MatchQ({2^a, b}, {2^x_Symbol, x_Symbol})", // "False"); check("MatchQ({a, b}, {a, __})", // "True"); check("MatchQ({a}, {a, __})", // "False"); check("MatchQ(1,_Integer)", // "True"); check("MatchQ(_Symbol, _Symbol)", // "False"); check("MatchQ(_Symbol, _Blank)", // "True"); check("MatchQ(_Symbol, test_Blank)", // "True"); check("MatchQ(name_Symbol, test_Pattern)", // "True"); check("MatchQ(_Symbol, s)", // "False"); check("MatchQ(1.5,_Integer)", // "False"); check("MatchQ(1.5,_Real)", // "True"); check("MatchQ(f(2*I), f(Complex(i_Integer, r_Integer)) )", // "True"); check("MatchQ(g(1/2), g(Rational(n_Integer, d_Integer)) )", // "True"); check("MatchQ(Simplify(1 + 1/GoldenRatio - GoldenRatio), 0)", // "True"); check("MatchQ(Sin(Cos(x)), HoldPattern(F_(G_(v_))) /; F==Sin&&G==Cos&&v==x )", // "True"); check("MatchQ(Sin(x*y), HoldPattern(F_(G_(v_))) /; Print(F,G,v) )", // "False"); check("MatchQ(Sin(Cos(x)), HoldPattern(F_(G_(v_))))", // "True"); check("MatchQ(Sin(3*y),Sin(u_*v_) /; IntegerQ(u))", // "True"); check("MatchQ(123, _Integer)", // "True"); check("MatchQ(123, _Real)", // "False"); check("MatchQ((-1-1*#^2-3*#)&, (a_.+c_.*#^2+b_.* #)&)", // "True"); check("MatchQ(#-1*#^2, b_.* #+c_.*#^2)", // "True"); check("MatchQ(_Integer)[123]", // "True"); check("MatchQ(22/7, _Rational)", // "True"); check("MatchQ(6/3, _Rational)", // "False"); check("MatchQ(22/7, _Rational)", // "True"); check("MatchQ(b*x,a_.+x^n_.*b_./;FreeQ({a,b,n},x))", // "True"); check("MatchQ(x,a_.+x^n_.*b_./;FreeQ({a,b,n},x))", // "True"); } @Test public void testMathMLForm() { check("MathMLForm(Sqrt(3)-I)", // "\n" // + "\n" // + "\n" // + "3-ⅈ"); check("MathMLForm(a/2+Tan(x)/4-Tan(x)^2/3+12)", // "\n" + "\n" + "\n" + "12-tan⁡(x)23+tan⁡(x)4+a2"); check("MathMLForm( Surd(a,-3) )", // "\n" + "\n" + "\n" + "1a3"); check("MathMLForm( Surd(a,3) )", // "\n" + "\n" + "\n" + "a3"); check("MathMLForm( f(#,#3)& )", // "\n" + "\n" + "\n" + "f⁡(#1,#3)&"); check("MathMLForm(D(sin(x)*cos(x),x))", "\n" + "\n" + "\n" + "∂sin⁡(x)·cos⁡(x)∂x"); } @Test public void testMax() { check("Max(Sequence())", // "-Infinity"); check("Refine(Max(Infinity,x), x>0)", // "Infinity"); check("Max(Interval({1,2}))", // "2"); check("Refine(Max(Infinity,x,y), x>0&&y>0)", // "Infinity"); check("Refine(Max(Infinity,x,y), x>0)", // "Max(Infinity,y)"); check("Refine(Max(x,Infinity), x>0)", // "Infinity"); check("Refine(Max(x,y,Infinity), x>0&&y>0)", // "Infinity"); check("Refine(Max(-Infinity,x), x>0)", // "x"); check("Refine(Max(-Infinity,x,y), x>0&&y>0)", // "Max(x,y)"); check("Refine(Max(x,-Infinity), x>0)", // "x"); check("Refine(Max(x,y,-Infinity), x>0&&y>0)", // "Max(x,y)"); check("Refine(Max(x,y,-Infinity), x>0)", // "Max(x,y)"); check("Max(4, -8, 1)", // "4"); check("Max({1,2},3,{-3,3.5,-Infinity},{{1/2}})", // "3.5"); check("Max(x, y)", // "Max(x,y)"); check("Max(5, x, -3, y, 40)", // "Max(40,x,y)"); check("Max()", // "-Infinity"); check("Max(x)", "x"); check("Max(Abs(x), Abs(y))", // "Max(Abs(x),Abs(y))"); } @Test public void testMaxFilter() { check("MaxFilter({a,b,c}, 1)", // "{Max(a,b),Max(a,b,c),Max(b,c)}"); check("MaxFilter({1, 2, 3, 2, 1}, 1)", // "{2,3,3,3,2}"); check("MaxFilter({0, 3, 8, 2}, 1)", // "{3,8,8,8}"); check("MaxFilter({a,b,c}, 1)", // "{Max(a,b),Max(a,b,c),Max(b,c)}"); } @Test public void testMaximize() { // print message - Maximize: The maximum is not attained at any point satisfying the // constraints. check("Maximize(1/x, x)", // "{}"); check("Maximize(-x^4-7*x^3+2*x^2 - 42,x)", // "{-42-7/512*(-21-Sqrt(505))^3+(21+Sqrt(505))^2/32-(21+Sqrt(505))^4/4096,{x->1/8*(-\n" + "21-Sqrt(505))}}"); check("Maximize(x^4+7*Tan(x)-2*x^2 + 42, x)", // "Maximize(42-2*x^2+x^4+7*Tan(x),x)"); check("Maximize(x^4+7*x^3-2*x^2 + 42, x)", // "{Infinity,{x->-Infinity}}"); check("Maximize(-2*x^2 - 3*x + 5, x)", // "{49/8,{x->-3/4}}"); } @Test public void testMean() { check("Mean(Array(Subscript(a, ##) &, {2, 2}))", // "{1/2*(Subscript(a,1,1)+Subscript(a,2,1)),1/2*(Subscript(a,1,2)+Subscript(a,2,2))}"); check("Mean(Array(Subscript(a, ##) &, {2, 2, 2}))", // "{{1/2*(Subscript(a,1,1,1)+Subscript(a,2,1,1)),1/2*(Subscript(a,1,1,2)+Subscript(a,\n" + "2,1,2))},{1/2*(Subscript(a,1,2,1)+Subscript(a,2,2,1)),1/2*(Subscript(a,1,2,2)+Subscript(a,\n" + "2,2,2))}}"); check("Mean({26, 64, 36})", // "42"); check("Mean({1, 1, 2, 3, 5, 8})", // "10/3"); check("Mean({a, b})", // "1/2*(a+b)"); check("Mean({{a, u}, {b, v}, {c, w}})", // "{1/3*(a+b+c),1/3*(u+v+w)}"); check("Mean({1.21, 3.4, 2.15, 4, 1.55})", // "2.462"); check("Mean({a,b,c,d})", // "1/4*(a+b+c+d)"); check("Mean(BetaDistribution(a,b))", // "a/(a+b)"); check("Mean(BernoulliDistribution(p))", // "p"); check("Mean(BinomialDistribution(n, m))", // "m*n"); check("Mean(ExponentialDistribution(n))", "1/n"); check("Mean(PoissonDistribution(p))", // "p"); check("Mean(BinomialDistribution(n, p))", // "n*p"); check("Mean(DiscreteUniformDistribution({l, r}))", // "1/2*(l+r)"); check("Mean(ErlangDistribution(n, m))", // "n/m"); check("Mean(LogNormalDistribution(m,s))", // "E^(m+s^2/2)"); check("Mean(NakagamiDistribution(n, m))", // "(Sqrt(m)*Pochhammer(n,1/2))/Sqrt(n)"); check("Mean(NormalDistribution(n, p))", // "n"); check("Mean(FrechetDistribution(n, m))", // "Piecewise({{m*Gamma(1-1/n),11}},Indeterminate)"); check("Mean(WeibullDistribution(n, m))", // "m*Gamma(1+1/n)"); } @Test public void testMeanFilter() { check("MeanFilter({-3, 3, 6, 0, 0, 3, -3, -9}, 2)", // "{2,3/2,6/5,12/5,6/5,-9/5,-9/4,-3}"); check("MeanFilter({1, 2, 3, 2, 1}, 1)", // "{3/2,2,7/3,2,3/2}"); check("MeanFilter({0, 3, 8, 2}, 1)", // "{3/2,11/3,13/3,5}"); check("MeanFilter({a,b,c}, 1)", // "{1/2*(a+b),1/3*(a+b+c),1/2*(b+c)}"); } @Test public void testMeanDeviation() { // Config.MAX_AST_SIZE=Integer.MAX_VALUE; // check( // "MeanDeviation(RandomReal(1, 10^4))", // // "0.243758"); check("MeanDeviation(SparseArray({{1, 2}, {4, 8}, {5, 3}, {2, 15}}))", // "{3/2,9/2}"); check("MeanDeviation(1+(-1)*1)", // "MeanDeviation(0)"); check("MeanDeviation({a, b, c})", // "1/3*(Abs(a+1/3*(-a-b-c))+Abs(b+1/3*(-a-b-c))+Abs(1/3*(-a-b-c)+c))"); check("MeanDeviation({{1, 2}, {4, 8}, {5, 3}, {2, 15}})", // "{3/2,9/2}"); check("MeanDeviation({1, 2, 3, 7})", // "15/8"); check("MeanDeviation({Pi, E, 2})//Together", // "2/9*(-4+E+Pi)"); } @Test public void testMedian() { check("Median(WeightedData({8, 3, 5,4}, " + // "{0.15, 0.09, 0.12,0.10}))", // "5"); check("Median(WeightedData({3, 4,5,8}, " + // "{0.09, 0.10,0.12,0.15 }))", // "5"); check("Median(WeightedData({8, 3, 5, 4, 9, 0, 4, 2, 2, 3}, " + // "{0.15, 0.09, 0.12, 0.10, 0.16, 0., 0.11, 0.08, 0.08, 0.09}))", // "4"); check("Median(WeightedData({a,b,c,g}, {d,e,f,h}))", // "b*Boole(d/(d+e+f+h)<1/2<=d/(d+e+f+h)+e/(d+e+f+h))+c*Boole(d/(d+e+f+h)+e/(d+e+f+h)<1/\n" + "2<=d/(d+e+f+h)+e/(d+e+f+h)+f/(d+e+f+h))+g*Boole(d/(d+e+f+h)+e/(d+e+f+h)+f/(d+e+f+h)<\n" + "1/2<=d/(d+e+f+h)+e/(d+e+f+h)+f/(d+e+f+h)+h/(d+e+f+h))+a*Boole(1/2<=d/(d+e+f+h))"); check("Median(WeightedData({a,b,c}, {d,e,f}))", // "b*Boole(d/(d+e+f)<1/2<=d/(d+e+f)+e/(d+e+f))+c*Boole(d/(d+e+f)+e/(d+e+f)<1/2<=d/(d+e+f)+e/(d+e+f)+f/(d+e+f))+a*Boole(\n" + // "1/2<=d/(d+e+f))"); check("Median(WeightedData({a,b}, {d,e}))", // "b*Boole(d/(d+e)<1/2<=d/(d+e)+e/(d+e))+a*Boole(1/2<=d/(d+e))"); check("Median({{100, 1, 10, 50}, {-1, 1, -2, 2}})", // "{99/2,1,4,26}"); check("Median({26, 64, 36})", // "36"); check("Median({-11, 38, 501, 1183})", // "539/2"); check("Median({{100, 1, 10, 50}, {-1, 1, -2, 2}})", // "{99/2,1,4,26}"); check("Median({1,2,3,4,5,6,7.0})", // "4.0"); check("Median({1,2,3,4,5,6,7.0,8})", // "4.5"); check("Median({1,2,3,4,5,6,7})", // "4"); check("Median(BernoulliDistribution(p))", // "Piecewise({{1,p>1/2}},0)"); check("Median(BetaDistribution(a,b))", // "InverseBetaRegularized(1/2,a,b)"); check("Median(BinomialDistribution(n, m))", // "Median(BinomialDistribution(n,m))"); check("Median(ExponentialDistribution(n))", // "Log(2)/n"); check("Median(PoissonDistribution(p))", // "Median(PoissonDistribution(p))"); check("Median(DiscreteUniformDistribution({l, r}))", // "-1+l+Max(1,Ceiling(1/2*(1-l+r)))"); check("Median(UniformDistribution({l, r}))", // "1/2*(l+r)"); check("Median(ErlangDistribution(n, m))", // "InverseGammaRegularized(n,0,1/2)/m"); check("Median(LogNormalDistribution(m,s))", // "E^m"); check("Median(NakagamiDistribution(n, m))", // "Sqrt((m*InverseGammaRegularized(n,0,1/2))/n)"); check("Median(NormalDistribution())", // "0"); check("Median(NormalDistribution(n, p))", // "n"); check("Median(FrechetDistribution(n, m))", // "m/Log(2)^(1/n)"); check("Median(GammaDistribution(n, m))", // "m*InverseGammaRegularized(n,0,1/2)"); check("Median(GammaDistribution(a,b,g,d))", // "d+b*InverseGammaRegularized(a,1/2)^(1/g)"); check("Median(GeometricDistribution(n))", // "Median(GeometricDistribution(n))"); check("Median(GumbelDistribution( ))", // "Log(Log(2))"); check("Median(GumbelDistribution(n, m))", // "n+m*Log(Log(2))"); check("Median(HypergeometricDistribution(n, ns, nt))", // "Median(HypergeometricDistribution(n,ns,nt))"); check("Median(StudentTDistribution(4))", // "0"); check("Median(StudentTDistribution(n))", // "0"); check("Median(StudentTDistribution(m,s,v))", // "m"); check("Median(WeibullDistribution(a, b))", // "b*Log(2)^(1/a)"); check("Median(WeibullDistribution(a, b, m))", // "m+b*Log(2)^(1/a)"); } @Test public void testMedianFilter() { // Wikipedia example with "shrinking the window near the boundaries" check("MedianFilter({2,3,80,6}, 1)", // "{5/2,3,6,43}"); check("MedianFilter({1, 2, 3, 2, 1}, 1)", // "{3/2,2,2,2,3/2}"); check("MedianFilter({0, 3, 8, 2}, 1)", // "{3/2,3,3,5}"); check("MedianFilter({a,b,c}, 1)", // "{1/2*(a+b),b,1/2*(b+c)}"); } @Test public void testMeijerG() { // TODO checkNumeric("N(MeijerG({{}, {2}}, {{1/2, 3/2}, {}}, 3), 50)", // "MeijerG({{},{2}},{{1/2,3/2},{}},3)"); checkNumeric("MeijerG({{}, {0.33}}, {{Pi}, {E}}, {-0.5,0.5})", // "{0.016502360637663107+I*0.007866512702226956,-0.3495252654770882}"); check("MeijerG({{}, {a2}}, {{b1}, {b2}}, z)", // "(z^b1*Hypergeometric1F1Regularized(1-a2+b1,1+b1-b2,z))/Gamma(a2-b1)"); check("MeijerG({{a1}, {}}, {{b1}, {b2}}, z)", // "z^b1*Gamma(1-a1+b1)*Hypergeometric1F1Regularized(1-a1+b1,1+b1-b2,-z)"); check("MeijerG({{a1}, {a2}}, {{b1}, {}}, z)", // "(Gamma(1-a1+b1)*Hypergeometric1F1Regularized(1-a1+b1,1-a1+a2,-1/z))/z^(1-a1)"); check("MeijerG({{a1}, {a2}}, {{}, {b2}}, z)", // "Hypergeometric1F1Regularized(1-a1+b2,1-a1+a2,1/z)/(z^(1-a1)*Gamma(a1-b2))"); check("MeijerG({{}, {}}, {{b1}, {-b1}}, z)", // "BesselJ(2*b1,2*Sqrt(z))"); check("MeijerG({{a1}, {a2}}, {{}, {}}, z)", // "BesselJ(-a1+a2,2/Sqrt(z))/z^(1-a1-(-a1+a2)/2)"); check("MeijerG({{a}, {}}, {{}, {b}}, 2)", // "2^b/Gamma(a-b)"); check("MeijerG({{a}, {}}, {{}, {}}, z) ", // "1/(E^(1/z)*z^(1-a))"); // print message check("MeijerG({{}, {}}, {{}, {}}, z) ", // "MeijerG({{},{}},{{},{}},z)"); } @Test public void testMemberQ() { check("MemberQ({Sin, Cos, Tan, Cot, Sec, Csc}, If(AtomQ(Cos),Cos,Head(Cos)))", // "True"); check("MemberQ(x,x)", // "False"); check("MemberQ({{x^2, y^2}}, x^_)", // "False"); check("MemberQ({{x^2, y^2}}, x^_, 2)", // "True"); check("MemberQ({{1, 1, 3, 0}, {2, 1, 2, 2}}, 0)", // "False"); check("MemberQ({{1, 1, 3, 0}, {2, 1, 2, 2}}, 0, 2)", // "True"); check("MemberQ({a, b, c}, b)", // "True"); check("MemberQ({a, b, c}, d)", // "False"); check("MemberQ({\"a\", b, f(x)}, _?NumericQ)", // "False"); check("MemberQ({\"a\", 42, f(x)}, _?NumericQ)", // "True"); check("MemberQ(_List)[{{}}]", // "True"); check("MemberQ(x^_)[{x^2, y^2, x^3}]", // "True"); check("MemberQ({1, 3, 4, 1, 2}, 2)", // "True"); check("MemberQ({x^2, y^2, x^3}, x^_)", // "True"); check("MemberQ(a + b + f(c), f)", // "False"); check("MemberQ(a + b + f(c), f, Heads->True)", // "False"); check("MemberQ(a + b + c, a + c)", // "False"); } @Test public void testMersennePrimeExponent() { check("Table(MersennePrimeExponent(i), {i,20})", "{2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253,4423}"); check("MersennePrimeExponent(1)", // "2"); check("MersennePrimeExponent(21)", // "9689"); check("MersennePrimeExponent(22)", // "9941"); check("MersennePrimeExponent(23)", // "11213"); check("MersennePrimeExponent(44)", // "32582657"); check("MersennePrimeExponent(45)", // "37156667"); check("MersennePrimeExponent(47)", // "43112609"); } @Test public void testMersennePrimeExponentQ() { check("Select(Range(10000), MersennePrimeExponentQ)", "{2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253,4423,9689,\n" + "9941}"); } @Test public void testMessage() { check("Message(f::argx, 1, 2)", // "f: 1 called with 2 arguments; 1 argument is expected."); check("a::b:=\"Hello world\"", // ""); check("Message(a::b)", // "a: Hello world"); check("a::c:=\"Hello `1`, Mr 00`2`!\"", // ""); check("Message(a::c, \"you\", 3 + 4)", // "a: Hello you, Mr 007!"); check("f::failure=\"`1` called with wrong argument; `2`, `3`.\"", // "`1` called with wrong argument; `2`, `3`."); check("Message(f::failure, f, x, y)", // "f: f called with wrong argument; x, y."); check("Message(Rule::argr, Rule, 2)", // "Rule: Rule called with 1 argument; 2 arguments are expected."); } @Test public void testMessages() { check("Messages(\"fa\")", // "Messages(fa)"); check("a::hello:=\"Hello world\"; a::james:=\"Hello `1`, Mr 00`2`!\"", // ""); check("Messages(a)", // "{HoldPattern(a::hello):>Hello world,HoldPattern(a::james):>Hello `1`, Mr 00`2`!}"); } @Test public void testMessageName() { // print "ValueQ - test whether a symbol can be considered to have a value" check("?ValueQ", // ""); check("FullForm(a::b)", // "MessageName(a, b)"); check("FullForm(a::\"b\")", // "MessageName(a, \"b\")"); // Set[MessageName(f,"usage"),"A usage message") check("f::usage=\"A usage message\"", // "A usage message"); // print "A usage message" on the console. Evaluation returns Null (i.e. no output) check("Information(f)", // ""); check("Information(Sin)", // ""); check("Information(Sin, LongForm->False)", // ""); // print "A usage message" on the console. Evaluation returns Null (i.e. no output) check("?f", // ""); check("??Sin;??Cos", // ""); } @Test public void testMin() { check("Min(Sequence())", // "Infinity"); check("Min(Interval({1,2}))", // "1"); check("Refine(Min(-Infinity,x), x>0)", // "-Infinity"); check("Refine(Min(-Infinity,x,y), x>0&&y>0)", // "-Infinity"); check("Refine(Min(-Infinity,x,y), x>0)", // "Min(-Infinity,y)"); check("Refine(Min(x,-Infinity), x>0)", // "-Infinity"); check("Refine(Min(x,y,-Infinity), x>0&&y>0)", // "-Infinity"); check("Refine(Min(Infinity,x), x>0)", // "x"); check("Refine(Min(Infinity,x,y), x>0&&y>0)", // "Min(x,y)"); check("Refine(Min(x,Infinity), x>0)", // "x"); check("Refine(Min(x,y,Infinity), x>0&&y>0)", // "Min(x,y)"); check("Refine(Min(x,y,Infinity), x>0&&y>0)", // "Min(x,y)"); check("Refine(Infinity0)", // "False"); check("Min(5, x, -3, y, 40)", // "Min(-3,x,y)"); check("Min(4, -8, 1)", // "-8"); check("Min({1,2},3,{-3,3.5,-Infinity},{{1/2}})", // "-Infinity"); check("Min(x, y)", // "Min(x,y)"); check("Min(5, x, -3, y, 40)", // "Min(-3,x,y)"); check("Min()", // "Infinity"); check("Min(x)", // "x"); check("Min(Abs(x), Abs(y))", // "Min(Abs(x),Abs(y))"); } @Test public void testMinMax() { check("MinMax({1, 2, 3, 4})", // "{1,4}"); check("MinMax({1, 2, 3, 4},.2)", // "{0.8,4.2}"); check("MinMax({1, 2, 3, 4}, Scaled(.2))", // "{0.4,4.6}"); check("MinMax({Pi, 1.3, E, Sqrt(10)})", // "{1.3,Sqrt(10)}"); check("MinMax({Pi, 1.3, E, Sqrt(10)}, 1)", // "{0.3,1+Sqrt(10)}"); check("MinMax({Pi, 1.3, E, Sqrt(10)}, Scaled(1/4))", // "{0.834431,3.62785}"); check("MinMax({Pi, 1.3, E, Sqrt(10)}, {0, 1})", // "{1.3,1+Sqrt(10)}"); check("Max({{1, 2}, {a, b}, {3, 2}})", // "Max(3,a,b)"); check("MinMax({{1, 2}, {a, b}, {3, 2}})", // "{Min(1,a,b),Max(3,a,b)}"); check("MinMax({ })", // "{Infinity,-Infinity}"); check("MinMax({3, 1, 2, 5, 4})", // "{1,5}"); check("Quantile({3, 1, 2, 5, 4}, {0, 1})", // "{1,5}"); } @Test public void testMinFilter() { check("MinFilter({1, 2, 3, 2, 1}, 1)", // "{1,1,2,1,1}"); check("MinFilter({0, 3, 8, 2}, 1)", // "{0,0,2,2}"); check("MinFilter({a,b,c}, 1)", // "{Min(a,b),Min(a,b,c),Min(b,c)}"); } @Test public void testMinimize() { // check("Minimize(Sin(x),x)", // // ""); // print message - Minimize: The minimum is not attained at any point satisfying the // constraints. check("Minimize(1/x, x)", // "{}"); check("Minimize(x^2+4*x+4, {x})", // "{0,{x->-2}}"); check("Minimize(x^4+7*x^3-2*x^2 + 42, x)", // "{42+7/512*(-21-Sqrt(505))^3-(21+Sqrt(505))^2/32+(21+Sqrt(505))^4/4096,{x->1/8*(-\n" + "21-Sqrt(505))}}"); check("Minimize(2*x^2 - 3*x + 5, x)", // "{31/8,{x->3/4}}"); } @Test public void testMinus() { check("Minus(a)", // "-a"); check("-a //FullForm", // "Times(-1, a)"); check("-(x - 2/3)", // "2/3-x"); check("-Range(10)", // "{-1,-2,-3,-4,-5,-6,-7,-8,-9,-10}"); } @Test public void testMissingQ() { check("MissingQ(Missing(\"Test message\"))", // "True"); } @Test public void testMod() { check("Mod(Infinity, 1+I)", // "Indeterminate"); check("Mod(Infinity, 3)", // "Indeterminate"); check("Mod(-1,I-1)", // "-1"); check("{a, b, c}[[Mod(Range(10), 3, 1)]]", // "{a,b,c,a,b,c,a,b,c,a}"); check("Mod(Range(10), 3, I)", // "{1,-1,0,1,-1,0,1,-1,0,1}"); check("Mod({1, 2, 3, 4, 5, 6, 7}, 3)", // "{1,2,0,1,2,0,1}"); check("Mod({1, 2, 3, 4, 5, 6, 7}, -3, 1)", // "{1,-1,0,1,-1,0,1}"); check("Mod({1, 2, 3, 4, 5, 6, 7}, -3, 4)", // "{4,2,3,4,2,3,4}"); check("Mod({1, 2, 3, 4, 5, 6, 7}, -3, -2)", // "{-2,-4,-3,-2,-4,-3,-2}"); check("Mod({-3, -2, -1, 0, 1, 2, 3}, -3)", // "{0,-2,-1,0,-2,-1,0}"); check("Mod(7,2,3)", // "3"); check("Mod(I,2,3)", // "4+I"); check("Mod(5-Pi/2,Pi)", // "5-3/2*Pi"); check("Mod(Sqrt(-113), 2)", // "-I*10+I*Sqrt(113)"); check("Mod(Exp(Pi), 2)", // "-22+E^Pi"); check("Mod(42,Pi)", // "42-13*Pi"); check("Mod(-42,Pi)", // "-42+14*Pi"); check("Mod(-10,3)", // "2"); check("Mod(10,3)", // "1"); check("Mod(10,-3)", // "-2"); check("Mod(-10,-3)", // "-1"); check("Mod(-23,7)", // "5"); check("Mod(23,7)", // "2"); check("Mod(23,-7)", // "-5"); check("Mod(-23,-7)", // "-2"); check("Mod(14, 6)", // "2"); check("Mod(-3,4)", // "1"); check("Mod(-3,-4)", // "-3"); check("Mod(2,-4)", // "-2"); check("Mod(3,-4)", // "-1"); check("Mod(5,0)", // "Indeterminate"); } @Test public void testModularInverse() { // message ModularInverse: 3 is not invertible modulo 9. check("ModularInverse(3, 9)", // "ModularInverse(3,9)"); check("ModularInverse(2, 3)", // "2"); check("ModularInverse(-3, 5)", // "3"); check("ModularInverse(3, 11)", // "4"); check("ModularInverse(-3, 11)", // "7"); check("ModularInverse(3, -11)", // "-7"); check("ModularInverse(-3, -5)", // "-2"); check("ModularInverse(3, -1)", // "0"); // Config.MAX_BIT_LENGTH = Integer.MAX_VALUE; // check("ModularInverse(10^100000, NextPrime(1000))", // // "942"); } @Test public void testModule() { EvalEngine.resetModuleCounter4JUnit(); // check("num=Sin(3*I);Module({v=N(num)},If(PossibleZeroQ(Re(v)),Im(v)>0,Re(v)>0))", // "True"); // check("Module({x=5}, Hold(x))", "Hold(x$1)"); check("xm=10;Module({xm=xm}, xm=xm+1;xm);xm", // "10"); check("xm=10;Module({t=xm}, xm=xm+1;t)", // "10"); check("xm=10;Module({t=xm}, xm=xm+1;t);xm", // "11"); EvalEngine.resetModuleCounter4JUnit(); check("{Module({a}, Block({a}, a)),Module({a}, Block({}, a))}", // "{a$1,a$2}"); check("t === Module({t}, t)", // "False"); check("$g(x_) := Module({v=x},int(v,x)/;v=!=x);$g(f(x))", // "$g(f(x))"); check("$g(x_) := Module({v=x},int1(v,x)/;v===x);$g(f(x))", // "int1(f(x),f(x))"); check("$h(x_) := Module({$u}, $u^2 /; (($u = x - 1) > 0));$h(6)", // "25"); checkNumeric( "$f(x0_) :=\n" + " Module({x = x0},\n" + " While(x > 0, x = Log(x));\n" + " x\n" + " );$f(2.0)", // "-0.36651292058166435"); check( "$fib(n_) :=\n" + " Module({$f},\n" + " $f(1) = $f(2) = 1;\n" + " $f(i0_) := $f(i0) = $f(i0 - 1) + $f(i0 - 2);\n" + " $f(n)\n" + " );$fib(5)", // "5"); check( "$gcd(m0_, n0_) :=\n" + " Module({m = m0, n = n0},\n" + " While(n != 0, {m, n} = {n, Mod(m, n)});\n" + " m\n" + " );$gcd(18, 21)", // "3"); EvalEngine.resetModuleCounter4JUnit(); check("{Module({x}, x), Module({x}, x)}", // "{x$1,x$2}"); check("Module({e = Expand((1 + x)^5)}, Function(x, e))", // "Function(x$3,e$3)"); EvalEngine.resetModuleCounter4JUnit(); check("Module({a,b}, Block({c}, c+a))", // "a$1+c"); if (Config.SERVER_MODE == false) { check("f(x0_) :=\n" + " Module({x = x0},\n" + " While(x > 0, x = Log(x));\n" + " x\n" + " );f(2.0)", "-0.366513"); check("fib(n_) :=\n" + " Module({f},\n" + " f(1) = f(2) = 1;\n" + " f(i_) := f(i) = f(i - 1) + f(i - 2);\n" + " f(n)\n" + " );fib(5)", "5"); check("myGCD(m0_, n0_) :=\n" + " Module({m = m0, n = n0},\n" + " While(n != 0, {m, n} = {n, Mod(m, n)});\n" + " m\n" + " );myGCD(18, 21)", "3"); } check("xm=10;Module({xm=xm}, xm=xm+1;Print(xm));xm", // "10"); check("Module({var1=2*2,var2=var1}, {var1,var2})", // "{4,var1}"); check("Module({x=y,y=z,z=3}, Print({Hold(x),Hold(y),Hold(z)});{x,y,z})", // "{y,z,3}"); check("Module({x,f}, f(0)=0;f(x_):=f(x-1)+x;f(3))", // "6"); EvalEngine.resetModuleCounter4JUnit(); check("Module({x},Function(y,x+y))", // "Function(y$1,x$1+y$1)"); // check("Module({y},Function(y,x+y))",// // "x$22$23+y"); check("Module({x}, g2(x_)=Integrate(Sqrt(1+z^2),{z,0,x}));Table(g2(i),{i,3})", // "{1/Sqrt(2)+ArcSinh(1)/2,Sqrt(5)+ArcSinh(2)/2,3*Sqrt(5/2)+ArcSinh(3)/2}"); check("v=Null;Module({w=v},Catch(Scan(Function(If(False ,Throw(False))),u); w))", // ""); check("t=42; Length(Expand((1 + t)^3)) ", // "0"); check("t=42;Module({t}, Length(Expand((1 + t)^3)))", // "4"); check("g(u_):= Module({t = u}, t += t/(1 + u)); g(a)", // "a+a/(1+a)"); check("t=17;Module({t = 6, u = t}, u^2)", // "289"); check("t=17;h(x_):=Module({t}, t^2 - 1 /; (t = x - 4) > 1); h(10)", // "35"); check("f(n_) := Module({p = Range(n),i,x,t},\n" + " Do(x = RandomInteger({1,i}); t = p[[i]]; p[[i]] = p[[x]]; p[[x]] = t,\n" + " {i,n,2,-1}\n" + " );\n" + " p\n" + " )\n", ""); check("MatchQ(f(4),{_Integer..})", // "True"); check("Length(f(6))", // "6"); } @Test public void testMoebiusMu() { check("MoebiusMu(-30)", // "-1"); check("FactorInteger(30)", // "{{2,1},{3,1},{5,1}}"); check("MoebiusMu(30)", // "-1"); check("Table(MoebiusMu(k), {k, 0,50})", // "{0,1,-1,-1,0,-1,1,-1,0,0,1,-1,0,-1,1,1,0,-1,0,-1,0,1,1,-1,0,0,1,0,0,-1,-1,-1,0,1,\n" + "1,1,0,-1,1,1,0,-1,-1,-1,0,0,1,-1,0,0,0}"); check("MoebiusMu({1000,10000})", // "{0,0}"); check("MoebiusMu(-a)", // "MoebiusMu(a)"); check("MoebiusMu(47)", // "-1"); check("MoebiusMu(51)", // "1"); check("MoebiusMu(17291)", // "-1"); check("MoebiusMu({2, 4, 7, 9})", // "{-1,0,-1,0}"); check("MoebiusMu(-100)", // "0"); check("Table(MoebiusMu(k), {k, 12})", // "{1,-1,-1,0,-1,1,-1,0,0,1,-1,0}"); check("Table(MoebiusMu(-k), {k, 12})", // "{1,-1,-1,0,-1,1,-1,0,0,1,-1,0}"); check("FactorInteger(183245)", // "{{5,1},{67,1},{547,1}}"); check("MoebiusMu(183245)", // "-1"); check("MoebiusMu(210)", // "1"); check("MoebiusMu(192)", // "0"); } @Test public void testMonomialList() { check("MonomialList(7*y^w, {y,z})", // "{7*y^w}"); check("MonomialList(7*y^(3*w), y )", // "{7*y^(3*w)}"); check("MonomialList(c*x^2+a+b*x,x)", // "{c*x^2,b*x,a}"); check("MonomialList(c*x^(-2)+a+b^2*x,b)", // "{b^2*x,a+c/x^2}"); check("MonomialList(c*x^(-2)+a+b*x,x)", // "{a+c/x^2+b*x}"); check("MonomialList((x + y)^3)", // "{x^3,3*x^2*y,3*x*y^2,y^3}"); check("MonomialList(x^2*y^2 + x^3, {x, y})", // "{x^3,x^2*y^2}"); check("MonomialList(x^2*y^2 + x^3, {x, y},DegreeLexicographic)", // "{x^2*y^2,x^3}"); check("MonomialList((x + 1)^5, x, Modulus -> 2)", // "{x^5,x^4,x,1}"); check( "MonomialList(-10*x^5*y^4*z^2 + 7*x^2*y^5*z^3 - 10*x^2*y*z^5 - 7*x*y^5*z^4 + 6*x*y^4*z^3 + 6*x*y^3*z^3 + 3*x*y^2*z + y^4*z - 7*y^2*z + 2*z^5, {x, y, z})", // "{-10*x^5*y^4*z^2,7*x^2*y^5*z^3,-10*x^2*y*z^5,-7*x*y^5*z^4,6*x*y^4*z^3,6*x*y^3*z^\n" + "3,3*x*y^2*z,y^4*z,-7*y^2*z,2*z^5}"); check( "MonomialList(-10*x^5*y^4*z^2 + 7*x^2*y^5*z^3 - 10*x^2*y*z^5 - 7*x*y^5*z^4 + 6*x*y^4*z^3 + 6*x*y^3*z^3 + 3*x*y^2*z + y^4*z - 7*y^2*z + 2*z^5, {x, y, z}, NegativeLexicographic)", // "{2*z^5,-7*y^2*z,y^4*z,3*x*y^2*z,6*x*y^3*z^3,6*x*y^4*z^3,-7*x*y^5*z^4,-10*x^2*y*z^\n" + "5,7*x^2*y^5*z^3,-10*x^5*y^4*z^2}"); check( "MonomialList(-10*x^5*y^4*z^2 + 7*x^2*y^5*z^3 - 10*x^2*y*z^5 - 7*x*y^5*z^4 + 6*x*y^4*z^3 + 6*x*y^3*z^3 + 3*x*y^2*z + y^4*z - 7*y^2*z + 2*z^5, {x, y, z}, DegreeLexicographic)", // "{-10*x^5*y^4*z^2,7*x^2*y^5*z^3,-7*x*y^5*z^4,-10*x^2*y*z^5,6*x*y^4*z^3,6*x*y^3*z^\n" + "3,y^4*z,2*z^5,3*x*y^2*z,-7*y^2*z}"); check( "MonomialList(-10*x^5*y^4*z^2 + 7*x^2*y^5*z^3 - 10*x^2*y *z^5 - 7*x*y^5*z^4 + 6*x*y^4*z^3 + 6*x*y^3*z^3 + 3*x*y^2*z + y^4*z - 7*y^2*z + 2*z^5, {x, y, z}, NegativeDegreeReverseLexicographic)", // "{-7*y^2*z,3*x*y^2*z,y^4*z,2*z^5,6*x*y^3*z^3,6*x*y^4*z^3,-10*x^2*y*z^5,7*x^2*y^5*z^\n" + "3,-7*x*y^5*z^4,-10*x^5*y^4*z^2}"); check( "MonomialList(-10*x^5*y^4*z^2 + 7*x^2*y^5*z^3 - 10*x^2*y*z^5 - 7*x*y^5*z^4 + 6*x*y^4*z^3 + 6*x*y^3*z^3 + 3*x*y^2*z + y^4*z - 7*y^2*z + 2*z^5, {x, y, z}, DegreeReverseLexicographic)", // "{-10*x^5*y^4*z^2,7*x^2*y^5*z^3,-7*x*y^5*z^4,6*x*y^4*z^3,-10*x^2*y*z^5,6*x*y^3*z^\n" + "3,y^4*z,2*z^5,3*x*y^2*z,-7*y^2*z}"); check( "MonomialList(-10*x^5*y^4*z^2 + 7*x^2*y^5*z^3 - 10*x^2*y*z^5 - 7*x*y^5*z^4 + 6*x*y^4*z^3 + 6*x*y^3*z^3 + 3*x*y^2*z + y^4*z - 7*y^2*z + 2*z^5, {x, y, z}, NegativeDegreeLexicographic)", // "{-7*y^2*z,3*x*y^2*z,y^4*z,2*z^5,6*x*y^3*z^3,-10*x^2*y*z^5,6*x*y^4*z^3,7*x^2*y^5*z^\n" + "3,-7*x*y^5*z^4,-10*x^5*y^4*z^2}"); } @Test public void testMost() { // TODO check("Most(SparseArray({{1,2},{3,4}}))", // "Most(SparseArray(Number of elements: 4 Dimensions: {2,2} Default value: 0))"); check("Most(<|1 :> a, 2 -> b, 3 :> c|>)", // "<|1:>a,2->b|>"); check("Most({a})", // "{}"); check("Most({a, b, c})", // "{a,b}"); check("Most(a + b + c)", // "a+b"); check("Most(Plus(d))", // "Most(d)"); check("Most(a)", // "Most(a)"); } @Test public void testMultinomial() { check("Multinomial(1,2,3,ByteArray({1}))", // "60*Binomial(6+ByteArray[1 Bytes],ByteArray[1 Bytes])"); check("Multinomial(2147483647,10007,-1,ByteArray({}))", // "{}"); // check("Multinomial(-5,3)", // // "-4"); check("Multinomial(-11,2,3,5)", // "2520"); check("Multinomial(-18,2,3,5,7)", // "-49008960"); check("Multinomial(-100,2,3,5)", // "39259781847205920"); check("Multinomial(-3,1,2,5)", // "0"); check("Multinomial(-4,2,3,5)", // "0"); check("Multinomial(2, .2, 5)", // "34.3178"); check("N(Multinomial(1/3, 1/7, 1/5, 1/6))", // "1.32595"); check("N(Multinomial(1/3, 1/11, 1/5, 1/6), 50)", // "1.2787822309985889320726165068248758021178962038957"); check("Multinomial(1 + I, .2, 4)", // "2.89406+I*9.10463"); check("Multinomial(1,1,1)", // "6"); check("Multinomial(1,k,1)", // "(1+k)*(2+k)"); check("Multinomial(10,f(x),2,3,4)", // "116396280*Binomial(19+f(x),f(x))"); check("Multinomial(0,0,0,0,0)", // "1"); check("Multinomial(a,b)", // "Binomial(a+b,b)"); check("Multinomial(2, 3, 4, 5)", // "2522520"); check("Multinomial( )", // "1"); check("Multinomial(1)", // "1"); check("Multinomial(2, 3)", // "10"); check("Multinomial(f(x))", // "1"); check("Multinomial(f(x), g(x))", // "Binomial(f(x)+g(x),g(x))"); check("Multinomial(n-k, k)", // "Binomial(n,-k+n)"); check("Multinomial(k, 2)", // "1/2*(1+k)*(2+k)"); } @Test public void testMultiplicativeOrder() { // https://oeis.org/A023394 check("Select(Prime(Range(500)), IntegerQ(Log(2, MultiplicativeOrder(2, # )))&) ", // "{3,5,17,257,641}"); check("Select(Range(2,200), MultiplicativeOrder(10, # )== # - 1 &)", // "{7,17,19,23,29,47,59,61,97,109,113,131,149,167,179,181,193}"); check("MultiplicativeOrder(-1,0)", // "MultiplicativeOrder(-1,0)"); check("MultiplicativeOrder(7, 108)", // "18"); check("MultiplicativeOrder(10^100 + 1, Prime(1000))", // "3959"); check("MultiplicativeOrder(-5, 7)", // "3"); check("Select(Range(43), MultiplicativeOrder(#, 43) == EulerPhi(43) &)", // "{3,5,12,18,19,20,26,28,29,30,33,34}"); } @Test public void testNApfloat() { ApfloatContext ac = ApfloatContext.getContext(); // messages // General: Overflow occurred in computation. // General: Overflow occurred in computation. // General: Overflow occurred in computation. // General: Overflow occurred in computation. // ApfloatContext MaxMemoryBlockSize: 786432 check("IntegerPart(N(3, 1000)^N(3, 3000)^N(3, 3000)^N(3, 3000)^N(3, 3000));", // ""); ac = ApfloatContext.getContext(); // System.out.println("ApfloatContext MaxMemoryBlockSize: " + ac.getMaxMemoryBlockSize()); } @Test public void testApfloatStorage() { try { Apfloat apfloat = new Apfloat("9".repeat(1_000_000) + "." + "9".repeat(1_000_000)); apfloat = ApfloatMath.pow(apfloat, new Apfloat("91212312" + ".1231236")); ApfloatNum apfloatNum = ApfloatNum.valueOf(apfloat); IInteger integerPart = apfloatNum.integerPart(); System.out.println(integerPart.bitLength()); fail("Should be fail"); } catch (OverflowException e) { // e.printStackTrace(); } } @Test public void testDeterminePrecision() { ApfloatNum zero = ApfloatNum.valueOf(new Apfloat(new BigDecimal(BigInteger.ZERO), 30)); ApfloatNum num = ApfloatNum.valueOf("1.7", 30); IASTMutable times = F.Times(num, zero); assertEquals(times.determinePrecision(), 30); } @Test public void testN() { check("N((-1)^(1/180), 50)", // "0.99984769515639123915701155881391485169274031058318+I*0.01745240643728351281941897851631619247225272030713"); // issue #942 check("Tan(Pi/2) // N", // "ComplexInfinity"); // issue #937 check("(x==-157079632679/100000000000) // N", // "x==-1.5708"); check("ConditionalExpression(x==-157079632679/100000000000*C(1),C(1)∈Integers) // N", // "ConditionalExpression(x==-1.5708*C(1),C(1)∈Integers)"); check("f(1/3)//N", // "f(0.333333)"); check("f(1/2*x)//N", // "f(0.5*x)"); check("N({Labeled(4/3,\"test\")})", // "{Labeled(1.33333,test)}"); check("N(Labeled(4/3,\"test\"))", // "Labeled(1.33333,test)"); check("N(1/7,2)", // "0.14"); check("N(1/7, 3)", // "0.143"); check("N(8 + 1*^28, 40) // InputForm", // "1.0000000000000000000000000008`40*^28"); check("N(8 + 1*^28, 40)", // "10000000000000000000000000008"); // 1.0000000000000000000000000008`40.*^28 check("N(8 + 1*^-28, 40)", // "8.0000000000000000000000000001"); // github #207 check("N(((2)/(3))*(4-3*Sqrt(2)), 100)", // "-0.1617604580795234309367107817527294904726770840872294796866928093147982902575474110341084019886164788"); check("N(Sqrt(2)^(-1), 100)", // "0.7071067811865475244008443621048490392848359376884740365883398689953662392310535194251937671638207863"); check("N(Sin(2)^(-1), 100)", // "1.099750170294616466756697397026312896658764443149845708742554443062569126995445980876791442481219894"); check("N(Sqrt(2)/2,2147483647)", // "N(Sqrt(2)/2,2147483647)"); check("N(Null)", // ""); // test precision 30 check("2/3 + Pi + 5.5`30", // "9.30825932025645990512931004994"); check("2/3 + Pi + 5.5``30", // "9.30825932025645990512931004994"); // imaginary part is zero check("I^I //N", // "0.20788"); check("I^(3*I)//N", // "0.00898329"); check("I^(2+3*I)//N", // "-0.00898329"); // TODO don't switch to numeric mode for Sqrt(10) check("(0.25)^x", // "0.25^x"); // github #151 check("N(Integrate(Sin(x*Pi/3), {x, 1, 2}))", // "0.95493"); check("expr=Integrate(Sin(x*Pi/3), {x, 1, 2}); N(expr)", // "0.95493"); // TODO don't switch to numeric mode for Sqrt(10) check("Sqrt(10)*(0.25)^x", // "0.25^x*Sqrt(10)"); check("{1, 2} /. x_Integer -> N(x)", // "{1,2}"); check("{1, 2} /. x_Integer :> N(x)", // "{1.0,2.0}"); // check("N(Pi)", "3.141592653589793"); // check("N(Pi, 50)", "3.1415926535897932384626433832795028841971693993751"); // check("N(1/7)", "0.14285714285714285"); // check("N(1/7, 20)", "1.4285714285714285714e-1"); } @Test public void testNameQ() { check("NameQ(\"foo\")", // "False"); check("NameQ(\"plot\")", // "True"); check("NameQ(\"ArcTan\")", // "True"); check("NameQ(\"ArcTan2\")", // "False"); } @Test public void testNames() { check("foo`f = 42", // "42"); check("Names(\"foo`*\")", // "{foo`f}"); check("sysnames = Names(\"System`*\");", // ""); check("Select(sysnames, MemberQ(Attributes(#), OneIdentity) &) // InputForm", // "{\"And\",\"Composition\",\"Dot\",\"GCD\",\"Intersection\",\"Join\",\"KroneckerProduct\",\"Max\",\"Min\",\"Or\",\"Plus\",\"Power\",\"RightComposition\",\"StringExpression\",\"StringJoin\",\"TensorProduct\",\"Times\",\"Union\",\"Xor\"}"); check("Names(\"System`\" ~~ _ ~~ _) // InputForm", // "{\"Do\",\"Dt\",\"If\",\"Im\",\"In\",\"ND\",\"On\",\"Or\",\"Pi\",\"Re\",\"Tr\"}"); check("Names(RegularExpression(\"System`...\")) // InputForm", // "{\"Abs\",\"All\",\"And\",\"Arg\",\"CDF\",\"Cos\",\"Cot\",\"Csc\",\"Det\",\"Div\",\"Dot\",\"End\",\"Erf\",\"Exp\"," // + "\"Fit\",\"For\",\"GCD\",\"Get\",\"Hue\",\"Key\",\"LCM\",\"Log\",\"Map\",\"Max\",\"Min\",\"Mod\",\"Nor\",\"Not\"," // + "\"Now\",\"Off\",\"Out\",\"PDF\",\"Put\",\"Red\",\"Row\",\"Sec\",\"Set\",\"Sin\",\"Sow\",\"Sum\",\"Tan\",\"Top\"," // + "\"Xor\"}"); check("Names(\"Int*\" )", // "{Integer,IntegerDigits,IntegerExponent,IntegerLength,IntegerName,IntegerPart,IntegerPartitions,IntegerQ,Integers,Integrate,InterpolatingFunction,InterpolatingPolynomial,Interpolation,InterpolationOrder,InterquartileRange,Interrupt,IntersectingQ,Intersection,Interval,IntervalComplement,IntervalData,IntervalIntersection,IntervalMemberQ,IntervalUnion}"); check("Names(\"Integer*\" )", // "{Integer,IntegerDigits,IntegerExponent,IntegerLength,IntegerName,IntegerPart,IntegerPartitions,IntegerQ,Integers}"); check("Names(\"IntegerPart\" )", // "{IntegerPart}"); } @Test public void testNand() { check("Nand( )", // "False"); check("Nand(a)", // "!a"); check("Nand(2+2)", // "!4"); check("Nand(x,y,z)", // "Nand(x,y,z)"); check("Nand(x,True,z)", // "Nand(x,z)"); check("Nand(x,False,z)", // "True"); check("Nand(True,False)", // "True"); check("Nand(False, True)", // "True"); check("Nand(Print(1); False, Print(2); True)", // "True"); check("Nand(Print(1); True, Print(2); True)", // "False"); } @Test public void testND() { check("ND(Exp(x), x, 1)", // "2.71828"); check("ND(Cos(x)^3, {x,2}, 0)", // "-3.0"); check("ND(Cos(x)^3, {x,2}, 1)", // "1.82226"); check("ND(BesselY(10.0,x), x, 1)", // "1.2094*10^9"); } @Test public void testNDSolve() { // check("model = NDSolve({x'(t) == -y(t) - x(t)^2, y'(t) == 2*x(t) - y(t)^3, x(0) == y(0) == // 1}, {x, y}, {t, // 20});", // // ""); // check("ListPlot(Table({Evaluate(x(t) /.model),Evaluate(y(t) /.model)}, {t, 20}) )", // // ""); check("model=NDSolve({ y(x)*Cos(x + y(x))== (y'(x)), y(0)==1}, y, {x, 0, 30});", // ""); // check("Evaluate(y(t) /.model)", // // ""); // check("ListPlot(Table({t,Evaluate(y(t) /.model)}, {t, 0, 30}) )", // // ""); // checkNumeric("NDSolve({ y(x)*Cos(x + y(x))== (y'(x)), y(0)==1}, y, {x, 0, 30})", // // "InterpolatingFunction(\n" // + "{{0.0,1.0486539247435627},\n" + " {0.1,1.0854808036771377},\n" + " // {0.2,1.1096485558561129},\n" // + " {0.30000000000000004,1.1212578599391958},\n" + " {0.4,1.1211098516670583},\n" // + " {0.5,1.110440971080707},\n" + " {0.6,1.0906930188004873},\n" + " // {0.7,1.0633460402333474},\n" // + " {0.7999999999999999,1.0298136072918775},\n" + " // {0.8999999999999999,0.991387315006244},\n" // + " {0.9999999999999999,0.9492149070968016},\n" + " // {1.0999999999999999,0.9042988579035411},\n" // + " {1.2,0.857505923891753},\n" + " {1.3,0.8095815052617051},\n" // + " {1.4000000000000001,0.7611651420556339},\n" + " // {1.5000000000000002,0.7128051392128717},\n" // + " {1.6000000000000003,0.6649713621384138},\n" + " // {1.7000000000000004,0.6180658664467911},\n" // + " {1.8000000000000005,0.5724313779772732},\n" + " // {1.9000000000000006,0.5283578293741383},\n" // + " {2.0000000000000004,0.48608725600029157},\n" + " // {2.1000000000000005,0.4458173974209415},\n" // + " {2.2000000000000006,0.4077043633624414},\n" + " // {2.3000000000000007,0.37186471548866024},\n" // + " {2.400000000000001,0.3383772924103512},\n" + " {2.500000000000001,0.3072850658079258},\n" // + " {2.600000000000001,0.2785972606942865},\n" + " {2.700000000000001,0.2522919043406724},\n" // + " {2.800000000000001,0.22831889029854097},\n" + " // {2.9000000000000012,0.20660356283726058},\n" // + " {3.0000000000000013,0.18705075124931517},\n" + " // {3.1000000000000014,0.1695491213425783},\n" // + " {3.2000000000000015,0.15397566999707005},\n" + " // {3.3000000000000016,0.14020017181526293},\n" // + " {3.4000000000000017,0.1280893946838693},\n" + " // {3.5000000000000018,0.11751092979804098},\n" // + " {3.600000000000002,0.10833652492796243},\n" + " // {3.700000000000002,0.10044485973079281},\n" // + " {3.800000000000002,0.09372375133539376},\n" + " // {3.900000000000002,0.08807182139220295},\n" // + " {4.000000000000002,0.0833996886046539},\n" + " // {4.100000000000001,0.07963077199182245},\n" // + " {4.200000000000001,0.07670180014927495},\n" + " // {4.300000000000001,0.07456312212288695},\n" // + " {4.4,0.07317890821085377},\n" + " {4.5,0.07252731596246077},\n" + " // {4.6,0.0726006791932994},\n" // + " {4.699999999999999,0.0734057565099308},\n" + " // {4.799999999999999,0.07496405020983263},\n" // + " {4.899999999999999,0.07731217510263196},\n" + " // {4.999999999999998,0.08050221749315989},\n" // + " {5.099999999999998,0.084601974272093},\n" + " // {5.1999999999999975,0.08969489746733304},\n" // + " {5.299999999999997,0.0958794879078716},\n" + " // {5.399999999999997,0.10326778201284252},\n" // + " {5.4999999999999964,0.11198246184539966},\n" + " // {5.599999999999996,0.12215200271817592},\n" // + " {5.699999999999996,0.13390318126361409},\n" + " // {5.799999999999995,0.14735024731166288},\n" // + " {5.899999999999995,0.16258018854901138},\n" + " // {5.999999999999995,0.17963388536831357},\n" // + " {6.099999999999994,0.19848366765525352},\n" + " // {6.199999999999994,0.21900890659080618},\n" // + " {6.299999999999994,0.24097273961477084},\n" + " // {6.399999999999993,0.2640045482014827},\n" // + " {6.499999999999993,0.2875938184944301},\n" + " {6.5999999999999925,0.311100756322707},\n" // + " {6.699999999999992,0.33378687199758955},\n" + " // {6.799999999999992,0.35486468555987505},\n" // + " {6.8999999999999915,0.37356070170896716},\n" + " // {6.999999999999991,0.38918166156437567},\n" // + " {7.099999999999991,0.401172598399326},\n" + " {7.19999999999999,0.4091571693969712},\n" // + " {7.29999999999999,0.4129553215557175},\n" + " {7.39999999999999,0.41257870289475035},\n" // + " {7.499999999999989,0.4082084528387488},\n" + " // {7.599999999999989,0.40016206914955754},\n" // + " {7.699999999999989,0.38885599961989714},\n" + " // {7.799999999999988,0.37476918269614945},\n" // + " {7.899999999999988,0.3584108421644447},\n" + " // {7.999999999999988,0.34029407839355436},\n" // + " {8.099999999999987,0.3209155086689302},\n" + " // {8.199999999999987,0.30074044115694204},\n" // + " {8.299999999999986,0.2801927248235081},\n" + " {8.399999999999986,0.2596483599261049},\n" // + " {8.499999999999986,0.23943205150206048},\n" + " // {8.599999999999985,0.21981604663931104},\n" // + " {8.699999999999985,0.20102075567302183},\n" + " // {8.799999999999985,0.18321678667386834},\n" // + " {8.899999999999984,0.1665281105852},\n" + " {8.999999999999984,0.15103612290345214},\n" // + " {9.099999999999984,0.136784386073114},\n" + " {9.199999999999983,0.12378383728408018},\n" // + " {9.299999999999983,0.11201824175272579},\n" + " // {9.399999999999983,0.10144967223258593},\n" // + " {9.499999999999982,0.09202380805440191},\n" + " // {9.599999999999982,0.08367487371122105},\n" // + " {9.699999999999982,0.07633007619745596},\n" + " // {9.799999999999981,0.06991344748031084},\n" // + " {9.89999999999998,0.06434904783208746},\n" + " {9.99999999999998,0.05956353167221671},\n" // + " {10.09999999999998,0.055488115733649444},\n" + " // {10.19999999999998,0.052060017293655024},\n" // + " {10.29999999999998,0.0492234472683428},\n" + " // {10.399999999999979,0.04693025003153322},\n" // + " {10.499999999999979,0.04514028068683145},\n" + " // {10.599999999999978,0.043821603367067995},\n" // + " {10.699999999999978,0.042950583025463014},\n" + " // {10.799999999999978,0.04251192976987961},\n" // + " {10.899999999999977,0.04249874014945849},\n" + " // {10.999999999999977,0.042912564384982844},\n" // + " {11.099999999999977,0.043763512208115654},\n" + " // {11.199999999999976,0.045070392103282626},\n" // + " {11.299999999999976,0.046860858299487156},\n" + " // {11.399999999999975,0.049171515562746765},\n" // + " {11.499999999999975,0.052047902387254485},\n" + " // {11.599999999999975,0.05554423757203267},\n" // + " {11.699999999999974,0.059722773229538936},\n" + " // {11.799999999999974,0.0646525504791017},\n" // + " {11.899999999999974,0.07040730672504374},\n" + " // {11.999999999999973,0.0770622441521745},\n" // + " {12.099999999999973,0.0846893525976165},\n" + " // {12.199999999999973,0.09335100838707118},\n" // + " {12.299999999999972,0.10309167339440412},\n" + " // {12.399999999999972,0.11392772849437467},\n" // + " {12.499999999999972,0.1258358199938911},\n" + " // {12.599999999999971,0.138740580936534},\n" // + " {12.69999999999997,0.15250316894309834},\n" + " // {12.79999999999997,0.16691262572026747},\n" // + " {12.89999999999997,0.18168242049828567},\n" + " // {12.99999999999997,0.19645445463107747},\n" // + " {13.09999999999997,0.2108120803325641},\n" + " // {13.199999999999969,0.22430228748955305},\n" // + " {13.299999999999969,0.23646536721975198},\n" + " // {13.399999999999968,0.24686856012190703},\n" // + " {13.499999999999968,0.25513903798118154},\n" + " // {13.599999999999968,0.26099149103034053},\n" // + " {13.699999999999967,0.26424665962609567},\n" + " // {13.799999999999967,0.26483900018855316},\n" // + " {13.899999999999967,0.26281370586093794},\n" + " // {13.999999999999966,0.2583149394045044},\n" // + " {14.099999999999966,0.2515680519994532},\n" + " // {14.199999999999966,0.24285873137419975},\n" // + " {14.299999999999965,0.2325116382150581},\n" + " // {14.399999999999965,0.220870422513877},\n" // + " {14.499999999999964,0.20828029902084735},\n" + " // {14.599999999999964,0.19507375354460899},\n" // + " {14.699999999999964,0.1815595106786453},\n" + " // {14.799999999999963,0.16801461631765874},\n" // + " {14.899999999999963,0.1546793400273539},\n" + " // {14.999999999999963,0.14175453929296386},\n" // + " {15.099999999999962,0.12940111187045478},\n" + " // {15.199999999999962,0.11774116741799541},\n" // + " {15.299999999999962,0.10686056081330114},\n" + " // {15.399999999999961,0.09681244213729613},\n" // + " {15.499999999999961,0.08762149329437179},\n" + " // {15.59999999999996,0.07928854218346183},\n" // + " {15.69999999999996,0.07179527544171443},\n" + " // {15.79999999999996,0.06510881121842255},\n" // + " {15.89999999999996,0.05918594276300758},\n" + " // {15.99999999999996,0.053976918199585305},\n" // + " {16.09999999999996,0.049428676909066306},\n" + " // {16.19999999999996,0.04548751365173981},\n" // + " {16.29999999999996,0.042101184130222284},\n" + " // {16.399999999999963,0.03922049785649547},\n" // + " {16.499999999999964,0.03680046534374525},\n" + " // {16.599999999999966,0.03480107758305633},\n" // + " {16.699999999999967,0.0331877982037784},\n" + " // {16.79999999999997,0.03193184479148035},\n" // + " {16.89999999999997,0.03101032767125873},\n" + " // {16.99999999999997,0.030406303862182932},\n" // + " {17.099999999999973,0.03010879219599716},\n" + " // {17.199999999999974,0.030112783566147657},\n" // + " {17.299999999999976,0.030419268228300628},\n" + " // {17.399999999999977,0.03103528987978064},\n" // + " {17.49999999999998,0.031974023436000365},\n" + " // {17.59999999999998,0.03325485929623045},\n" // + " {17.69999999999998,0.034903460631464545},\n" + " // {17.799999999999983,0.036951741050493675},\n" // + " {17.899999999999984,0.03943768737279855},\n" + " // {17.999999999999986,0.042404926190700305},\n" // + " {18.099999999999987,0.04590190449334592},\n" + " // {18.19999999999999,0.049980526549024254},\n" // + " {18.29999999999999,0.054694066601254296},\n" + " // {18.39999999999999,0.06009416801910799},\n" // + " {18.499999999999993,0.0662267563624869},\n" + " // {18.599999999999994,0.07312675184871771},\n" // + " {18.699999999999996,0.08081158301761861},\n" + " // {18.799999999999997,0.0892736922498442},\n" // + " {18.9,0.09847248889531121},\n" + " {19.0,0.10832652953813567},\n" + " // {19.1,0.11870703751609235},\n" // + " {19.200000000000003,0.12943412780911714},\n" + " // {19.300000000000004,0.1402771628385532},\n" // + " {19.400000000000006,0.15096041573160082},\n" + " // {19.500000000000007,0.16117459959331792},\n" // + " {19.60000000000001,0.1705938815306118},\n" + " // {19.70000000000001,0.17889692028539034},\n" // + " {19.80000000000001,0.18578953051456235},\n" + " // {19.900000000000013,0.19102607653255335},\n" // + " {20.000000000000014,0.19442681148735713},\n" + " // {20.100000000000016,0.19588908551204787},\n" // + " {20.200000000000017,0.19539143760805033},\n" + " // {20.30000000000002,0.19299074958941248},\n" // + " {20.40000000000002,0.188813589734067},\n" + " {20.50000000000002,0.18304344050912236},\n" // + " {20.600000000000023,0.1759056646182722},\n" + " // {20.700000000000024,0.1676519017849422},\n" // + " {20.800000000000026,0.15854523818283722},\n" + " // {20.900000000000027,0.14884707766919583},\n" // + " {21.00000000000003,0.13880625822789994},\n" + " // {21.10000000000003,0.12865064403209947},\n" // + " {21.20000000000003,0.11858119433695793},\n" + " // {21.300000000000033,0.10876835547392645},\n" // + " {21.400000000000034,0.09935052412493195},\n" + " // {21.500000000000036,0.09043427196672443},\n" // + " {21.600000000000037,0.08209599140343246},\n" + " // {21.70000000000004,0.07438461231024102},\n" // + " {21.80000000000004,0.06732504714496039},\n" + " // {21.90000000000004,0.0609220448460617},\n" // + " {22.000000000000043,0.05516417096178315},\n" + " // {22.100000000000044,0.05002767965231217},\n" // + " {22.200000000000045,0.045480098453626217},\n" + " // {22.300000000000047,0.04148340402665843},\n" // + " {22.40000000000005,0.03799672158222671},\n" + " // {22.50000000000005,0.03497852815326329},\n" // + " {22.60000000000005,0.032388377671356924},\n" + " // {22.700000000000053,0.030188192781695093},\n" // + " {22.800000000000054,0.02834318482532842},\n" + " // {22.900000000000055,0.026822470808221865},\n" // + " {23.000000000000057,0.025599456420398434},\n" + " // {23.10000000000006,0.02465204936600566},\n" // + " {23.20000000000006,0.023962759329861603},\n" + " // {23.30000000000006,0.023518731365109482},\n" // + " {23.400000000000063,0.023311749398506023},\n" + " // {23.500000000000064,0.02333823650818959},\n" // + " {23.600000000000065,0.02359926881772662},\n" + " // {23.700000000000067,0.024100610123988526},\n" // + " {23.800000000000068,0.02485276434553134},\n" + " // {23.90000000000007,0.025871031998059613},\n" // + " {24.00000000000007,0.027175544570715412},\n" + " // {24.100000000000072,0.02879123634710425},\n" // + " {24.200000000000074,0.030747696564390598},\n" + " // {24.300000000000075,0.03307882595701917},\n" // + " {24.400000000000077,0.035822201576675955},\n" + " // {24.500000000000078,0.03901803437743281},\n" // + " {24.60000000000008,0.04270758911304822},\n" + " // {24.70000000000008,0.046930931420902475},\n" // + " {24.800000000000082,0.051723880711205865},\n" + " // {24.900000000000084,0.05711408982254241},\n" // + " {25.000000000000085,0.06311625424637678},\n" + " // {25.100000000000087,0.06972658382886275},\n" // + " {25.200000000000088,0.07691685011526753},\n" + " // {25.30000000000009,0.0846285415836176},\n" // + " {25.40000000000009,0.09276788599437955},\n" + " // {25.500000000000092,0.10120268026019423},\n" // + " {25.600000000000094,0.10976193177974276},\n" + " // {25.700000000000095,0.11823918766143336},\n" // + " {25.800000000000097,0.12640006310087093},\n" + " // {25.900000000000098,0.13399389013035107},\n" // + " {26.0000000000001,0.14076868583650626},\n" + " {26.1000000000001,0.14648794906949023},\n" // + " {26.200000000000102,0.1509473266388399},\n" + " // {26.300000000000104,0.15398909090144997},\n" // + " {26.400000000000105,0.15551268333713533},\n" + " // {26.500000000000107,0.15548022163602201},\n" // + " {26.600000000000108,0.15391666739307647},\n" + " // {26.70000000000011,0.15090510975131846},\n" // + " {26.80000000000011,0.14657818306953294},\n" + " // {26.900000000000112,0.14110693216447398},\n" // + " {27.000000000000114,0.13468847749049695},\n" + " // {27.100000000000115,0.1275336799610958},\n" // + " {27.200000000000117,0.11985574493622606},\n" + " // {27.300000000000118,0.11186041177815408},\n" // + " {27.40000000000012,0.1037381005484644},\n" + " // {27.50000000000012,0.09565815735831991},\n" // + " {27.600000000000122,0.08776516222812088},\n" + " // {27.700000000000124,0.08017713485435946},\n" // + " {27.800000000000125,0.07298538709313364},\n" + " // {27.900000000000126,0.06625571890495106},\n" // + " {28.000000000000128,0.06003063117527128},\n" + " // {28.10000000000013,0.0543322298578955},\n" // + " {28.20000000000013,0.04916551743387415},\n" + " // {28.300000000000132,0.04452180553916086},\n" // + " {28.400000000000134,0.04038203184386874},\n" + " // {28.500000000000135,0.03671981933966998},\n" // + " {28.600000000000136,0.03350417158494679},\n" + " // {28.700000000000138,0.03070174835662014},\n" // + " {28.80000000000014,0.02827870903992453},\n" + " // {28.90000000000014,0.026202144002981702},\n" // + " {29.000000000000142,0.02444113673212715},\n" + " // {29.100000000000144,0.0229675124577755},\n" // + " {29.200000000000145,0.02175633398892615},\n" + " // {29.300000000000146,0.02078620446123},\n" // + " {29.400000000000148,0.02003943163828367},\n" + " // {29.50000000000015,0.019502100971413434},\n" // + " {29.60000000000015,0.019164096103692605},\n" + " // {29.700000000000152,0.01901909674905609},\n" // + " {29.800000000000153,0.019064575332356216},\n" + " // {29.900000000000155,0.019301805546317868}})"); // 10, 28, 8/3 as constants for the Lorenz equations // https://socialinnovationsimulation.com/2013/07/19/tutorial-differential-equations-2/ check( "model=NDSolve({x'(t) == 10*(y(t) - x(t)), \n" + " y'(t) == x(t)*(28 - z(t)) - y(t), z'(t) == x(t)*y(t) - 8/3*z(t),\n" + " x(0)== 0, y(0) == 1, z(0) == 0}, {x, y, z}, {t, 0, 20});", // ""); } @Test public void testNegative() { check("Negative(Infinity)", // "False"); check("Negative(-Infinity)", // "True"); check("Negative(-9/4)", // "True"); check("Negative(0.1+I)", // "False"); check("Negative(0)", // "False"); check("Negative(-3)", // "True"); check("Negative(10/7)", // "False"); check("Negative(1+2*I)", // "False"); check("Negative(a + b)", // "Negative(a+b)"); check("Negative(-E)", // "True"); check("Negative(Sin({11, 14}))", // "{True,False}"); } @Test public void testNearest() { check("Nearest({1, 2, 4, 8, 16, 32}, 20)", // "{16}"); check("Nearest({1, 2, 4, 8, 16, 24, 32}, 20)", // "{16,24}"); } @Test public void testNearestTo() { check("NearestTo(20)[{1, 2, 4, 8, 16, 32}]", // "{16}"); // TODO improve Nearest check("NearestTo(20,3)[{1, 2, 4, 8, 16, 32}]", // "Nearest({1,2,4,8,16,32},20,3)"); } @Test public void testNeeds() { check("Needs({-1/2,{{1}},3})", // "Needs({-1/2,{{1}},3})"); } @Test public void testNest() { // iteration limit exceeded check("Nest(-I,Null,2147483647)", // "Hold(Nest(-I,Null,2147483647))"); check("Nest(f, x, 3)", // "f(f(f(x)))"); check("Nest((1+#) ^ 2 &, x, 2)", // "(1+(1+x)^2)^2"); check("Nest(f, x, 3)", // "f(f(f(x)))"); check("Nest((1 + #)^2 &, 1, 3)", // "676"); check("Nest((1 + #)^2 &, x, 5)", // "(1+(1+(1+(1+(1+x)^2)^2)^2)^2)^2"); check("Nest(Sqrt, 100.0, 4)", // "1.33352"); } @Test public void testNestList() { check("NestList(4*#*(1 - #) &, 1/3, 5)", // "{1/3,8/9,32/81,6272/6561,7250432/43046721,1038154236987392/1853020188851841}"); check("Length(NestList(#2,{},50))", // "51"); check("NestList(#2,{},3)", // "{{},#2[{}],#2[#2[{}]],#2[#2[#2[{}]]]}"); check("NestList(f, x, 4)", // "{x,f(x),f(f(x)),f(f(f(x))),f(f(f(f(x))))}"); check("NestList(2*# &, 1, 8)", // "{1,2,4,8,16,32,64,128,256}"); check("NestList(Cos, 1.0, 10)", // "{1.0,0.540302,0.857553,0.65429,0.79348,0.701369,0.76396,0.722102,0.750418,0.731404,0.744237}"); check("NestList((1 + #)^2 &, x, 3)", // "{x,(1+x)^2,(1+(1+x)^2)^2,(1+(1+(1+x)^2)^2)^2}"); check("seq=NestList(3/2 (# + Mod(#, 2)) &, 1, 499);Take(seq, 10)", // "{1,3,6,9,15,24,36,54,81,123}"); } @Test public void testNestWhile() { check("NestWhile(#^2 &, 2, # < 256 &)", // "256"); check("NestWhile(#+1 &, 1, # + #4 < 10 &, 4)", // "7"); check("NestWhile(#+1 &, 1, True &, 1, 4)", // "5"); check("NestWhile(#+1 &, 1, True &, 1, 4,5)", // "10"); check("NestWhile(#+1 &, 1, False &, 1, 4,5)", // "6"); check("NestWhile(Floor(#/2) &, 10, (Print({##}); UnsameQ(##)) &, All)", // "0"); check("NestWhile(Floor(#/2) &, 10, UnsameQ, 2)", // "0"); check("NestWhile(x[[1]],-2147483648,EvenQ(#1)&)", // "x[[1]][-2147483648]"); check("NestWhile(#/2&, 10000, IntegerQ)", // "625/2"); check("NestWhile(#/2 &, 123456, EvenQ)", // "1929"); check("NestWhile(Log, 100, # > 0 &)", // "Log(Log(Log(Log(100))))"); } @Test public void testNestWhileList() { check("NestWhileList(Function((#+3/#)/2), 1., Function(# =!= #2), 2)", // "{1.0,2.0,1.75,1.73214,1.73205,1.73205,1.73205}"); // from fuzz testing: check("NestWhileList(10007,{ByteArray()},True&,-0.8)", // "NestWhileList(10007,{ByteArray()},True&,-0.8)"); check("NestWhileList(f,g,127,0,5)", // "{g}"); check("NestWhileList(f,g(1,2,3),{Sqrt(2)/2},42,7)", // "{g(1,2,3),f(g(1,2,3)),f(f(g(1,2,3))),f(f(f(g(1,2,3)))),f(f(f(f(g(1,2,3))))),f(f(f(f(f(g(\n" + "1,2,3)))))),f(f(f(f(f(f(g(1,2,3))))))),f(f(f(f(f(f(f(g(1,2,3))))))))}"); check("NestWhileList(f,g,False&,9,7)", // "{g,f(g),f(f(g)),f(f(f(g))),f(f(f(f(g)))),f(f(f(f(f(g))))),f(f(f(f(f(f(g)))))),f(f(f(f(f(f(f(g)))))))}"); check("NestWhileList(f,g,False&,8,8)", // "{g,f(g),f(f(g)),f(f(f(g))),f(f(f(f(g)))),f(f(f(f(f(g))))),f(f(f(f(f(f(g)))))),f(f(f(f(f(f(f(g)))))))}"); check("NestWhileList(f,g,False&,7,8)", // "{g,f(g),f(f(g)),f(f(f(g))),f(f(f(f(g)))),f(f(f(f(f(g))))),f(f(f(f(f(f(g))))))}"); check("NestWhileList(#+1 &, 1, # + #4 < 10 &, 4)", // "{1,2,3,4,5,6,7}"); check("NestWhileList(#+1 &, 1, True &, 1, 4, 5)", // "{1,2,3,4,5,6,7,8,9,10}"); check("NestWhileList(#+1 &, 1, False &, 1, 4, 5)", // "{1,2,3,4,5,6}"); check("NestWhileList(Floor(#/2) &, 20, # > 1 &,1,Infinity,1)", // "{20,10,5,2,1,0}"); check("NestWhileList(Floor(#/2) &, 20, # > 1 &,1,Infinity)", // "{20,10,5,2,1}"); check("NestWhileList(Floor(#/2) &, 20, # > 1 &,1,Infinity,-1)", // "{20,10,5,2}"); check("NestWhileList(#+1 &, 1, True &, 1, 4)", // "{1,2,3,4,5}"); check("NestWhileList(#^2 &, 2, # < 256 &)", // "{2,4,16,256}"); // TODO improve error handling check("NestWhileList(x[[1]],-2147483648,EvenQ(#1)&)", // "{-2147483648,x[[1]][-2147483648]}"); check("NestWhileList(Floor(#/2) &, 10, (Print({##}); UnsameQ(##)) &, All)", // "{10,5,2,1,0,0}"); check("NestWhileList(Floor(#/2) &, 10, UnsameQ, 2)", // "{10,5,2,1,0,0}"); check("NestWhileList(#/2&, 10000, IntegerQ)", // "{10000,5000,2500,1250,625,625/2}"); check("NestWhileList(#^2 &, 2, # < 256 &)", // "{2,4,16,256}"); check("NestWhileList(#/2 &, 123456, EvenQ)", // "{123456,61728,30864,15432,7716,3858,1929}"); check("NestWhileList(Log, 100, # > 0 &)", // "{100,Log(100),Log(Log(100)),Log(Log(Log(100))),Log(Log(Log(Log(100))))}"); } @Test public void testNextPrime() { // print: iteration limit check("NextPrime(13,2147483647)", // "Hold(NextPrime(13,2147483647))"); // print NextPrime: Non-negative integer expected. check("NextPrime(-10000)", // "NextPrime(-10000)"); // NextPrime: Positive integer (less equal 2147483647) expected at position 2 in // NextPrime(10000,-3). check("NextPrime(10000, -3)", // "NextPrime(10000,-3)"); check("NextPrime(10000)", // "10007"); check("NextPrime(10000, 3)", // "10037"); // TODO // check("NextPrime(100, -5)", "73"); // check("NextPrime(10, -5)", "-2"); // check("NextPrime(5.5, 100)", "563"); } @Test public void testNHoldAll() { check("N(f(2, 3))", // "f(2.0,3.0)"); check("SetAttributes(f, NHoldAll)", ""); check("N(f(2, 3))", // "f(2,3)"); } @Test public void testNIntegrate() { // https://github.com/Hipparchus-Math/hipparchus/issues/279 checkNumeric("NIntegrate(Exp(-x),{x,0,Infinity})", // "1.0"); checkNumeric("NIntegrate(Exp(-x^2),{x,0,Infinity})", // "0.886226925452758"); checkNumeric("NIntegrate(Exp(-x^2),{x,-Infinity,Infinity})", // "1.772453850905516"); // TOTO integrable singularity at x==0 checkNumeric("NIntegrate(1/Sqrt(x),{x,0,1}, Method->GaussKronrod)", // "NIntegrate(1/Sqrt(x),{x,0,1},Method->gausskronrod)"); checkNumeric("NIntegrate(1/Sqrt(x),{x,0,1}, Method->LegendreGauss )", // "1.9913364016175945"); checkNumeric("NIntegrate(Cos(200*x),{x,0,1}, Method->GaussKronrod)", // "-0.0043664864860701"); checkNumeric("NIntegrate(Cos(200*x),{x,0,1}, Method->LegendreGauss )", // "-0.0043664864860699"); // github #150 // NIntegrate: (method=LegendreGauss) 1,001 is larger than the maximum (1,000) checkNumeric("NIntegrate(1/x, {x, 0, 1}, MaxPoints->1001)", // "NIntegrate(1/x,{x,0,1},MaxPoints->1001)"); // wrong result checkNumeric("NIntegrate(1/x, {x,0,5}, Method->LegendreGauss)", // "10.374755035279286"); // github #61 // these methods correctly show "NIntegrate(method=method-nsme) maximal count (xxxxx) exceeded" checkNumeric("NIntegrate(1/x, {x,0,5}, Method->Romberg)", // "NIntegrate(1/x,{x,0,5},Method->romberg)"); checkNumeric("NIntegrate(1/x, {x,0,5}, Method->Simpson)", // "NIntegrate(1/x,{x,0,5},Method->simpson)"); checkNumeric("NIntegrate(1/x, {x,0,5}, Method->Trapezoid)", // "NIntegrate(1/x,{x,0,5},Method->trapezoid)"); // github #26 checkNumeric( "NIntegrate(ln(x^2), {x, -5, 99}, Method->Romberg, MaxPoints->400, MaxIterations->10000000)", // "717.9282476448197"); checkNumeric("NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1})", // "-0.0208333333333333"); // LegendreGauss is default method checkNumeric("NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->LegendreGauss)", // "-0.0208333333333333"); checkNumeric("NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->Simpson)", // "-0.0208333320915699"); checkNumeric("NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->Trapezoid)", // "-0.0208333271245165"); checkNumeric( "NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->Trapezoid, MaxIterations->5000)", // "-0.0208333271245165"); checkNumeric("NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->Romberg)", // "-0.0208333333333333"); checkNumeric("NIntegrate (x, {x, 0,2}, Method->Simpson)", // "2.0"); checkNumeric("NIntegrate(Cos(x), {x, 0, Pi})", // "1.0E-16"); checkNumeric("NIntegrate(1/Sin(Sqrt(x)), {x, 0, 1}, PrecisionGoal->10)", // "2.1108620052"); } @Test public void testNMaximize() { checkNumeric("NMaximize(-x^4 - 3* x^2 + x, x)", // "{0.08258881886826407,{x->0.16373996720676331}}"); check("NMaximize({-2*x+y-5, x+2*y<=6 && 3*x + 2*y <= 12 }, {x, y})", // "{-2.0,{x->0.0,y->3.0}}"); check("NMaximize({-x - y, 3*x + 2*y >= 7 && x + 2*y >= 6}, {x, y})", // "{-3.25,{x->0.5,y->2.75}}"); } @Test public void testNMinimize() { check("NMinimize({-5-2*x+y,x+2*y<=6&&3*x+2*y<=12},{x,y})", // "{-13.0,{x->4.0,y->0.0}}"); check("NMinimize({-Sinc(x)-Sinc(y)}, {x, y})", // "{-2.0,{x->0.0,y->0.0}}"); check("NMinimize(x^2 + y^2 + 2, {x,y})", // "{2.0,{x->0.0,y->0.0}}"); check("NMinimize({Sinc(x)+Sinc(y)}, {x, y})", // "{-0.434467,{x->4.49341,y->4.49341}}"); checkNumeric("NMinimize({Sinc(x)+Sinc(y)}, {x, y})", // "{-0.4344672564224433,{x->4.493409457896563,y->4.493409457738778}}"); checkNumeric("NMinimize(x^4 - 3*x^2 - x, x)", // "{-3.513905038934788,{x->1.3008395656679863}}"); // TODO non-linear not supported // check("NMinimize({x^2 - (y - 1)^2, x^2 + y^2 <= 4}, {x, y})", ""); check("NMinimize({-2*y+x-5, x+2*y<=6 && 3*x + 2*y <= 12 }, {x, y})", // "{-11.0,{x->0.0,y->3.0}}"); check("NMinimize({-2*y+x-5, x+2*y<=6 && 3*x + 2*y <= 12 }, {x, y})", // "{-11.0,{x->0.0,y->3.0}}"); check("NMinimize({-2*x+y-5, x+2*y<=6 && 3*x + 2*y <= 12 }, {x, y})", // "{-13.0,{x->4.0,y->0.0}}"); check("NMinimize({x + 2*y, -5*x + y == 7 && x + y >= 26 && x >= 3 && y >= 4}, {x, y})", // "{48.83333,{x->3.16667,y->22.83333}}"); check("NMinimize({x + y, 3*x + 2*y >= 7 && x + 2*y >= 6 }, {x, y})", // "{3.25,{x->0.5,y->2.75}}"); } @Test public void testNonCommutativeMultiply() { check("{0 ** a, 1 ** a}", // "{0**a,1**a}"); check("{a*b == b*a, a ** b == b ** a}", // "{True,a**b==b**a}"); check("a ** (b ** c) == (a ** b) ** c", // "True"); check("NonCommutativeMultiply(a)", // "NonCommutativeMultiply(a)"); } @Test public void testNoneTrue() { check("NoneTrue({1, 3, 5}, EvenQ)", // "True"); check("NoneTrue({1, 4, 5}, EvenQ)", // "False"); check("NoneTrue({}, EvenQ)", // "True"); check("NoneTrue({1, 2, 3, 4, 5, 6}, EvenQ)", // "False"); check("NoneTrue({1, 3, 5, 7}, EvenQ)", // "True"); check("NoneTrue({12, 16, x, 14, y}, # < 10 &)", // "Nor(x<10,y<10)"); check("NoneTrue({12, 16, x, 14, y}, TrueQ(# < 10) &)", // "True"); check("NoneTrue(f(1, 7, 3), OddQ)", // "False"); } @Test public void testNonNegative() { check("NonNegative(-Infinity)", // "False"); check("NonNegative(Infinity)", // "True"); check("NonNegative(-Infinity)", // "False"); check("NonNegative(-9/4)", // "False"); check("NonNegative(0.1+I)", // "False"); check("NonNegative(I)", // "False"); check("{Positive(0), NonNegative(0)}", // "{False,True}"); check("NonNegative({1.6, 3/4, Pi, 0, -5, 1 + I, Sin(10^5)})", // "{True,True,True,True,False,False,True}"); check("NonNegative({x, Sin(y)})", // "{NonNegative(x),NonNegative(Sin(y))}"); } @Test public void testNonPositive() { check("NonPositive(-9/4)", // "True"); check("NonPositive(-0.1+I)", // "False"); check("NonPositive(I)", // "False"); check("{Negative(0), NonPositive(0)}", // "{False,True}"); check("NonPositive({1.6, 3/4, Pi, 0, -5, 1 + I, Sin(10^5)})", // "{False,False,False,True,True,False,False}"); } @Test public void testNor() { check("Nor( )", // "True"); check("Nor(2+2)", // "!4"); check("Nor(True,False)", // "False"); check("Nor(x,y,z)", // "Nor(x,y,z)"); check("Nor(x,True,z)", // "False"); check("Nor(x,False,z)", // "Nor(x,z)"); check("BooleanConvert(Nor(p, q, r))", // "!p&&!q&&!r"); check("BooleanConvert(! Nor(p, q, r))", // "p||q||r"); } @Test public void testNorm() { // message Power: BigInteger bit length 76493 exceeded check("Norm({10,100,200},10007)", // "Norm({10,100,200},10007)", // 60); // message: Norm: The first Norm argument should be a scalar, vector or matrix.)) check("Norm({})", // "Norm({})"); check("Norm({{}})", // "Norm({{}})"); check("mat={{1.1284111012048381, 6.059642563882402, 4.016005969894351},\n" + // "{6.953004075736082, 2.0349603837230656, 1.9793505188774905},\n" + // "{7.9963143348211325, 0.18947057304877646, 3.1653764788092467}};", // ""); check("Norm(mat)", // "11.93914"); check("Norm(mat,\"Frobenius\")", // "13.58384"); check("Norm({a,b,c}, \"Frobenius\")", // "Sqrt(Abs(a)^2+Abs(b)^2+Abs(c)^2)"); check("Norm(0)", // "0"); check("Norm({x, y}, 0)", // "Norm({x,y},0)"); check("Norm({x, y}, 0.5)", // "Norm({x,y},0.5)"); check("Norm({})", // "Norm({})"); check("Norm({1, 2, 3, 4}, 2)", // "Sqrt(30)"); check("Norm({10, 100, 200}, 1)", // "310"); check("Norm({0,0,a,0,0})", // "Abs(a)"); check("Norm({a,b,c})", // "Sqrt(Abs(a)^2+Abs(b)^2+Abs(c)^2)"); check("Norm(SparseArray({x, y, z}), Infinity)", // "Max(Abs(x),Abs(y),Abs(z))"); check("Norm({x, y, z}, Infinity)", // "Max(Abs(x),Abs(y),Abs(z))"); check("Norm({x, y, z})", // "Sqrt(Abs(x)^2+Abs(y)^2+Abs(z)^2)"); check("Norm({x, y, z}, p)", // "(Abs(x)^p+Abs(y)^p+Abs(z)^p)^(1/p)"); check("Norm(-2+I)", // "Sqrt(5)"); check("Norm(SparseArray({1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1}))", // "Sqrt(5)"); check("Norm({1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1})", // "Sqrt(5)"); check("Norm(N({1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1}))", // "2.23607"); check("Norm({1, 2, 3, 4}, 2)", // "Sqrt(30)"); check("Norm({10, 100, 200}, 1)", // "310"); check("Norm({a, b, c})", // "Sqrt(Abs(a)^2+Abs(b)^2+Abs(c)^2)"); check("Norm({-100, 2, 3, 4}, Infinity)", // "100"); check("Norm(1 + I)", // "Sqrt(2)"); check("Norm({1, {2, 3}}) ", // "Norm({1,{2,3}})"); check("Norm({x, y})", // "Sqrt(Abs(x)^2+Abs(y)^2)"); check("Norm({x, y}, 0)", // "Norm({x,y},0)"); check("Norm({x, y}, 0.5)", // "Norm({x,y},0.5)"); check("Norm({})", // "Norm({})"); } @Test public void testNormal() { check("Normal( ConditionalExpression( 1, Element(a,Reals)&&b>0&&n>0 ) + z^3 )", // "1+z^3"); check("Normal( ConditionalExpression( 1, Element(a,Reals)&&b>0&&n>0 ) + z^3, ByteArray)", // "ConditionalExpression(1+z^3,a∈Reals&&b>0&&n>0)"); check( "Normal( ConditionalExpression( 1, Element(a,Reals)&&b>0&&n>0 ) + z^3, {ConditionalExpression})", // "1+z^3"); } @Test public void testNormalize() { check( "Normalize({0.9999999999999999, -0.12609662354252538+I*0.3870962681438435, 0.3692814336284687+I*0.0968290630091466})", // "{0.8732080940136610352,-0.1101085923051267364+I*0.33801559450568667,0.3224595368133474565+I*0.0845519215553456008}"); check("Normalize({0})", // "{0}"); check("Normalize(0)", // "0"); check("Normalize({1,5,1})", // "{1/(3*Sqrt(3)),5/3*1/Sqrt(3),1/(3*Sqrt(3))}"); check("Normalize({x,y})", // "{x/Sqrt(Abs(x)^2+Abs(y)^2),y/Sqrt(Abs(x)^2+Abs(y)^2)}"); check("Normalize({x,y}, f)", // "{x/f({x,y}),y/f({x,y})}"); check("Normalize({1, 2*I, 3, 4*I, 5, 6*I})", // "{1/Sqrt(91),(I*2)/Sqrt(91),3/Sqrt(91),(I*4)/Sqrt(91),5/Sqrt(91),(I*6)/Sqrt(91)}"); check("Normalize(N({1, 2*I, 3, 4*I, 5, 6*I}))", // "{0.104828,I*0.209657,0.314485,I*0.419314,0.524142,I*0.628971}"); check("Normalize({{1, 2}, {4, 5}}, Norm)", // "{{0.147758,0.295516},{0.591031,0.738789}}"); check("Normalize(1 + x + x^2, Integrate(#^2, {x, -1, 1}) &)", // "5/22*(1+x+x^2)"); check("Normalize({1, 1, 1, 1})", // "{1/2,1/2,1/2,1/2}"); check("Normalize(1 + I)", // "(1+I)/Sqrt(2)"); check("Normalize(0)", // "0"); check("Normalize({0})", // "{0}"); check("Normalize({})", // "{}"); } @Test public void testNot() { check("!True", // "False"); check("!False", // "True"); check("!b", // "!b"); check("Not(Not(x))", // "x"); check("Not(a=b"); check("Not(a<=b)", // "a>b"); check("Not(a>b)", // "a<=b"); check("Not(a>=b)", // "a1)", // "x<=1"); check("!Exists(x, f(x))", // "ForAll(x,!f(x))"); check("!ForAll(x, f(x))", // "Exists(x,!f(x))"); } @Test public void testNotElement() { check("NotElement(Pi, Integers)", // "True"); check("NotElement(a, Reals)", // "a∉Reals"); // TODO improve Rationals and Algebraics domains check("NotElement(Sqrt(2), #)& /@ {Complexes, Algebraics, Reals, Rationals, Integers, Primes}", // "{False,Sqrt(2)∉Algebraics,False,Sqrt(2)∉Rationals,True,True}"); } @Test public void testNothing() { check("Nothing(a,b,c)", // "Nothing"); check("{a, Nothing, Nothing, d}", // "{a,d}"); check("bar(a, Nothing, baz(Nothing), c)", // "bar(a,Nothing,baz(Nothing),c)"); check("{1, 2, Nothing, 4, 5, Nothing}", // "{1,2,4,5}"); check("ReplacePart({a, b, c, d, e, f, g}, {1 -> Nothing, 3 -> Nothing})", // "{b,d,e,f,g}"); } @Test public void testNumberQ() { check("NumberQ(3,4)", // "NumberQ(3,4)"); check("NumberQ(3+I)", // "True"); check("NumberQ(5!)", // "True"); check("NumberQ(Pi)", // "False"); } @Test public void testNumericalOrder() { check("NumericalOrder(Sqrt(2)+5, E+Pi)", // "-1"); check("NumericalOrder(E+Pi,Sqrt(2)+5)", // "1"); check("NumericalOrder(6,Pi)", // "-1"); check("NumericalOrder(Exp(I), Sin(1))", // "1"); check("NumericalOrder(E^I,(-10)*I+Cos(1))", // "1"); check("NumericalOrder(-Infinity, GoldenRatio)", // "1"); check("NumericalOrder(Infinity, 0)", // "-1"); check("NumericalOrder(3/2, 1)", // "-1"); check("NumericalOrder(3/2, 1.5)", // "0"); check("NumericalOrder(Infinity,4)", // "-1"); check("NumericalOrder(-Infinity,3/4)", // "1"); check("NumericalOrder(Pi, E^2)", // "1"); check("Order(Pi, E^2)", // "-1"); // TODO this is canonical ordered check("NumericalOrder(Quantity(1, \"Meters\"), Quantity(3, \"Feet\"))", // "-1"); check("NumericalOrder(Quantity(3, \"Feet\"), Quantity(1, \"Meters\"))", // "1"); check("lst = {1, Pi, E, Infinity, I*Sqrt(-2), -Infinity}", // "{1,Pi,E,Infinity,-Sqrt(2),-Infinity}"); check("ord = Ordering(lst, All, NumericalOrder)", // "{6,5,1,3,2,4}"); check("lst[[ord]]", // "{-Infinity,-Sqrt(2),1,E,Pi,Infinity}"); } @Test public void testNumericalSort() { check("NumericalSort({1,2,3,Infinity,-Infinity,E,Pi,GoldenRatio,Degree})", // "{-Infinity,Pi/180,1,GoldenRatio,2,E,3,Pi,Infinity}"); check( "NumericalSort({ Infinity, Sqrt(2), -1, 0, -Infinity, Quantity(1, \"Meters\"), Quantity(3, \"Feet\")})", // "{-Infinity,-1,0,Sqrt(2),Infinity,3[Feet],1[Meters]}"); check("NumericalSort({1, Pi, E, Infinity, -Sqrt[2], -Infinity})", // "{-Infinity,-Sqrt(2),1,E,Pi,Infinity}"); // TODO unequals MMA sort check("Sort({1, Pi, E, Infinity, -Sqrt[2], -Infinity})", // "{1,-Infinity,Infinity,-Sqrt(2),E,Pi}"); } @Test public void testNumericQ() { // NumericQ calls expr.isNumericFunction( false ) check("NumericQ({1,2,3})", // "False"); check("NumericQ(1+GoldenAngle)", // "True"); check("NumericQ(GoldenRatio)", // "True"); check("NumericQ(Sqrt(3))", // "True"); check("NumericQ(Glaisher)", // "True"); check("1True)", // "1"); check("Numerator(Csc(x)^4)", // "Csc(x)^4"); check("Numerator(Csc(x)^4, Trig->True)", // "1"); check("Numerator(42*Csc(x))", // "42*Csc(x)"); check("Numerator(42*Csc(x), Trig->True)", // "42"); check("Numerator(42*Csc(x)^3)", // "42*Csc(x)^3"); check("Numerator(42*Csc(x)^3, Trig->True)", // "42"); check("Numerator(E^(-x)*x^(1/2))", // "Sqrt(x)"); check("Numerator(Sec(x))", // "Sec(x)"); check("Numerator(Sec(x), Trig->True)", // "1"); check("Numerator(Tan(x))", // "Tan(x)"); check("Numerator(Tan(x), Trig->True)", // "Sin(x)"); check("Numerator(2 / 3)", // "2"); check("Numerator(a + b)", // "a+b"); } @Test public void testOddQ() { check("OddQ(1/(b-a*c)[[2]])", // "False"); check("OddQ((1/(b-a*c))[[2]])//Trace", // "{{(1/(b-a*c))[[2]],-1},True}"); check("OddQ({1,3}) && OddQ({5,7})", // "{True,True}&&{True,True}"); check("OddQ(2+4*I, GaussianIntegers->True)", // "False"); check("OddQ(2-3*I, GaussianIntegers->True)", // "True"); check("OddQ(1+4*I, GaussianIntegers->True)", // "True"); check("OddQ(1+I, GaussianIntegers->True)", // "False"); check("OddQ(4*I, GaussianIntegers->True)", // "False"); check("OddQ(6, GaussianIntegers->True)", // "False"); check("OddQ(I, GaussianIntegers->True)", // "True"); check("OddQ(3, GaussianIntegers->True)", // "True"); } @Test public void testEvenQ() { check("EvenQ(2+4*I, GaussianIntegers->True)", // "True"); check("EvenQ(2-3*I, GaussianIntegers->True)", // "False"); check("EvenQ(1+4*I, GaussianIntegers->True)", // "False"); check("EvenQ(1+I, GaussianIntegers->True)", // "False"); check("EvenQ(4*I, GaussianIntegers->True)", // "True"); check("EvenQ(6, GaussianIntegers->True)", // "True"); check("EvenQ(I, GaussianIntegers->True)", // "False"); check("EvenQ(3, GaussianIntegers->True)", // "False"); } @Test public void testOneIdentity() { check("SetAttributes(f, OneIdentity)", // ""); // with a default argument, the pattern does match: check("a /. f(x_:0, u_) -> {u}", // "{a}"); // without a default argument, the pattern does not match: check("a /. f(u_) -> {u}", // "a"); // OneIdentity does not affect evaluation: check("f(a)", // "f(a)"); } @Test public void testOneIdentityOrderless() { // github issue 89 check( "Module[{e}, ClearAll[eqv]; SetAttributes[eqv, {Flat}]; eqv[p, q, r] /. {eqv[x_, y_] :> {x, y}}]", // "{eqv(p),eqv(q,r)}"); check( "Module[{e}, ClearAll[eqv]; SetAttributes[eqv, {Flat, OneIdentity}]; eqv[p, q, r] /. {eqv[x_, y_] :> {x, y}}]", // "{p,eqv(q,r)}"); // See discussion here: // https://mathematica.stackexchange.com/questions/183322/subtle-order-of-evaluation-issues-when-pattern-matching-with-attributes check( "Module[{e}, ClearAll[eqv]; SetAttributes[eqv, {Flat, Orderless}]; eqv[p, q, r] /. {eqv[x_, y_] :> {x, y}}]", // "{p,eqv(q,r)}"); check( "Module[{e}, ClearAll[eqv]; SetAttributes[eqv, {Flat, OneIdentity, Orderless}]; eqv[p, q, r] /. {eqv[x_, y_] :> {x, y}}]", // "{p,eqv(q,r)}"); check("SetAttributes(f,{Orderless,OneIdentity})", // ""); check("f(p, q) /. {f(x_,y_) :> {x,y}}", // "{p,q}"); check("f(q,f(p,r)) /. {f(x_,y_) :> {x,y}}", // "{q,f(p,r)}"); } @Test public void testOperate() { check("Operate(a, (a*c)[f(x)])", // "a(a*c)[f(x)]"); check("Through(Operate(a, (a*c)[f(x)]))", // "a((a*c)[f(x)])"); check("Through(Operate(p, f(x)))", // "p(f(x))"); check("Composition(p, f)[x]", // "p(f(x))"); check("Operate(g &, f(a, b, c))", // "g(a,b,c)"); check("Operate(p, f(a, b))", // "p(f)[a,b]"); check("Operate(p, f(a, b), 1)", // "p(f)[a,b]"); check("Operate(p, f(a)[b][c], 0)", // "p(f(a)[b][c])"); check("Operate(p, f(a)[b][c])", // "p(f(a)[b])[c]"); check("Operate(p, f(a)[b][c], 1)", // "p(f(a)[b])[c]"); check("Operate(p, f(a)[b][c], 2)", // "p(f(a))[b][c]"); check("Operate(p, f(a)[b][c], 3)", // "p(f)[a][b][c]"); check("Operate(p, f(a)[b][c], 4)", // "f(a)[b][c]"); check("Operate(p, f, 0)", // "p(f)"); check("Operate(p, f, -1)", // "Operate(p,f,-1)"); check("Operate(p, f)", // "f"); check("Operate(p, f, 0)", // "p(f)"); check("Operate(p, f(a)[b][c],0)", // "p(f(a)[b][c])"); check("Operate(p, f(a)[b][c])", // "p(f(a)[b])[c]"); check("Operate(p, f(a)[b][c],1)", // "p(f(a)[b])[c]"); check("Operate(p, f(a)[b][c],2)", // "p(f(a))[b][c]"); check("Operate(p, f(a)[b][c],3)", // "p(f)[a][b][c]"); check("Operate(p, f(a)[b][c],4)", // "f(a)[b][c]"); check("Operate(p, f(x, y))", // "p(f)[x,y]"); } @Test public void testDP() { check("DP(k_,w_):=Sum(w^d/d, {d, Divisors(k)})", // ""); check("DP(6,w)", // "w+w^2/2+w^3/3+w^6/6"); } @Test public void testOptimizeExpression() { check("OptimizeExpression( (x+1)^2+(x+1)^3)", // "{v1^2+v1^3,{v1->1+x}}"); check("OptimizeExpression(Sqrt(Sin(x)))", // "{Sqrt(Sin(x)),{}}"); check("OptimizeExpression(Sqrt(Sin(x)+5)*Sqrt(Sin(x)+4))", // "{Sqrt(4+v1)*Sqrt(5+v1),{v1->Sin(x)}}"); check("OptimizeExpression(Sqrt(Sin(x+1) + 5 + Cos(y))*Sqrt(Sin(x+1) + 4 + Cos(y)))", // "{Sqrt(4+v1+v2)*Sqrt(5+v1+v2),{v2->Cos(y),v1->Sin(1+x)}}"); check("OptimizeExpression((x-y)*(z-y) + sqrt((x-y)*(z-y)))", // "{Sqrt(v1)+v1,{v1->(x-y)*(-y+z)}}"); check("OptimizeExpression(#1+1+(#1+1)*(#1+1)&)", // "{v1*v1+v1&,{v1->1+#1}}"); check("OptimizeExpression(f(x))", // "{f(x),{}}"); check( "OptimizeExpression(-3*a - 2*a^3 + 4*Sqrt(1 + a^2)*(5 - 9*Log(2)) + \n" + " 4*a^2*Sqrt(1 + a^2)*(5 - 9*Log(2)) + \n" + " 12*(1 + a^2)^(3/2)*Log(1 + Sqrt(1 + 1/a^2)) - \n" + " 6*(4*(Sqrt(1 + a^2) - a*(2 + a^2 - a*Sqrt(1 + a^2)))*Log(a) + a*Log(1 + a^2)))", // // "{-3*a-2*a^3+4*v1*v2+4*v1*v2*v4+12*v3^(3/2)*Log(1+Sqrt(1+1/a^2))-6*(4*(v1-a*(2-a*v1+v4))*Log(a)+a*Log(v3))," // + "{v4->a^\n" // + "2," // + "v3->1+v4," // + "v2->5-9*Log(2)," // + "v1->Sqrt(1+v4)}}"); check( "OptimizeExpression((3 + 3*a^2 + Sqrt(5 + 6*a + 5*a^2) + a*(4 + Sqrt(5 + 6*a + 5*a^2)))/6)", // "{1/6*(3+v1+a*(4+v1)+3*v2),{v2->a^2,v1->Sqrt(5+6*a+5*v2)}}"); check("OptimizeExpression( Sin(x) + Cos(Sin(x)))", // "{v1+Cos(v1),{v1->Sin(x)}}"); check("ReplaceRepeated@@OptimizeExpression( Sin(x) + Cos(Sin(x)))", // "Cos(Sin(x))+Sin(x)"); } @Test public void testReplaceRepeated() { check("ReplaceRepeated(x, x -> x + 1, MaxIterations -> 4)", // "4+x"); // example from https://en.wikipedia.org/wiki/Wolfram_Language check("sortRule := {x___,y_,z_,k___} /; y>z -> {x,z,y,k}", // ""); check("{ 9, 5, 3, 1, 2, 4 } //. sortRule", // "{1,2,3,4,5,9}"); check("f(g(x),y)//.{f(x_,y_):>k(g(x),g(y)),g(g(x_)):>g(x)}", // "k(g(x),g(y))"); check("x//.x -> 1", // "1"); check("a+b+c //. c->d", // "a+b+d"); check("logrules = {Log(x_ * y_) :> Log(x) + Log(y), Log(x_^y_) :> y * Log(x)};", // ""); check("Log(a * (b * c) ^ d ^ e * f) //. logrules", // "Log(a)+d^e*(Log(b)+Log(c))+Log(f)"); // `ReplaceAll` just performs a single replacement: check("Log(a * (b * c) ^ d ^ e * f) /. logrules", // "Log(a)+Log((b*c)^d^e*f)"); check("{f(f(x)), f(x), g(f(x)), f(g(f(x)))} //. f(x_) -> x", // "{x,x,g(x),g(x)}"); check("ReplaceRepeated(f(x_) -> x)[{f(f(x)), f(g(f(x)))}]", // "{x,g(x)}"); check("Log(Sqrt(a*(b*c^d)^e)) //. logrules", // "1/2*(Log(a)+e*(Log(b)+d*Log(c)))"); check("Log(Sqrt(a(b*c^d)^e)) /. logrules", // "1/2*e*Log(a(b*c^d))"); check("ReplaceRepeated(1/6*(3+3*v1+v2+a*(4+v2)), {v1->a^2, v2->Sqrt(5+6*a+5*v1)})", // "1/6*(3+3*a^2+Sqrt(5+6*a+5*a^2)+a*(4+Sqrt(5+6*a+5*a^2)))"); check("ReplaceRepeated(1/6*(3+3*v1+v2+a*(4+v2)), {v2->Sqrt(5+6*a+5*v1), v1->a^2})", // "1/6*(3+3*a^2+Sqrt(5+6*a+5*a^2)+a*(4+Sqrt(5+6*a+5*a^2)))"); check("x //. {a -> 42, b -> -1}", // "x"); check("x //. {{x -> 42}, {b -> -1}}", // "{42,x}"); } @Test public void testOr() { check("Or(z, z)", // "z||z"); check("Or(a, z, z)", // "a||z||z"); check("Attributes(Or)", // "{Flat,HoldAll,OneIdentity,Protected}"); check("Or(p, p, p) /. Or(a_, b_) :> {a, b}", // "{p,p||p}"); check("Or(p, p, p) /. Or(a_., b_.) :> {a, b}", // "{p,p||p}"); check("Or(p, p, p)", // "p||p||p"); check("Or(p, q) === Or(q, p)", // "False"); check("False || True", // "True"); check("a || False || b", // "a||b"); check("Or( )", // "False"); check("Or(2+2)", "4"); check("FullForm( Or(x, Or(y, z)) )", // "Or(x, y, z)"); check("Or(x, False, z)", // "x||z"); check("Or(x, True, z)", // "True"); } @Test public void testOrder() { // Order compares expressions structurally check("Order(6, Pi)", // "1"); check("Order(3,4)", // "1"); check("Order(4,3)", // "-1"); check("Order(6,Pi)", // "1"); check("Order(6,N(Pi))", // "-1"); } @Test public void testOrdering() { check("Ordering({1,3,4,2,5,9,6})", // "{1,4,2,3,5,7,6}"); check("Ordering({1,3,4,2,5,9,6},All,Greater)", // "{6,7,5,3,2,4,1}"); check("Ordering({2, 6, 1, 9, 1, 2, 3}, -1)", // "{4}"); check("Ordering({2, 6, 1, 9, 1, 2, 3}, -3)", // "{4,2,7}"); check("Ordering({c,a,b})", // "{2,3,1}"); check("Ordering(f(3, 1, 2))", // "{2,3,1}"); check("Ordering({2, 6, 1, 9, 1, 2, 3},4)", // "{3,5,1,6}"); check("Ordering({2, 6, 1, 9, 1, 2, 3},All,Greater)", // "{4,2,7,1,6,3,5}"); check("l={2, 6, 1, 9, 1, 2, 3}", // "{2,6,1,9,1,2,3}"); check("l[[ Ordering(l) ]]", // "{1,1,2,2,3,6,9}"); check("Ordering({2, 6, 1, 9, 1, 2, 3}, -20)", // "{4,2,7,6,1,5,3}"); check("Ordering({2, 6, 1, 9, 1, 2, 3}, 20)", // "{3,5,1,6,7,2,4}"); } @Test public void testOrderedQ() { check("OrderedQ({{1,2,3}, {1,4}})", // "False"); check("OrderedQ(<|2 -> c, 7 -> b, 3 -> a|>)", // "False"); check("OrderedQ(<|2 -> c, 7 -> b, 3 -> a|>, Greater)", // "True"); check("OrderedQ(<|2 -> a, 7 -> b, 3 -> c|>)", // "True"); check("OrderedQ(<|1 -> 10, 2 -> 5, 3 -> 0|>)", // "False"); check("OrderedQ({{a, 3}, {d, 2}, {c, 1}}, #1[[2]] < #2[[2]] &)", // "False"); check("OrderedQ({{a, 3}, {d, 2}, {c, 1}}, #1[[2]] > #2[[2]] &)", // "True"); check("OrderedQ({1, Sqrt(2), 2, E, 3, Pi})", // "False"); check("OrderedQ({1, Sqrt(2), 2, E, 3, Pi}, Less)", // "True"); check("OrderedQ({a, b})", // "True"); check("OrderedQ({b, a})", // "False"); check("OrderedQ({x^2, 4+6*x})", // "False"); check("OrderedQ({x^2,x^3})", // "True"); check("OrderedQ({x,x^6.0 })", // "True"); check("OrderedQ({4.0*x,33.0*x^6.0 })", // "True"); check("OrderedQ({x^3,4+4*a })", // "False"); check("OrderedQ({x^2, 6*x})", // "False"); check("OrderedQ({6*x,x^2})", // "True"); check("OrderedQ({a,a})", // "True"); check("OrderedQ({x, y, x + y})", // "True"); check("p(_?NumberQ _Symbol):= -1;\n"// + "p(_Symbol,_?NumberQ):= 1;\n" // + "p(_Symbol,_Symbol):= 0;\n" // + "p(x_?NumberQ,y_?NumberQ):= x <= y;", // ""); check("OrderedQ({t,e,s,t,3,7,11,13}, p)", // "True"); } @Test public void testOrderless() { check("SetAttributes(to, Orderless)", // ""); check("to(b_.*x_^3, x_) := {b,x}", // ""); check("to(x, x)", // "to(x,x)"); check("to(a*x, x)", // "to(x,a*x)"); check("to(x^3, x)", // "{1,x}"); check("to(a*x^3, x)", // "{a,x}"); check("to(a*x*z, x)", // "to(x,a*x*z)"); check("to(a*x^3*z, x)", // "{a*z,x}"); check("to(b_.*x_^n_., x_) := {b,n,x}", // ""); check("to(x, x)", // "{1,1,x}"); check("to(a*x, x)", // "{a,1,x}"); check("to(x^2, x)", // "{1,2,x}"); check("to(a*x^2, x)", // "{a,2,x}"); check("to(a*x*z, x)", // "{a*z,1,x}"); check("to(a*x^2*z, x)", // "{a*z,2,x}"); // see https://github.com/mathics/Mathics/issues/747 check("SetAttributes(ordl,{OneIdentity,Orderless});ordl(p,p,p)/.ordl(p_.,p_.):>p", // "ordl(p,p,p)"); check("SetAttributes(f, Orderless)", // ""); check("f(c, a, b, a + b, 3, 1.0)", // "f(1.0,3,a,b,a+b,c)"); check("f(a, b) == f(b, a)", // "True"); check("SetAttributes(f, Flat)", // ""); check("Attributes(f)", // "{Flat,Orderless}"); check("f(a, b, c) /. f(a, c) -> d", // "f(b,d)"); check("SetAttributes(f1, Orderless)", // ""); check("f1(x_Symbol, y_Integer, z_Real) := {x,y,z}", // ""); check("{f1(x,3.0,2),f1(3.0,x,2),f1(2,3.0,x)}", // "{{x,2,3.0},{x,2,3.0},{x,2,3.0}}"); } @Test public void testOut() { check("Expand((x + y)^2)", // "x^2+2*x*y+y^2"); check("N(Pi, 30)", // "3.14159265358979323846264338327"); check("Out( )", // "3.14159265358979323846264338327"); check("Out(-3)", // "x^2+2*x*y+y^2"); check("Out(-5)", // "Out(-5)"); check("Out(1)", // "x^2+2*x*y+y^2"); check("Out(2)", // "3.14159265358979323846264338327"); } @Test public void testUnderflow() { check("5*Underflow() // N", // "0.0"); check("5*Underflow() ", // "Underflow()"); check("Underflow() // N", // "0.0"); check("1-Underflow()", // "1+Underflow()"); check("1-Underflow() // N", // "1.0"); check("Sin(7)+x+Underflow() // N", // "0.656987+x"); check("Sin(7)+x+Underflow()", // "x+Sin(7)+Underflow()"); } @Test public void testOverflow() { check("5*Overflow() // N", // "Overflow()"); check("5*Overflow() ", // "Overflow()"); check("Overflow() // N", // "Overflow()"); check("Sin(7)+x+Overflow() // N", // "x+Overflow()"); check("Sin(7)+x+Overflow()", // "x+Overflow()"); } @Test public void testOwnValues() { check("a=42", // "42"); check("OwnValues(a)", // "{HoldPattern(a):>42}"); check("a=21", // "21"); // TODO check("Hold(a) /. OwnValues(a)", // "Hold(21)"); } @Test public void testPadLeft() { // TODO // check("PadLeft({1, 2, 3}, 10, {a, b, c}, 2)", // // "{b, c, a, b, c, 1, 2, 3, a, b}"); if (Config.EXPENSIVE_JUNIT_TESTS) { check("PadLeft(x^2,1009)", // "Recursion depth of 256 exceeded during evaluation of Null."); } // https://oeis.org/A196023 check( "Select(Table(FromDigits@Join(Flatten@IntegerDigits@PadLeft({666}, 2, n), Reverse@IntegerDigits(n)), {n, 397}), PrimeQ)", // "{16661,76667,3166613,3466643,7466647,7666667,145666541,148666841,152666251,\n" + // "155666551,169666961,176666671,181666181,304666403,305666503,307666703,308666803,\n" + // "329666923,347666743,349666943,373666373,374666473,383666383,391666193,397666793}"); check("PadLeft({1, 2, 3}, 5)", // "{0,0,1,2,3}"); check("PadLeft(x(a, b, c), 5) ", // "x(0,0,a,b,c)"); check("PadLeft({1, 2, 3}, 2)", // "{2,3}"); check("PadLeft({1, 2, 3}, 1)", // "{3}"); check("PadLeft({{a, b, d}, {c}}, {3,5})", // "{{0,0,0,0,0},{0,0,a,b,d},{0,0,0,0,c}}"); check("PadLeft(f(g(a, b, d, e, f), {c}), {3,4},1)", // "f(f(1,1,1,1),g(b,d,e,f),{1,1,1,c})"); check("PadLeft({{a, b, d, e, f}, {c}}, {3,4})", // "{{0,0,0,0},{b,d,e,f},{0,0,0,c}}"); check("PadLeft({{a, b, d, e}, {c}}, {3,4})", // "{{0,0,0,0},{a,b,d,e},{0,0,0,c}}"); check("PadLeft({{a, b, d}, {c}}, {3,4})", // "{{0,0,0,0},{0,a,b,d},{0,0,0,c}}"); check("PadLeft({{a, b}, {c}}, {3,4})", // "{{0,0,0,0},{0,0,a,b},{0,0,0,c}}"); check("PadLeft({{a, b}, c}, {3,4})", // "PadLeft({{a,b},c},{3,4})"); check("PadLeft({1, 2, 3}, 5)", // "{0,0,1,2,3}"); check("PadLeft(x(a, b, c), 5) ", // "x(0,0,a,b,c)"); check("PadLeft({1, 2, 3}, 2)", // "{2,3}"); check("PadLeft({1, 2, 3}, 1)", // "{3}"); check("PadLeft({{}, {1, 2}, {1, 2, 3}})", // "{{0,0,0},{0,1,2},{1,2,3}}"); check("PadLeft({a, b, c}, 10)", // "{0,0,0,0,0,0,0,a,b,c}"); check("PadLeft({a, b, c}, 10, {x, y, z})", // "{z,x,y,z,x,y,z,a,b,c}"); check("PadLeft({a, b, c}, 9, {x, y, z})", // "{x,y,z,x,y,z,a,b,c}"); check("PadLeft({a, b, c}, 8, {x, y, z})", // "{y,z,x,y,z,a,b,c}"); check("PadLeft({a, b, c}, 10, 42)", // "{42,42,42,42,42,42,42,a,b,c}"); } @Test public void testPadRight() { check("PadRight(Slot(<|s1-><|a->0,b:>1|>,s2:><|a->0,b:>1|>|>),{1},{1,2,3,a}+1)", // "Slot(Association(s1->Association(a->0,b:>1),s2:>Association(a->0,b:>1)))"); check("PadRight(Slot(<|s1-><|a->0,b:>1|>,s2:><|a->0,b:>1|>|>),{1,11,1},{1,2,3,a}+1)", // "Slot(Association(Rule(s1),RuleDelayed(s2),Slot({2,3,4,1+a}),Slot({2,3,4,1+a}),Slot({\n" + "2,3,4,1+a}),Slot({2,3,4,1+a}),Slot({2,3,4,1+a}),Slot({2,3,4,1+a}),Slot({2,3,4,1+a}),Slot({\n" + "2,3,4,1+a}),Slot({2,3,4,1+a})))"); check("With({r = Map(Fibonacci, Range(2, 14))}, " + // "Position(#, {1, 0, 1})[[All, 1]] &@ Table(If(Length@ # < 3, {}, Take(#, -3)) &@ IntegerDigits@ Total@ Map(FromDigits@ PadRight({1}, Flatten@ #) &@ Reverse@ Position(r, #) &, Abs@ Differences@ NestWhileList(Function(k, k - SelectFirst(Reverse@ r, # < k &)), n + 1, # > 1 &)), {n, 373}))", // "{4,12,17,25,33,38,46,51,59,67,72,80,88,93,101,106,114,122,127,135,140,148,156,\n" + // "161,169,177,182,190,195,203,211,216,224,232,237,245,250,258,266,271,279,284,292,\n" + // "300,305,313,321,326,334,339,347,355,360,368,373}"); check("PadRight({1, 2, 3}, 5)", // "{1,2,3,0,0}"); check("PadRight(x(a, b, c), 5) ", // "x(a,b,c,0,0)"); check("PadRight({1, 2, 3}, 2)", // "{1,2}"); check("PadRight({1, 2, 3}, 1)", // "{1}"); check("PadRight(f(g(a, b, d, e, f), {c}), {3,4},1)", // "f(g(a,b,d,e),{c,1,1,1},f(1,1,1,1))"); check("PadRight({{a, b, d, e, f}, {c}}, {3,4})", // "{{a,b,d,e},{c,0,0,0},{0,0,0,0}}"); check("PadRight({{a, b, d, e}, {c}}, {3,4})", // "{{a,b,d,e},{c,0,0,0},{0,0,0,0}}"); check("PadRight({{a, b, d}, {c}}, {3,4})", // "{{a,b,d,0},{c,0,0,0},{0,0,0,0}}"); check("PadRight({{a, b}, {c}}, {3,4})", // "{{a,b,0,0},{c,0,0,0},{0,0,0,0}}"); check("PadRight({{a, b}, c}, {3,4})", // "PadRight({{a,b},c},{3,4})"); check("PadRight({{}, {1, 2}, {1, 2, 3}})", // "{{0,0,0},{1,2,0},{1,2,3}}"); check("PadRight({a, b, c}, 10)", // "{a,b,c,0,0,0,0,0,0,0}"); check("PadRight({a, b, c}, 10, {x, y, z})", // "{a,b,c,x,y,z,x,y,z,x}"); check("PadRight({a, b, c}, 9, {x, y, z})", // "{a,b,c,x,y,z,x,y,z}"); check("PadRight({a, b, c}, 8, {x, y, z})", // "{a,b,c,x,y,z,x,y}"); check("PadRight({a, b, c}, 10, 42)", // "{a,b,c,42,42,42,42,42,42,42}"); check("PadRight({{0}},{{1,0},{0,1}})", // "PadRight({{0}},{{1,0},{0,1}})"); } @Test public void testParenthesis() { check("x+Parenthesis(a+b+c)", // "x+(a+b+c)"); check("TeXForm(x+Parenthesis(a+b+c))", // "x + (a + b + c)"); check("MathMLForm(x+Parenthesis(a+b+c))", // "\n" + "\n" + "\n" + "(c+b+a)+x"); } @Test public void testParametricPlot() { // wrong parameter call check("ParametricPlot(17,Heads->False,-1009,True)", // "ParametricPlot(17,Heads->False,-1009,True)"); } @Test public void testParserFixedPoint() { try { Parser p = new Parser(true); ASTNode obj = p.parse("{28, 21} /. {a_, b_} /; b != 0 -> {b, Mod(a, b)}"); assertEquals(obj.toString(), "ReplaceAll(List(28, 21), Rule(Condition(List(a_, b_), Unequal(b, 0)), List(b, Mod(a, b))))"); } catch (Exception e) { e.printStackTrace(); assertEquals("", e.getMessage()); } } @Test public void testPartition() { check("Partition({-1/2,-2,3},3,2147483647)", // "{{-1/2,-2,3}}"); check("Partition(f(),1)", // "f()"); check("Partition(f(x),1)", // "f(f(x))"); check("Partition({a,b,c,d,e,f},3,0)", // "Partition({a,b,c,d,e,f},3,0)"); check("Partition({a, b, c, d, e, f}, -1)", // "Partition({a,b,c,d,e,f},-1)"); check("Partition({a, b, c, d, e, f}, 2)", // "{{a,b},{c,d},{e,f}}"); check("Partition({a, b, c, d, e, f}, 3, 1)", // "{{a,b,c},{b,c,d},{c,d,e},{d,e,f}}"); check("Partition({a, b, c, d, e}, 2)", // "{{a,b},{c,d}}"); } @Test public void testPartitionsP() { // iteration limit check("PartitionsP(10001)", // "Hold(PartitionsP(10001))"); check("PartitionsP(101)", // "214481126"); check("PartitionsP(0)", // "1"); check("PartitionsP(-5)", // "0"); check("Table(PartitionsP(k), {k, 0, 12})", // "{1,1,2,3,5,7,11,15,22,30,42,56,77}"); check("PartitionsP(5)", // "7"); check("PartitionsP(6)", // "11"); check("PartitionsP(9)", // "30"); check("PartitionsP(50)", // "204226"); check("PartitionsP(100)", // "190569292"); check("PartitionsP(200)", // "3972999029388"); check("PartitionsP(300)", // "9253082936723602"); // check("PartitionsP(1000)", "24061467864032622473692149727991"); } @Test public void testPartitionsQ() { check("PartitionsQ(0)", // "1"); check("PartitionsQ(-5)", // "0"); check("PartitionsQ(3)", // "2"); check("PartitionsQ(5)", // "3"); check("PartitionsQ(6)", // "4"); check("PartitionsQ(10)", // "10"); check("PartitionsQ(15)", // "27"); check("PartitionsQ(16)", // "32"); check("PartitionsQ(17)", // "38"); check("PartitionsQ(18)", // "46"); check("PartitionsQ(20)", // "64"); check("PartitionsQ(50)", // "3658"); // upper limit to avid stack overflow check("PartitionsQ(201)", // "PartitionsQ(201)"); } @Test public void testPerfectNumber() { check("PerfectNumber(2^101)", // "PerfectNumber(2535301200456458802993406410752)"); // test Listable attribute check("PerfectNumber(Range(3))", // "{6,28,496}"); check("Table(PerfectNumber(i), {i,5})", // "{6,28,496,8128,33550336}"); check("PerfectNumber(1)", // "6"); check("PerfectNumber(2)", // "28"); check("PerfectNumber(3)", // "496"); check("PerfectNumber(6)", // "8589869056"); check("PerfectNumber(7)", // "137438691328"); check("PerfectNumber(8)", // "2305843008139952128"); // big integer results: check("PerfectNumber(9)", // "2658455991569831744654692615953842176"); check("PerfectNumber(10)", // "191561942608236107294793378084303638130997321548169216"); check("PerfectNumber(48)", // "PerfectNumber(48)"); } @Test public void testPerfectNumberQ() { check("PerfectNumberQ(6)", // "True"); check("PerfectNumberQ(1)", // "False"); check("PerfectNumberQ(35)", // "False"); check("Select(Range(1000), PerfectNumberQ)", // "{6,28,496}"); } @Test public void testPatternAndRules() { check("a + 2 + b + c + x * y /. n_Integer + s__Symbol + r_ -> {n, s, r}", // "{2,a,b+c+x*y}"); check( "f((-1)^i_*x_^(2*i_+1)/(2*i_+1)!, {i_Symbol,0,Infinity}) := Sin(x) /; FreeQ(x,i); f((-1)^i*x^(2*i+1)/(2*i+1)!, {i,0,Infinity})", // "Sin(x)"); check("f(a_.*x_^j_.,x_):={a,x,j}; f(a*x*z,x)", // "{a*z,x,1}"); check("f(a_.*x_^j_.,x_):={a,x,j}; f(a*b*x^3,x)", // "{a*b,x,3}"); check("f(a_.*x_^j_.,x_):={a,x,j}; f(a*b*x^3*y*z,x)", // "{a*b*y*z,x,3}"); check("a + b + c /. a + b -> t", // "c+t"); check("a + 2 + b + c + x * y /. n_Integer + s__Symbol + r_ -> {n, s, r}", // "{2,a,b+c+x*y}"); check("f(a, b, c, d) /. f(first_, rest___) -> {first, {rest}}", // "{a,{b,c,d}}"); check("f(4) /. f(x_?(# > 0&)) -> x ^ 2", // "16"); check("f(4) /. f(x_) /; x > 0 -> x ^ 2", // "16"); check("f(a, b, c, d) /. f(start__, end__) -> {{start}, {end}}", // "{{a},{b,c,d}}"); check("f(a) /. f(x_, y_:3) -> {x, y}", // "{a,3}"); // check("f(y, a->3) /. f(x_, OptionsPattern({a->2, b->5})) -> {x, // OptionValue(a), OptionValue(b)}", ""); } @Test public void testPattern() { // TODO parse this as Optional(Pattern(a,b),Pattern(c,d)) check("a:b:c:d", // "Optional(a:b,(c:d))"); // Pattern: First element in Pattern(3,3) is not a valid pattern name. check("Pattern(3,3)", // "3:3"); check("me:f(___,_Plus,___):={Unevaluated(me),Plus}", // ""); check("f(a,b,c,d+e,f,g)", // "{Unevaluated(f(a,b,c,d+e,f,g)),Plus}"); check("x:{___List} //FullForm", // "Pattern(x, List(BlankNullSequence(List)))"); check("me:CircleTimes(___,_Plus,___) //FullForm", // "Pattern(me, CircleTimes(BlankNullSequence(), Blank(Plus), BlankNullSequence()))"); check("x:{{_,_}...} // FullForm", // "Pattern(x, List(RepeatedNull(List(Blank(), Blank()))))"); check("x y_ : z", // "x*y_:z"); check("x y : z", // "x*(y:z)"); // check( // "a:b:c:d", // // "Optional(Pattern(a,b),Pattern(c,d))"); check("Options(f) = { a -> 1, b -> 2 }", // "{a->1,b->2}"); check("f(x_, opts : OptionsPattern()) := {x, Automatic, opts}", // ""); check("f(a)", // "{a,Automatic}"); check("f(a,c -> Automatic)", // "{a,Automatic,c->Automatic}"); } @Test public void testPatternSequence() { check("integersQ(__Integer) = True", // "True"); check("integersQ(__) = False", // "False"); check("integersQ(1,2,3)", // "True"); check("integersQ(1,2,a)", // "False"); } @Test public void testPatternOrder() { // see https://mathematica.stackexchange.com/questions/8619 check("PatternOrder(x_, 1)", // "-1"); // check("PatternOrder(g(_, _List), g(_, {___}))", // // "-1"); // check("PatternOrder(g({}, _List), g(_, _List))", // // "1"); check("PatternOrder(g({}, _List), g(_, {___}))", // "-1"); check("PatternOrder(g(a), g(_))", // "1"); check("PatternOrder(a,b)", // "1"); check("PatternOrder(g(a), g(b))", // "1"); // check("PatternOrder(__, (_) ..)", // // "-1"); } @Test public void testPatternTest() { // warning message: Pattern p_ appears on the right-hand-side of condition p_/;EvenQ(p_). check("{1, 2, 3, 4, 5} /. (p_ /; EvenQ(p_)) :> 0", // "{1,2,3,4,5}"); check("{1, 2, 3, 4, 5} /. (p_ /; EvenQ(p)) :> 0", // "{1,0,3,0,5}"); check("MatchQ({1,8,Pi},{__?Positive})", // "True"); check("$j(x_, y_:1, z_:2) := jp(x, y, z); $j(a,b)", // "jp(a,b,2)"); check("$j(x_, y_:1, z_:2) := jp(x, y, z); $j(a)", // "jp(a,1,2)"); check("$f(x_:2):={x};$f()", // "{2}"); check("$f(x_:2):={x};$f(a)", // "{a}"); check("MatchQ(3, _Integer?(#>0&))", // "True"); check("MatchQ(-3, _Integer?(#>0&))", // "False"); check("Cases({1,2,3,5,x,y,4},_?NumberQ)", // "{1,2,3,5,4}"); check("MatchQ({1,8,Pi},{__?Positive})", // "True"); check("MatchQ({1,I,0},{__?Positive})", // "False"); check("f(x_?NumericQ):= NIntegrate(Sin(t^3), {t, 0, x})", // ""); check("f(2)", // "0.451948"); check("f((1+Sqrt(2))/5)", // "0.0135768"); check("f(a)", // "f(a)"); check("{3,-5,2,7,-6,3} /. _?Negative:>0", // "{3,0,2,7,0,3}"); check("Cases(Range(0,350),_?(Divisible(#,7)&&Divisible(#,5)&))", // "{0,35,70,105,140,175,210,245,280,315,350}"); check("$f(n_?NonNegative, p_?PrimeQ):=n^p; $f(2,3)", // "8"); check("$f(n_?NonNegative, p_?PrimeQ):=n^p; $f(2,4)", // "$f(2,4)"); check("MatchQ({{a,b},{c,d}},{_,_}?MatrixQ)", // "True"); check("MatchQ({a,b},{_,_}?MatrixQ)", // "False"); check("Cases({{a,b},{1,2,3},{{d,6},{d,10}}}, {_,_}?VectorQ)", // "{{a,b}}"); check("Cases({{a,b},{1,2,3},{{d,6},{d,10}}}, {x_,y_}/;!ListQ(x)&&!ListQ(y))", // "{{a,b}}"); } @Test public void testPermutations() { // TODO // check("Permutations({1, 2, 1} )", // // ""); // TODO // check( // "\"ABCA\" // Characters // Permutations ", // // // "{{A,A,B,C},{A,A,C,B},{A,B,A,C},{A,B,C,A},{A,C,A,B},{A,C,B,A},{B,A,A,C},{B,A,C,A},{B,C,A,A},{C,A,A,B},{C,A,B,A},{C,B,A,A}}"); check("Permutations(x^2,{3})", // "{}"); check("Permutations(x^2,{2})", // "{x^2,2^x}"); check("Permutations(x^2,{1})", // "{x,2}"); check("Permutations(x^2,{0})", // "{{}}"); check("Permutations(x^2,{-1})", // "Permutations(x^2,{-1})"); check("Permutations({1, 2, 3}, 2)", // "{{},{1},{2},{3},{1,2},{1,3},{2,1},{2,3},{3,1},{3,2}}"); check("Permutations({1, 2, 3}, {2})", // "{{1,2},{1,3},{2,1},{2,3},{3,1},{3,2}}"); check("Permutations({a,b,c})", // "{{a,b,c},{a,c,b},{b,a,c},{b,c,a},{c,a,b},{c,b,a}}"); check("Permutations({a,b,c}, {2})", // "{{a,b},{a,c},{b,a},{b,c},{c,a},{c,b}}"); check("Permutations({a},{0})", // "{{}}"); check("Permutations({a,b,c,d},{3})", // "{{a,b,c},{a,b,d},{a,c,b},{a,c,d},{a,d,b},{a,d,c},{b,a,c},{b,a,d},{b,c,a},{b,c,d},{b,d,a},{b,d,c},{c,a,b},{c,a,d},{c,b,a},{c,b,d},{c,d,a},{c,d,b},{d,a,b},{d,a,c},{d,b,a},{d,b,c},{d,c,a},{d,c,b}}"); check("Permutations({a,a,b})", // "{{a,a,b},{a,b,a},{b,a,a}}"); check("Permutations({a,a,b,b})", // "{{a,a,b,b},{a,b,a,b},{a,b,b,a},{b,a,a,b},{b,a,b,a},{b,b,a,a}}"); check("Permutations({a,a,b,b},{3})", // "{{a,a,b},{a,b,a},{a,b,b},{b,a,a},{b,a,b},{b,b,a}}"); } @Test public void testPi() { check("N(E, 10)", // "2.718281828"); check("N(Pi, 10)", // "3.141592654"); check("N(Pi, 11)", // "3.1415926536"); check("N(Pi, 12)", // "3.14159265359"); check("N(Pi, 13)", // "3.14159265359"); check("N(Pi, 14)", // "3.1415926535898"); check("N(Pi, 15)", // "3.14159265358979"); check("N(Pi, 16)", // "3.141592653589793"); check("N(Pi, 17)", // "3.1415926535897932"); check("N(Pi, 18)", // "3.14159265358979323"); check("N(Pi, 19)", // "3.141592653589793238"); check("N(Pi, 20)", // "3.1415926535897932384"); } @Test public void testPick() { // check( // "Pick(<|s1-><|a->0,b:>1|>,s2:><|a->0,b:>1|>|>,(1+Sqrt(5))/2,5)", // // "{RuleDelayed(Association(0))}"); check("Pick({{1, 2}, {2, 3}, {5, 6}}, {{1}, {2, 3}, {{3, 4}, {4, 5}}}, {1} | 2 | {4, 5})", // "{{1,2},{2},{6}}"); // message: Pick: Expressions {{1,2},{2,3},{5,6}} and {{1},{2,3},{{3,4},{4,5}}} have // incompatible shapes. check("Pick({{1, 2}, {2, 3}, {5, 6}}, {{1}, {2, 3}, {{3, 4}, {4, 5}}}, {4, 5})", // "Pick({{1,2},{2,3},{5,6}},{{1},{2,3},{{3,4},{4,5}}},{4,5})"); check("Pick({2, {3, 4}}, {3, {4, 5}}, 5)", // "{{4}}"); check("Pick({2, {3, 4}}, {3, {4, 5}}, {4, 5})", // "{{3,4}}"); check("data = SparseArray({{1, 3} -> 2, {2, 2} -> 3, {3, 3} -> 5})", // "SparseArray(Number of elements: 3 Dimensions: {3,3} Default value: 0)"); check("Pick(data, IdentityMatrix(3), 1)", // "{{0},{3},{5}}"); check("sel = SparseArray({1 -> True, 100 -> True, _ -> False}, 100)", // "SparseArray(Number of elements: 2 Dimensions: {100} Default value: False)"); check("Pick(Range(100), sel)", // "{1,100}"); check("Pick(Characters(\"ABC\"), {True, False, True})", // "{A,C}"); check("Pick({a, b, c, d, e}, {1, 0, 1, 0, 0}, Except(1, _Integer))", // "{b,d,e}"); check("Pick({a, b, c, d, e}, {1, 0, 1, 0, 0}, Except(1))", // "{a,b,c,d,e}"); check("Pick({1, 2, 3}, False)", // "Identity()"); check("Pick(x, {1, 2, 3}, _?NumericQ)", // "Identity()"); check("Pick(x, {1, 2, 3}, _List)", // "x"); check("Pick({a, b, c, d, e}, {1, 0, 1, 0, 0}, 1)", // "{a,c}"); check("Pick({{a, b, c}, {d, e, f}}, {{1, 0, 0}, {0, 1, 1}}, 1)", // "{{a},{e,f}}"); check("Pick({a, b, c, d}, {True, False, False, True})", // "{a,d}"); check("Pick({a, b, c, d}, {1, 2, 3, 4}, 2 | 4)", // "{b,d}"); check("Pick(f(1, 2, 3, 4, 5, 6), {1, 0, 1, 0, 1, 1}, 1)", // "f(1,3,5,6)"); } @Test public void testPiecewise() { // message Piecewise: The first argument x of Piecewise is not a list of pairs. check("Piecewise(x)", // "Piecewise(x)"); check("Piecewise({{(-1)^(1+n)/n,n>=1},{0,n==0}},0)", // "Piecewise({{(-1)^(1+n)/n,n>=1}},0)"); check("Piecewise({{x^2, x < 0}, {x, x > 0}})", // "Piecewise({{x^2,x<0},{x,x>0}},0)"); check("Piecewise({{-Log(x),x<=(0+(-1)*0)*1/1}},Log(x))", // "Piecewise({{-Log(x),x<=0}},Log(x))"); check("Piecewise({{x^2, x < 0}, {x, x > 0}}) /. x->3", // "3"); check("Piecewise({{(a^0*Log(a)^n)/n!,n>=0}},0)", // "Piecewise({{Log(a)^n/n!,n>=0}},0)"); check("Piecewise({})", // "0"); check("Piecewise({},0)", "0"); check("Piecewise({{0, x <= 0}}, 1)", // "Piecewise({{0,x<=0}},1)"); check("Piecewise({{1, False}})", // "0"); check("Piecewise({{0 ^ 0, False}}, -1)", // "-1"); check( "$pw = Piecewise({{Sin(x)/x, x < 0}, {1, x == 0}}, -x^2/100 + 1); $pw /. {{x -> -5}, {x -> 0}, {x -> 5}}", // "{Sin(5)/5,1,3/4}"); check("Piecewise({{e1, True}, {e2, d2}, {e3, d3}}, e0)", // "e1"); check("Piecewise({{e1, d1}, {e2, d2}, {e3, True}, {e4, d4}, {e5, d5}}, e0)", // "Piecewise({{e1,d1},{e2,d2}},e3)"); check("Piecewise({{e1, d1}, {e2, d2}, {e3, d2 && d3}, {e4, d4}}, e0)", // "Piecewise({{e1,d1},{e2,d2},{e3,d2&&d3},{e4,d4}},e0)"); check("Piecewise({{e1, d1}, {e2, d2}, {e3, False}, {e4, d4}, {e5, d5}}, e0)", // "Piecewise({{e1,d1},{e2,d2},{e4,d4},{e5,d5}},e0)"); } @Test public void testPiecewiseExpand() { check("PiecewiseExpand(KroneckerDelta(x, y,z,u,v))", // "Piecewise({{1,u-v==0&&v-x==0&&x-y==0&&y-z==0}},0)"); // PiecewiseExpand check("PiecewiseExpand(f(x) + Piecewise({{g(x),x>=0}},0) + z(x) )", // "Piecewise({{f(x)+g(x)+z(x),x>=0}},f(x)+z(x))"); check("PiecewiseExpand(f(x) + Piecewise({{g(x),x>=0}},0) )", // "Piecewise({{f(x)+g(x),x>=0}},f(x))"); check("PiecewiseExpand(f(x) * Piecewise({{g(x),x>=0}},0) * z(x) )", // "Piecewise({{f(x)*g(x)*z(x),x>=0}},0)"); check("PiecewiseExpand(f(x) * Piecewise({{g(x),x>=0}},0) )", // "Piecewise({{f(x)*g(x),x>=0}},0)"); check("PiecewiseExpand(f(x)*Boole(x))", // "Piecewise({{f(x),x}},0)"); check("PiecewiseExpand(KroneckerDelta(x))", // "Piecewise({{1,x==0}},0)"); check("PiecewiseExpand(DiscreteDelta(x))", // "Piecewise({{1,x==0}},0)"); check("PiecewiseExpand(KroneckerDelta(x, y))", // "Piecewise({{1,x-y==0}},0)"); check("PiecewiseExpand(DiscreteDelta(x, y))", // "Piecewise({{1,x==0&&y==0}},0)"); check("PiecewiseExpand(KroneckerDelta(x, y,z,u,v))", // "Piecewise({{1,u-v==0&&v-x==0&&x-y==0&&y-z==0}},0)"); check("PiecewiseExpand(DiscreteDelta(x, y,z,u,v))", // "Piecewise({{1,u==0&&v==0&&x==0&&y==0&&z==0}},0)"); check("PiecewiseExpand(Abs(x), Reals)", // "Piecewise({{-x,x<0}},x)"); check("PiecewiseExpand(Arg(x), Reals)", // "Piecewise({{Pi,x<0}},0)"); check("PiecewiseExpand(Sign(x), Reals)", // "Piecewise({{-1,x<0},{1,x>0}},0)"); check("PiecewiseExpand(Abs(x))", // "Abs(x)"); check("PiecewiseExpand(Clip(x))", // "Piecewise({{-1,x<-1},{1,x>1}},x)"); check("PiecewiseExpand(Clip(x,{-7,5}))", // "Piecewise({{-7,x<-7},{5,x>5}},x)"); check("PiecewiseExpand(If(x, y, z))", // "Piecewise({{y,x}},z)"); check("PiecewiseExpand(UnitStep(x, y, z))", // "Piecewise({{1,x>=0&&y>=0&&z>=0}},0)"); check("PiecewiseExpand(Ramp(x))", // "Piecewise({{x,x>=0}},0)"); } @Test public void testPlus() { check("(1*Plus+0)[10,20]", // "30"); check("-2*Cosh(x)^2+5*Sinh(x)^2", // "-2+3*Sinh(x)^2"); check("a+3*Cos(x)^2-2*Cosh(x)^2+11*Sin(x)^2+5*Sinh(x)^2", // "1+a+8*Sin(x)^2+3*Sinh(x)^2"); check("Cosh(Log(3)/2)^2-Sinh(Log(3)/2)^2", // "1"); check("-Cosh(x)^2-Sinh(x)^2", // "-Cosh(x)^2-Sinh(x)^2"); check("Cosh(x)^2+Sinh(x)^2", // "Cosh(x)^2+Sinh(x)^2"); check("Cosh(x)^2-Sinh(x)^2", // "1"); check("7*Cosh(x)^2-2*Sinh(x)^2", // "2+5*Cosh(x)^2"); check("2*Cosh(x)^2-5*Sinh(x)^2", // "2-3*Sinh(x)^2"); check("-Cosh(x)^2+Sinh(x)^2", // "-1"); check("-7*Cosh(x)^2+2*Sinh(x)^2", // "-2-5*Cosh(x)^2"); check("x+1/(3!*E)-Infinity+1/(5!*E)+1/(6!*E)", // "-Infinity+x"); check("Refine(Infinity+x, x>0)", // "Infinity"); check("1+I", // "1+I"); check("Infinity - Infinity", // "Indeterminate"); check("-I+y+Interval({c,d})", // "-I+y+Interval({c,d})"); check("-I+<|x->y|>+Interval({c,d})", // "<|x->-I+y+Interval({c,d})|>"); check("Sin(0.1851851851851852*Cos(7/11)*x)", // "Sin(0.148937*x)"); check("1-{0,1,2}", // "{1,0,-1}"); check("-Infinity+0.0", // "-Infinity"); check("Infinity+0.0", // "Infinity"); check("-Infinity+Sin(-2)", // "-Infinity"); check("-Infinity+Log(2)", // "-Infinity"); check("Infinity+Sin(-2)", // "Infinity"); check("Infinity+Log(2)", // "Infinity"); check("{1,2}+{4,5,6}", // "{1,2}+{4,5,6}"); // check("2+4/3*2^b/c", // // "2+2^(2+b)/(3*c)"); check("Refine(Infinity+x, x>0)", // "Infinity"); // String s = System.getProperty("os.name"); // if (s.contains("Windows")) { check("N(Pi, 30) + N(E, 30)", // "5.85987448204883847382293085463"); check("N(Pi, 30) + N(E, 30) // Precision", // "30"); check("N(Pi, 30) + I", // "3.14159265358979323846264338327+I*1"); check("N(Pi, 30) + E", // "5.85987448204883847382293085463"); // } check("1 + 2", // "3"); check("a + b + a", // "2*a+b"); check("a + a + 3 * a", // "5*a"); check("a + b + 4.5 + a + b + a + 2 + 1.5*b", // "6.5+3*a+3.5*b"); check("Plus @@ {2, 4, 6}", // "12"); check("Plus @@ Range(1000)", // "500500"); check("a /. n_. + x_ :> {n, x}", // "{0,a}"); check("-2*a - 2*b", // "-2*a-2*b"); check("1 - I * Sqrt(3)", // "1-I*Sqrt(3)"); check("Head(3 + 2*I)", // "Complex"); check("Interval({1,6})+Interval({0,2})", // "Interval({1,8})"); check("Interval({a,b})+z", // "z+Interval({a,b})"); check("(Interval({-1,1})+1/2)^2 - 1/4", // "Interval({-1/4,2})"); check("f+Interval({a,b})+Interval({c,d})", // "f+Interval({a+c,b+d})"); check("Interval({a,b})+Interval({c,d})", // "Interval({a+c,b+d})"); check("1+Interval({2,3})", // "Interval({3,4})"); check("Plus()", // "0"); } @Test public void testPlusMinus() { check("\\[PlusMinus] x", // "±x"); check("x \\[PlusMinus] y", // "x±y"); } @Test public void testPochhammer() { check("Pochhammer(1.011111111111000000000000000, 8)", // "41552.27584908778038088829576"); check("Pochhammer(2.4, 8.5)", // "2.31022*10^6"); check("Pochhammer(0, 1285)", // "0"); check("N(Pochhammer(1/3, 7),50)", // "505.97165066300868770004572473708276177411979881115"); check("Pochhammer(2.0+5.0*I, 8.0*I)", // "2.13868*10^-6+I*(-0.0000142187)"); // iteration limit exceeded check("Pochhammer(3/4,10007)", // "Hold(Pochhammer(3/4,10007))"); check("Pochhammer(2-b,1)", // "2-b"); check("Pochhammer({-7,-6,-5,-4,-3,-2,-1,0,1,2,3},-5)", // "{-1/95040,-1/55440,-1/30240,-1/15120,-1/6720,-1/2520,-1/720,-1/120,ComplexInfinity,ComplexInfinity,ComplexInfinity}"); check("Pochhammer({-2,-1,0,1,2,3},-2)", // "{1/12,1/6,1/2,ComplexInfinity,ComplexInfinity,1/2}"); check("Pochhammer(m, n) // FunctionExpand", // "Gamma(m+n)/Gamma(m)"); check("Pochhammer(2.4, 8.5)", // "2.31022*10^6"); // http://oeis.org/A054654 check( "crow(n_) := Reverse( CoefficientList( (-1)^n*Pochhammer(-x, n), x) ); Flatten( Table(crow(n), {n, 0, 8}))", // "{1,1,0,1,-1,0,1,-3,2,0,1,-6,11,-6,0,1,-10,35,-50,24,0,1,-15,85,-225,274,-120,0,1,-\n" + "21,175,-735,1624,-1764,720,0,1,-28,322,-1960,6769,-13132,13068,-5040,0}"); check("Pochhammer(0, 0)", // "1"); check("Pochhammer(0, 42)", // "0"); check("Pochhammer(0, -42)", // "1/1405006117752879898543142606244511569936384000000000"); check("Pochhammer(a, -3)", // "1/((-3+a)*(-2+a)*(-1+a))"); check("Pochhammer(a, -1)", // "1/(-1+a)"); check("Pochhammer(b-c, -10)", // "1/((-10+b-c)*(-9+b-c)*(-8+b-c)*(-7+b-c)*(-6+b-c)*(-5+b-c)*(-4+b-c)*(-3+b-c)*(-2+b-c)*(-\n" + "1+b-c))"); check("Pochhammer(b-c, 2)", // "(b-c)*(1+b-c)"); check("Pochhammer(b-c, 3)", // "(b-c)*(1+b-c)*(2+b-c)"); check("Pochhammer(c-b,42)", // "(-b+c)*(1-b+c)*(2-b+c)*(3-b+c)*(4-b+c)*(5-b+c)*(6-b+c)*(7-b+c)*(8-b+c)*(9-b+c)*(\n" + // "10-b+c)*(11-b+c)*(12-b+c)*(13-b+c)*(14-b+c)*(15-b+c)*(16-b+c)*(17-b+c)*(18-b+c)*(\n" + // "19-b+c)*(20-b+c)*(21-b+c)*(22-b+c)*(23-b+c)*(24-b+c)*(25-b+c)*(26-b+c)*(27-b+c)*(\n" + // "28-b+c)*(29-b+c)*(30-b+c)*(31-b+c)*(32-b+c)*(33-b+c)*(34-b+c)*(35-b+c)*(36-b+c)*(\n" + // "37-b+c)*(38-b+c)*(39-b+c)*(40-b+c)*(41-b+c)"); check("Pochhammer(2,3)", // "24"); check("Pochhammer(4, 8)", // "6652800"); check("Pochhammer(10, 6)", // "3603600"); check("Pochhammer(10, -6)", // "1/60480"); check("Pochhammer(-10, -6)", // "1/5765760"); check("Pochhammer(-10, -7)", // "-1/98017920"); check("Pochhammer(-10, -12)", // "1/309744468633600"); check("Pochhammer(3/2, 1/2)", // "2/Sqrt(Pi)"); check("Pochhammer(-5, -3)", // "-1/336"); } @Test public void testPolyGamma() { checkNumeric("PolyGamma(0, 0.166667)", // "-6.332115065894639"); checkNumeric("PolyGamma(0, 0.166667+1/2)", // "-1.3182333944951956"); check("PolyGamma(-0.8)", // "-4.03904"); // http://fungrim.org/entry/ea2482/ check("PolyGamma(2147483647,3.1415926535897930)", // "6.8635973023279951*10^18039905265"); check("N(PolyGamma(22/10), 50)", // "0.54429343674114503778612537088338122850774505912665"); check("PolyGamma(2.20000000000000000000000)", // "0.544293436741145037786125"); check("PolyGamma(3, 1)", // "Pi^4/15"); check("PolyGamma(1, 1)", // "Pi^2/6"); check("PolyGamma(100.5)", // "4.60517"); check("PolyGamma(2.2)", // "0.544293"); check("PolyGamma(1)", // "-EulerGamma"); // http://fungrim.org/entry/ada157/ check("PolyGamma(2)", // "1-EulerGamma"); check("PolyGamma(3)", // "3/2-EulerGamma"); check("PolyGamma(0,-42)", // "ComplexInfinity"); check("PolyGamma(-1,z)", // "LogGamma(z)"); check("PolyGamma(-1,0)", // "Infinity"); check("PolyGamma(-1,12)", // "Log(39916800)"); check("PolyGamma(-1,-7)", // "Infinity"); check("PolyGamma(-1)", // "ComplexInfinity"); check("PolyGamma(-1,1)", // "0"); check("PolyGamma(-2)", // "ComplexInfinity"); check("PolyGamma(1,1/4)", // "8*Catalan+Pi^2"); check("PolyGamma(1,3/4)", // "-8*Catalan+Pi^2"); check("PolyGamma(2,5/6)", // "4*Sqrt(3)*Pi^3-182*Zeta(3)"); check("PolyGamma({1,2,3,4,5})", // "{-EulerGamma,1-EulerGamma,3/2-EulerGamma,11/6-EulerGamma,25/12-EulerGamma}"); check("D(PolyGamma(x),{x,n})", // "PolyGamma(n,x)"); } @Test public void testPolyLog() { // check("PolyLog(10007,-1.5707963267948966)", // // ""); check("PolyLog(-42,Infinity)", // "Indeterminate"); check("PolyLog(0,Infinity)", // "Indeterminate"); check("PolyLog(2,Infinity)", // "-Infinity"); check("PolyLog(42,-Infinity)", // "-Infinity"); checkNumeric("PolyLog(1, 0.333333)", // "0.4054646081082894"); checkNumeric("PolyLog(2, 0.9)", // "1.2997147230049588"); checkNumeric("PolyLog(0, 5.0)", // "-1.25"); checkNumeric("N(PolyLog(1, 1/3), 50)", // "0.40546510810816438197801311546434913657199042346249"); checkNumeric("PolyLog(2, 0.300000000000000000)", // "0.326129510075476069"); checkNumeric("PolyLog(0.2 + I, 0.5 - I)", // "-0.08985258966284129+I*(-0.5958648241210646)"); // issue #929 // message Infinite or NaN number in z1 calculation. checkNumeric("(PolyLog(2,E^(I*1/270*Pi^2)))/Pi // N", // "0.5054280619497805+I*0.0501372676125785"); checkNumeric("PolyLog(2,0.9993319736282411 + 0.03654595031305655*I)", // "1.5878490863395573+I*0.1575108716027421"); check("PolyLog(2,z) + PolyLog(2,1-z)", // "Pi^2/6-Log(1-z)*Log(z)"); check("PolyLog(2,Sin(7)) + PolyLog(2,1-Sin(7))", // "Pi^2/6-Log(1-Sin(7))*Log(Sin(7))"); check("PolyLog(2,E^(4*I*Pi))", // "Pi^2/6"); check("PolyLog(2,E^(42*I*Pi))", // "Pi^2/6"); check("PolyLog(2,E^(41*I*Pi))", // "-Pi^2/12"); // TODO https://github.com/mtommila/apfloat/issues/34 // check("PolyLog(2147483647,-3.1415)", // // " "); check("PolyLog(2147483647,1)", // "Zeta(2147483647)"); check("PolyLog(n,1,z)", // "PolyLog(1+n,z)"); check("PolyLog(0, 1, z)", // "-Log(1-z)"); check("PolyLog(-4,z)", // "(z+11*z^2+11*z^3+z^4)/(1-z)^5"); check("PolyLog(-2147483648,2.718281828459045)", // "PolyLog(-2.14748*10^9,2.71828)"); check("PolyLog(2,0)", // "0"); check("PolyLog(2,-1)", // "-Pi^2/12"); check("PolyLog(2,1)", // "Pi^2/6"); check("PolyLog(2,1/2)", // "Pi^2/12-Log(2)^2/2"); check("PolyLog(2,2)", // "Pi^2/4-I*Pi*Log(2)"); check("PolyLog(2,I)", // "I*Catalan-Pi^2/48"); check("PolyLog(2,-I)", // "-I*Catalan-Pi^2/48"); check("PolyLog(2,1-I)", // "-I*Catalan+Pi^2/16-I*1/4*Pi*Log(2)"); check("PolyLog(2,1+I)", // "I*Catalan+Pi^2/16+I*1/4*Pi*Log(2)"); check("PolyLog(3,1)", // "Zeta(3)"); check("PolyLog(f(x),-1)", // "(-1+2^(1-f(x)))*Zeta(f(x))"); check("PolyLog(0,f(x))", // "f(x)/(1-f(x))"); check("PolyLog(1,f(x))", // "-Log(1-f(x))"); check("PolyLog(-1,f(x))", // "f(x)/(1-f(x))^2"); check("PolyLog(-2,f(x))", // "(f(x)+f(x)^2)/(1-f(x))^3"); check("PolyLog(-3,f(x))", // "(f(x)+4*f(x)^2+f(x)^3)/(1-f(x))^4"); check("Table(PolyLog(n, 1), {n, 1, 4})", // "{Infinity,Pi^2/6,Zeta(3),Pi^4/90}"); check("Table(PolyLog(n, z), {n, -2, 1})", // "{(z+z^2)/(1-z)^3,z/(1-z)^2,z/(1-z),-Log(1-z)}"); check("PolyLog(n,-1)", // "(-1+2^(1-n))*Zeta(n)"); checkNumeric("PolyLog(1,1)", // "Infinity"); checkNumeric("PolyLog(1.0,1.0)", // "Infinity"); checkNumeric("Table(PolyLog(1.0,z), {z,-2.0,2.0,0.1})", // "{-1.0986122886681098,-1.0647107369924282,-1.0296194171811581,-0.9932517730102833,-0.9555114450274362," // + "-0.9162907318741549,-0.8754687373538997,-0.8329091229351038,-0.7884573603642698,-0.7419373447293769," // + "-0.6931471805599448,-0.6418538861723944,-0.5877866649021186,-0.5306282510621699,-0.4700036292457351," // + "-0.40546510810816394,-0.33647223662121256,-0.26236426446749056,-0.18232155679395404,-0.09531017980432434," // + "0.0,0.10536051565782702,0.22314355131421054,0.3566749439387334,0.5108256237659918,0.6931471805599466,0.9162907318741567,1.2039728043259381,1.6094379124341034,2.3025850929940517," // + "Indeterminate,2.3025850929940384+I*(-3.141592653589793),1.609437912434096+I*(-3.141592653589793),1.2039728043259328+I*(-3.141592653589793),0.9162907318741526+I*(-3.141592653589793),0.6931471805599431+I*(-3.141592653589793),0.5108256237659887+I*(-3.141592653589793),0.35667494393873056+I*(-3.141592653589793),0.22314355131420804+I*(-3.141592653589793),0.10536051565782467+I*(-3.141592653589793),-1.332267629550187E-15+I*(-3.141592653589793)}"); checkNumeric("Table(N(PolyLog(1,z),20), {z,-2,2,1/10})", // "{-1.0986122886681096913,-1.0647107369924283431,-1.0296194171811582399,-0.99325177301028339016,-0.95551144502743636145,-0.91629073187415506518,-0.87546873735389993562,-0.83290912293510400678,-0.78845736036427016946,-0.74193734472937731248,Indeterminate,-0.64185388617239477599,-0.58778666490211900818,-0.53062825106217039623,-0.47000362924573555365,-0.40546510810816438197,-0.3364722366212129305,-0.26236426446749105203,-0.18232155679395462621,-0.095310179804324860043," + "0,0.10536051565782630122,0.22314355131420975576,0.35667494393873237891,0.5108256237659906832,0.69314718055994530941,0.91629073187415506518,1.2039728043259359926,1.6094379124341003746,2.302585092994045684," + "Infinity,2.302585092994045684+I*(-3.1415926535897932384),1.6094379124341003746+I*(-3.1415926535897932384),1.2039728043259359926+I*(-3.1415926535897932384),0.9162907318741550651+I*(-3.1415926535897932384),0.6931471805599453094+I*(-3.1415926535897932384),0.5108256237659906832+I*(-3.1415926535897932384),0.3566749439387323789+I*(-3.1415926535897932384),0.2231435513142097557+I*(-3.1415926535897932384),0.1053605156578263012+I*(-3.1415926535897932384),I*(-3.1415926535897932384)}"); } @Test public void testPolynomialExtendedGCD() { check("PolynomialExtendedGCD(e*x^2+d,-2*d*e^2*Sqrt(-e/d)*x+2*d*e^2,z)", // "{1,{0,1/(2*d*e^2-2*d*e^2*Sqrt(-e/d)*x)}}"); check("PolynomialExtendedGCD(e*x^2+d,-2*d*e^2*Sqrt(-e/d)*x+2*d*e^2,Infinity)", // "PolynomialExtendedGCD(e*x^2+d,-2*d*e^2*Sqrt(-e/d)*x+2*d*e^2,Infinity)"); check("PolynomialExtendedGCD({},3*x,f(x,y))", // "PolynomialExtendedGCD({},3*x,f(x,y))"); check("PolynomialExtendedGCD(e*x^2+d,-2*d*e^2*Sqrt(-e/d)*x+2*d*e^2,0)", // "PolynomialExtendedGCD(e*x^2+d,-2*d*e^2*Sqrt(-e/d)*x+2*d*e^2,0)"); check("PolynomialExtendedGCD(Infinity,3*x,f(x,y))", // "PolynomialExtendedGCD(Infinity,3*x,f(x,y))"); check("PolynomialExtendedGCD(2*x^2+3,3*x,f(x,y))", // "{1,{0,1/(3*x)}}"); check("PolynomialExtendedGCD(a[x],b[x],x)", // "{b(x),{0,1}}"); check("PolynomialExtendedGCD(a[x],b,x)", // "{1,{0,1/b}}"); check("PolynomialExtendedGCD(a,b,x)", // "{1,{0,1/b}}"); // TODO make result consistent with PolynomiaGCD check("PolynomialExtendedGCD(e*x^2 + d, ( -2*d*e^2*Sqrt(-e/d) )*x + 2*d*e^2, x )", // "{-1/Sqrt(-e/d)+x,{0,-1/(2*d*e^2*Sqrt(-e/d))}}"); // Wikipedia: finite field GF(28) - p = x8 + x4 + x3 + x + 1, and a = x6 + x4 + // x + 1 check("PolynomialExtendedGCD(x^8 + x^4 + x^3 + x + 1, x^6 + x^4 + x + 1, x, Modulus->2)", // "{1,{1+x^2+x^3+x^4+x^5,x+x^3+x^6+x^7}}"); // check("PolynomialExtendedGCD((x - a)*(b*x - c)^2, (x - a)*(x^2 - // b*c), x)", ""); check("PolynomialExtendedGCD((x - 1)*(x - 2)^2, (x - 1)*(x^2 - 3), x)", // "{-1+x,{7+4*x,9-4*x}}"); check("PolynomialExtendedGCD((x - 1)^2*(x - 2)^2, (x - 1)*(x^2 - 3), x)", // "{-1+x,{1/2*(19+11*x),1/2*(-26+36*x-11*x^2)}}"); check("PolynomialExtendedGCD((x - 1)^2*(x - 2)^2, (x - 1)*(x^2 - 3), x, Modulus -> 2)", // "{1+x^2,{1,1+x}}"); check("PolynomialExtendedGCD(a*x^2 + b*x + c, x - r, x)", // "{1,{1/(c+b*r+a*r^2),(-b-a*r-a*x)/(c+b*r+a*r^2)}}"); } @Test public void testPolynomialGCD() { // TODO https://github.com/kredel/java-algebra-system/issues/15 check("PolynomialGCD(-1/2,x^2-5*x+(-1)*6)", // "1/2"); check("PolynomialGCD(3*x+9,-3.14159)", // "PolynomialGCD(9+3*x,-3.14159)"); check("PolynomialGCD({},0.5,x^4+(-1)*1,x^5+(-1)*1,x^6+(-1)*1,x^7+(-1)*1)", // "{}"); check("PolynomialGCD(f(x),f(x)*x^2)", // "f(x)"); // wikipedia example https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor check("PolynomialGCD(x^2 + 7*x + 6, x^2-5*x-6)", // "1+x"); check("PolynomialGCD(a,b )", // "1"); check("PolynomialGCD(e*x^2 + d, ( -2*d*e^2*Sqrt(-e/d) )*x + 2*d*e^2 )", // "1"); // TODO difference to MMA handle Extension->Automatic correctly check("PolynomialGCD(x^2 - 2, x - Sqrt(2))", // "-Sqrt(2)+x"); // check("PolynomialGCD(I*2,12)", "2"); check("PolynomialGCD(a+b*x,c+d*x)", // "1"); check("PolynomialGCD()", // "PolynomialGCD()"); check("PolynomialGCD(x)", // "x"); check("PolynomialGCD(-12)", // "12"); check("PolynomialGCD(x,x)", // "x"); check("PolynomialGCD((x + 1)^3, x^3 + x, Modulus -> 2)", // "(1+x)^2"); check("PolynomialGCD((x - a)*(b*x - c)^2, (x - a)*(x^2 - b*c))", // "-a+x"); check("PolynomialGCD((1 + x)^2*(2 + x)*(4 + x), (1 + x)*(2 + x)*(3 + x))", // "2+3*x+x^2"); check("PolynomialGCD(x^4 - 4, x^4 + 4*x^2 + 4)", // "2+x^2"); check("PolynomialGCD(x^2 + 2*x*y + y^2, x^3 + y^3)", // "x+y"); check("PolynomialGCD(x^2 - 1, x^3 - 1, x^4 - 1, x^5 - 1, x^6 - 1, x^7 - 1)", // "-1+x"); check("PolynomialGCD(x^2 - 4, x^2 + 4*x + 4)", // "2+x"); check("PolynomialGCD(3*x + 9, 6*x^3 - 3*x + 12)", // "3"); } @Test public void testPolynomialLCM() { // TODO https://github.com/kredel/java-algebra-system/issues/15 check("PolynomialLCM(x^2+7*x+6,-1/2)", // "-6-7*x-x^2"); check("PolynomialGCD(1/2,2)", // "1/2"); check("PolynomialLCM(1/2,2)", // "2"); check("PolynomialLCM({},0.5,x^4+(-1)*1,x^5+(-1)*1,x^6+(-1)*1,x^7+(-1)*1)", // "{}"); check("PolynomialLCM(f(x)*y^3,f(x)*x^2)", // "x^2*y^3*f(x)"); // wikipedia example https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor check("PolynomialLCM(x^2 + 7*x + 6, x^2-5*x-6)", // "-36-36*x+x^2+x^3"); check("PolynomialLCM(a+b*x,c+d*x)", // "(a+b*x)*(c+d*x)"); check("PolynomialLCM()", // "PolynomialLCM()"); check("PolynomialLCM(x)", // "x"); check("PolynomialLCM(x,x)", // "x"); check("PolynomialLCM(-12)", // "12"); check( "Expand((-1+x)*(1+x)*(1+x^2)*(1-x+x^2)*(1+x+x^2)*(1+x+x^2+x^3+x^4)*(1+x+x^2+x^3+x^4+x^5+x^6))", // "-1-2*x-4*x^2-6*x^3-8*x^4-9*x^5-9*x^6-7*x^7-4*x^8+4*x^10+7*x^11+9*x^12+9*x^13+8*x^\n" + "14+6*x^15+4*x^16+2*x^17+x^18"); check("PolynomialLCM((1 + x)^2*(2 + x)*(4 + x), (1 + x)*(2 + x)*(3 + x))", // "24+74*x+85*x^2+45*x^3+11*x^4+x^5"); check("Expand((1+x)^2*(2+x)*(3+x)*(4+x))", // "24+74*x+85*x^2+45*x^3+11*x^4+x^5"); check("PolynomialLCM(x^2 + 2*x*y + y^2, x^3 + y^3)", // "x^4+x^3*y+x*y^3+y^4"); check("Expand((x+y)*(x^3+y^3))", // "x^4+x^3*y+x*y^3+y^4"); check("PolynomialLCM(x^2 - 1, x^3 - 1, x^4 - 1, x^5 - 1, x^6 - 1, x^7 - 1)", // "-1-2*x-4*x^2-6*x^3-8*x^4-9*x^5-9*x^6-7*x^7-4*x^8+4*x^10+7*x^11+9*x^12+9*x^13+8*x^\n" + "14+6*x^15+4*x^16+2*x^17+x^18"); } @Test public void testPolynomialQ() { check("PolynomialQ(x, 1234)", // "PolynomialQ(x,1234)"); // message: General: x+y is not a valid variable. check("PolynomialQ(x, x+y)", // "PolynomialQ(x,x+y)"); check("PolynomialQ(7*y^w, y )", // "False"); check("PolynomialQ(7*y^(3*w), y )", // "False"); check("PolynomialQ(c*x^(-2)+a+b*x,x)", // "False"); check("PolynomialQ(x^2 + 7*x + 6)", // "True"); check("PolynomialQ(x^(1/2) + 6*Sin(x), {})", // "True"); // only 1 arg gives always True ? check("PolynomialQ(x^(1/2) + 6*Sin(x))", // "True"); check("PolynomialQ(Cos(x*y), Cos(x*y))", // "True"); check("PolynomialQ(x^3,x^2)", // "False"); check("PolynomialQ(2*x^3,x^2)", // "False"); check("PolynomialQ(2*x,x^2)", // "False"); check("PolynomialQ(x,x^2)", // "False"); check("PolynomialQ(x^2,x^2)", // "True"); check("PolynomialQ(3*a,x)", // "True"); check("PolynomialQ(x^2*y^3+34*x^2+7-Sin(z^3)*x^34, {x,y})", // "True"); check("PolynomialQ(x^2*y^3+34*x^2+7-Sin(z^3)*x^34, {x,y,z})", // "False"); check("PolynomialQ(E^f(x),x)", // "False"); check("PolynomialQ(E^f(y),x)", // "True"); check("PolynomialQ(Tan(x),x)", // "False"); check("PolynomialQ(f(x), x)", // "False"); check("PolynomialQ(f(a)+f(a)^2, f(a))", // "True"); check("PolynomialQ(Sin(f(a))+f(a)^2, f(a))", // "False"); check("PolynomialQ(x^3 - 2*x/y + 3*x*z, x)", // "True"); check("PolynomialQ(x^3 - 2*x/y + 3*x*z, y)", // "False"); check("PolynomialQ(x^2 + a*x*y^2 - b*Sin(c), {x, y})", // "True"); check("PolynomialQ(x^2 + a*x*y^2 - b*Sin(c), {a, b, c})", // "False"); check("PolynomialQ((1+x)^3*(1-y-x)^2, x)", // "True"); check("PolynomialQ(x+Sin(x), x)", // "False"); check("PolynomialQ(x^2 + a*x*y^2 - b*Sin(c), {x, y})", // "True"); check("PolynomialQ(x^2 + a*x*y^2 - b*Sin(c), {a, b, c})", // "False"); check("PolynomialQ(f(a)+f(a)^2,f(a))", // "True"); check("PolynomialQ(I*x^(3)+(x+2)^2,x)", // "True"); check("PolynomialQ(I,x)", // "True"); check("PolynomialQ(a,x)", // "True"); check("PolynomialQ(a,{x,y,z})", // "True"); check("PolynomialQ(x,x)", // "True"); check("PolynomialQ(x,{x,y,z})", // "True"); } @Test public void testPolynomialQuotient() { check("PolynomialQuotient(x^2+4*x+1,-10,x,Modulus->2)", // "PolynomialQuotient(1+4*x+x^2,-10,x,Modulus->2)"); // check( // "PolynomialQuotientRemainder((2+x^2+x^3)/x,1-x^2,x)", // // "(2-x)/x"); check("PolynomialQuotient(0,2,x,Modulus->2)", // "PolynomialQuotient(0,2,x,Modulus->2)"); check("PolynomialQuotient(x^2+4*x+1,Indeterminate,x,Modulus->3)", // "PolynomialQuotient(1+4*x+x^2,Indeterminate,x,Modulus->3)"); check("PolynomialQuotient(x^2,1+(-1)*1,x)", // "PolynomialQuotient(x^2,0,x)"); check("PolynomialQuotient(x^2 + 7*x + 6, x^2-5*x-6, x)", // "1"); check("PolynomialQuotient(a+b*x,1,x)^3", // "(a+b*x)^3"); check("PolynomialQuotient(x^2, x + a,x)", // "-a+x"); check("PolynomialQuotient(x^2 + x + 1, 2*x + 1, x)", // "1/4+x/2"); check("PolynomialQuotient(x^2 + b*x + 1, a*x + 1, x)", // "-1/a^2+b/a+x/a"); check("PolynomialQuotient(x^2 + 4*x + 1, 2*x + 1, x, Modulus -> 2)", // "1+x^2"); check("PolynomialQuotient(x^2 + 4*x + 1, 2*x + 1, x, Modulus -> 3)", // "1+2*x"); } @Test public void testPolynomialQuotientRemainder() { check("PolynomialQuotientRemainder(1+b*x+x^2,-2147483648,x)", // "{-1/2147483648-1/2147483648*b*x-x^2/2147483648,0}"); check("PolynomialQuotientRemainder(x^2 + x + 1, Pi*x + 1, x)", // "{-1/Pi^2+1/Pi+x/Pi,1+1/Pi^2-1/Pi}"); check("PolynomialQuotientRemainder(x^2,1+(-1)*1,x)", // "PolynomialQuotientRemainder(x^2,0,x)"); // test with Integer.MIN_VALUE check("PolynomialQuotientRemainder(1+b*x+x^2,-2147483648,x)", // "{-1/2147483648-1/2147483648*b*x-x^2/2147483648,0}"); check("PolynomialQuotientRemainder(1+b*x+x^2,-2147483646,x)", // "{-1/2147483646-1/2147483646*b*x-x^2/2147483646,0}"); check("PolynomialQuotientRemainder(6+7*x+x^2,Indeterminate,x)", // "PolynomialQuotientRemainder(6+7*x+x^2,Indeterminate,x)"); check("PolynomialQuotientRemainder(2*x^2+3,3*x,f(x,y))", // "{(3+2*x^2)/(3*x),0}"); check("PolynomialQuotientRemainder(x^2 + 7*x + 6, x^2-5*x-6, x)", // "{1,12+12*x}"); check("PolynomialQuotientRemainder[a,b,x]", // "{a/b,0}"); check("PolynomialQuotientRemainder(e*x^2 + d, ( -2*d*e^2*Sqrt(-e/d) )*x + 2*d*e^2, x )", // "{1/(2*e^2)-x/(2*d*e*Sqrt(-e/d)),0}"); check("PolynomialQuotientRemainder(x^2, x + a,x)", // "{-a+x,a^2}"); check("PolynomialQuotientRemainder(x^2 + x + 1, 2*x + 1, x)", // "{1/4+x/2,3/4}"); check("PolynomialQuotientRemainder(x^2 + b*x + 1, a*x + 1, x)", // "{-1/a^2+b/a+x/a,1+1/a^2-b/a}"); check("PolynomialQuotientRemainder(x^2 + 4*x + 1, 2*x + 1, x, Modulus -> 2)", // "{1+x^2,0}"); check("PolynomialQuotientRemainder(x^2 + 4*x + 1, 2*x + 1, x, Modulus -> 3)", // "{1+2*x,0}"); } @Test public void testPolynomialRemainder() { check("PolynomialRemainder(Indeterminate,Indeterminate,Indeterminate)", // "PolynomialRemainder(Indeterminate,Indeterminate,Indeterminate)"); check("PolynomialRemainder(x^2 + 7*x + 6, x^2-5*x-6, x)", // "12+12*x"); check("PolynomialRemainder(1,Sin(e+f*x),x)", // "PolynomialRemainder(1,Sin(e+f*x),x)"); check("PolynomialRemainder(x^2, x + a,x)", // "a^2"); check("PolynomialRemainder(x^2 + 4*x + 1, 2*x + 1, x, Modulus -> 2)", // "0"); check("PolynomialRemainder(x^2 + 4*x + 1, 2*x + 1, x, Modulus -> 5)", "3"); } @Test public void testPosition() { // github issue #859 check("Position(2,2)", // "{{}}"); check("Position(2,_?NumberQ)", // "{{}}"); check("Position(2,_?IntegerQ)", // "{{}}"); check("Position(2,3)", // "{}"); check("Position(_Integer)[{1.5, 2, 2.5}]", // "{{2}}"); check("Position(<|1->List,2-><|\"a\"->x^2|>,3->List,4->a+(1+x^2)^2|>,x_)", // "{{0},{Key(1)},{Key(2),0},{Key(2),Key(a),0},{Key(2),Key(a),1},{Key(2),Key(a),2},{Key(\n" + // "2),Key(a)},{Key(2)},{Key(3)},{Key(4),0},{Key(4),1},{Key(4),2,0},{Key(4),2,1,0},{Key(\n" + // "4),2,1,1},{Key(4),2,1,2,0},{Key(4),2,1,2,1},{Key(4),2,1,2,2},{Key(4),2,1,2},{Key(\n" + // "4),2,1},{Key(4),2,2},{Key(4),2},{Key(4)}}"); check("Position(<|1->1+x^2,2-><|\"a\"->x^2|>,3->x^4,4->a+(1+x^2)^2|>,x_)", // "{{0},{Key(1),0},{Key(1),1},{Key(1),2,0},{Key(1),2,1},{Key(1),2,2},{Key(1),2},{Key(\n" + // "1)},{Key(2),0},{Key(2),Key(a),0},{Key(2),Key(a),1},{Key(2),Key(a),2},{Key(2),Key(a)},{Key(\n" + // "2)},{Key(3),0},{Key(3),1},{Key(3),2},{Key(3)},{Key(4),0},{Key(4),1},{Key(4),2,0},{Key(\n" + // "4),2,1,0},{Key(4),2,1,1},{Key(4),2,1,2,0},{Key(4),2,1,2,1},{Key(4),2,1,2,2},{Key(\n" + // "4),2,1,2},{Key(4),2,1},{Key(4),2,2},{Key(4),2},{Key(4)}}"); check( "Position(<|{1 -> 1 + x^2, 2 -> <|\"a\" -> x^2|>, 3 -> x^4, 4 -> a + (1 + x^2)^2}|>, x^_)", // "{{Key(1),2},{Key(2),Key(a)},{Key(3)},{Key(4),2,1,2}}"); check("Position(<|\"a\" -> 1, \"b\" -> 2, \"c\" -> 3, \"d\" -> 4|>, _Integer?PrimeQ)", // "{{Key(b)},{Key(c)}}"); check("Count({1, \"f\", g, \"h\", \"7\"}, _?StringQ)", // "3"); check("Length(Position({1, \"f\", g, \"h\", \"7\"}, _?StringQ))", // "3"); check("Position({1 + x^2, 5, x^4, a + (1 + x^2)^2}, x^_)", // "{{1,2},{3},{4,2,1,2}}"); check("Extract({1 + x^2, 5, x^4, a + (1 + x^2)^2}, {{1,2},{3},{4,2,1,2}})", // "{x^2,x^4,x^2}"); check("Position(x^2 + y^2, Power, Heads->False)", // "{}"); check("Position(x^2 + y^2, Power)", // "{{1,0},{2,0}}"); check("Position(f(g(h(x))), _, Infinity)", // "{{0},{1,0},{1,1,0},{1,1,1},{1,1},{1}}"); check("Position({a, b, a, a, b, c, b, a, b}, b, 1, 2)", // "{{2},{5}}"); check("Position({1 + x^2, 5, x^4, a + (1 + x^2)^2}, x^_)", // "{{1,2},{3},{4,2,1,2}}"); check("Position({1 + x^2, 5, x^4, a + (1 + x^2)^2}, x^_, 2)", // "{{1,2},{3}}"); check("Position({1, 2, 2, 1, 2, 3, 2}, 2)", // "{{2},{3},{5},{7}}"); check("Position({1 + Sin(x), x, (Tan(x) - y)^2}, x, 3)", // "{{1,2,1},{2}}"); check("Position({1 + x^2, x*y ^ 2, 4*y, x ^ z}, x^_)", // "{{1,2},{4}}"); check("Position(_Integer)[{1.5, 2, 2.5}]", // "{{2}}"); check("Position({1.0, 2+3, b}, _Integer)", // "{{2}}"); check("Position(_Integer)[{1.0, 2+3, b}]", // "{{2}}"); check("Position(_Integer)[{1.0, 2, b}]", // "{{2}}"); check("Position(_Integer)[{a, 2, b}]", // "{{2}}"); check("Position({x, {x, y}, y},x,1)", // "{{1}}"); check("Position({x, {x, y}, y},x,2)", // "{{1},{2,1}}"); check("Position({x, {x, y}, y},x,{2})", // "{{2,1}}"); check("Position(f(f(g(a), a), a, h(a), f), a, {2, Infinity})", // "{{1,1,1},{1,2},{3,1}}"); check("Position(f(f(g(a), a), a, h(a), f), f, Heads->False)", // "{{4}}"); check("Position(f(f(g(a), a), a, h(a), f), f, Heads->True)", // "{{0},{1,0},{4}}"); check("Position({f(a), g(b), f(c)}, f(x_))", // "{{1},{3}}"); check("Position(Range(-1, 1, 0.05), 0.1)", // "{}"); check("Position(Range(-1, 1, 0.05), n_ /; n == 0.1)", // "{{23}}"); } @Test public void testPositive() { check("Positive(Infinity)", // "True"); check("Positive(-Infinity)", // "False"); check("Positive(-9/4)", // "False"); check("Positive(0.1+I)", // "False"); check("Positive(1)", // "True"); check("Positive(0)", // "False"); check("Positive(1 + 2*I)", // "False"); check("Positive(Pi)", // "True"); check("Positive(x)", // "Positive(x)"); check("Positive(Sin({11, 14}))", // "{False,True}"); } @Test public void testPossibleZeroQ() { check("PossibleZeroQ((x + 1) (x - 1) - x^2 + 1)", // "True"); check("PossibleZeroQ(Sqrt(x^2)-x,Assumptions -> Re(x)>0)", // "True"); check("PossibleZeroQ(Sqrt(x^2)-x)", // "False"); // check( // "(-99.12580575458303)*I", // // "I*(-99.12581)"); // check( // // "-Cos[95.78967105119972+I*(-99.12580575458303)]/8+1/2*Cos[Pi/4+(95.78967105119972+I*(-99.12580575458303))/2]^3*Sin[Pi/4+(95.78967105119972+I*(-99.12580575458303))/2]+1/8*Cos[95.78967105119972+I*(-99.12580575458303)]*Sin[95.78967105119972+I*(-99.12580575458303)]", // // // ""); // check( // // "-Cos[95.78967105119972+I*(-99.12580575458303)]/8+1/2*Cos[Pi/4+(95.78967105119972+I*(-99.12580575458303))/2]^3*Sin[Pi/4+(95.78967105119972+I*(-99.12580575458303))/2]", // // // "-2.27086*10^83+I*(-3.92378*10^84)"); // check( // // "+1/8*Cos[95.78967105119972+I*(-99.12580575458303)]*Sin[95.78967105119972+I*(-99.12580575458303)]", // // // "2.27086*10^83+I*3.92378*10^84"); // check( // // "PossibleZeroQ(((-Cosh(a+b*x)+Sinh(a+b*x))*(-b*Cosh(a+b*x)+b*Sinh(a+b*x)))/b+(-Cosh(a+b*x)+Sinh(a+b*x))/(Cosh(a+b*x)+Sinh(a+b*x)))", // // // "True"); // check("-2.27086*10^83+I*(-3.92378*10^84)+2.27086*10^83+I*3.92378*10^84", // "0.0"); // check( // "PossibleZeroQ(-Cos(x)/8+1/2*Cos(Pi/4+x/2)^3*Sin(Pi/4+x/2)+1/8*Cos(x)*Sin(x))", // // "True"); check("PossibleZeroQ(E^(I*Pi/4)-(-1)^(1/4))", // "True"); check("E^(I*Pi/4) - (-1)^(1/4)", // "-(-1)^(1/4)+(1+I)/Sqrt(2)"); check("PossibleZeroQ(E^(I*Pi/4)-(-1)^(1/4))", // "True"); check("PossibleZeroQ(Erf(Log(4)+2*Log(Sin(Pi/8)))-Erf(Log(2-Sqrt(2))))", // "True"); check("PossibleZeroQ(x*E^(I*Pi/4) - x*(-1)^(1/4))", // "True"); check("PossibleZeroQ(-Cos(x)/(1-Cos(x))+Sin(x)^2/(1-Cos(x))^2-1/(1-Cos(x)))", // "True"); check("PossibleZeroQ(2^(2*I) - 2^(-2*I) - 2*I*Sin(Log(4)))", // "True"); check("PossibleZeroQ(E^Pi - Pi^E)", // "False"); check("PossibleZeroQ((E + Pi)^2 - E^2 - Pi^2 - 2*E*Pi)", // "True"); check("PossibleZeroQ(E^(I*Pi/4) - (-1)^(1/4))", // "True"); check("PossibleZeroQ((x + 1)*(x - 1) - x^2 + 1)", // "True"); check("PossibleZeroQ(1/x + 1/y - (x + y)/(x*y))", // "True"); check("PossibleZeroQ(Sqrt(x^2) - x)", // "False"); } @Test public void testPower() { check("Power(-Infinity, 43)", // "-Infinity"); check("Sqrt(-Infinity)", // "I*Infinity"); check("Power(-Infinity, 4/3) // FullForm", // "DirectedInfinity(Times(-1, Power(-1, Rational(1,3))))"); check("Power(-Infinity, 4/3)", // "DirectedInfinity(-(-1)^(1/3))"); check("Power(5,2,3) // FullForm", // "390625"); check("Power(Power(5,2),3) // FullForm", // "15625"); // check( // "22610175337329362245620630780795110213748908671958118609721101133417890222511288803123590513070561131892027191395369936042326256168653778870546242363369977629202359754270184318045654379854509946171340376686223573580224107124150403623923011308302977397847548580593006903821021518558458596423345897023275437136962636706163753880297496880232736919213061706006731771987945729565465391441847486930782906711101531982421875^(1/500) // //N", // // ""); check("(2*x*y)^n", // "2^n*(x*y)^n"); check("Sqrt(-d) // FullForm", // "Power(Times(-1, d), Rational(1,2))"); check("(-27)^(1/3) // FullForm", // "Times(3, Power(-1, Rational(1,3)))"); check("(-27/Pi)^(2/3) // FullForm", // "Times(9, Power(Times(-1, Power(Pi, -1)), Rational(2,3)))"); check("(-Pi/27)^(1/3) // FullForm", // "Times(Rational(1,3), Power(Times(-1, Pi), Rational(1,3)))"); check("(Pi/27)^(1/3) // FullForm", // "Times(Rational(1,3), Power(Pi, Rational(1,3)))"); check("(27/Pi)^(1/3) // FullForm", // "Times(3, Power(Pi, Rational(-1,3)))"); check("Sqrt(Pi/4) // FullForm", // "Times(Rational(1,2), Power(Pi, Rational(1,2)))"); check("Sqrt(4/Pi) // FullForm", // "Times(2, Power(Pi, Rational(-1,2)))"); check("Sqrt(Pi/2) // FullForm", // "Power(Times(Rational(1,2), Pi), Rational(1,2))"); check("Sqrt(2/Pi) // FullForm", // "Power(Times(2, Power(Pi, -1)), Rational(1,2))"); check("1/(-7) // FullForm", // "Rational(-1,7)"); // TODO improve output - if base is Sqrt avoid parnethesis check("x^Sqrt(y)^a", // "x^(Sqrt(y))^a"); check("a^(1/Log(a)^4)", // "E^(1/Log(a)^3)"); check("a^(Log(a)^7)", // "E^Log(a)^8"); check("a^(3*b/Log(a)^3)", // "E^((3*b)/Log(a)^2)"); check("a^(b/Log(a))", // "E^b"); check("a^(1/Log(a))", // "E"); check("1/Overflow()", // "Underflow()"); check("1/Underflow()", // "Overflow()"); if (Config.EXPENSIVE_JUNIT_TESTS) { check( "(-9223372036854775807/9223372036854775808-I*9223372036854775808/9223372036854775807)^10007", // "BigInteger bit length 229469 exceeded"); } check("Power(p,q,2,65)", // "p^q^36893488147419103232"); check("Power(q,2,65)", // "q^36893488147419103232"); check("3^2^65", // "3^36893488147419103232"); check("x^(-2)^(-3)", // "1/x^(1/8)"); check("(Sqrt[a])^(1/4)", // "a^(1/8)"); check("(Sqrt[a])^(-1/4)", // "1/a^(1/8)"); check("z^i / i^n //FullForm", // "Times(Power(i, Times(-1, n)), Power(z, i))"); check("Sqrt(-7 + 24*I)", // "3+I*4"); // message BigInteger bit length 254105 exceeded check("(-8/27*(-2/3)^(2/5))^2147483647", // "(-8/27*(-2/3)^(2/5))^2147483647"); // SLOW in factorSmallPrimes() // message BigInteger bit length 258048 exceeded check("(85070591730234615764386559452539518976/121)^(13479/14641)", // "(85070591730234615764386559452539518976/121)^(13479/14641)"); check("(I*1/2)^x^2", // "(I*1/2)^x^2"); check("Sqrt(Sqrt(3/5)/2) // FullForm", // "Times(Power(Rational(3,5), Rational(1,4)), Power(2, Rational(-1,2)))"); check("Sqrt(Sqrt(3/5)) // FullForm", // "Power(Rational(3,5), Rational(1,4))"); check("(-1062961)^(2/3)", // "1031*(-1)^(2/3)*1031^(1/3)"); // TODO // check("Power({{1,0},{0,1}},{{0}},{x,5,-3},1/2,{x,-2,3})", // // "{{1,0^{{0}}^{x^2^(-x),625,(-3)^(1/8)}},{0^{{0}}^{x^2^(-x),625,(-3)^(1/8)},1}}"); check("Power(<|x->y|>,5,-1/2)", // "<|x->y^(1/Sqrt(5))|>"); check("Power(<|x->y|>,5)", // "<|x->y^5|>"); check("(-Infinity)^(-3/5)", // "0"); check("1/Sqrt(-Infinity)", // "0"); check("0^I", // "Indeterminate"); check("0^(-I)", // "Indeterminate"); // Test Config.MAX_BIT_COUNT = Short.MAX_VALUE; // check("(3/7)^7625597484987", // // "Maximum AST size 45891 exceeded"); // check("3^3^3^3^3^3^3", // // "Maximum AST size 52046 exceeded"); // check("(3/7)^762559748498700000000000", // // "Maximum AST size 45891 exceeded"); check("(((3/7)^3)^3)^3", // "7625597484987/65712362363534280139543"); check("((((3/7)^3)^3)^3)^3", // "443426488243037769948249630619149892803/283753509180010707824461062763116716606126555757084586223347181136007"); // check("(((((3/7)^3)^3)^3)^3)^3", // // "8718964248596095820291107058586077169696407240473175008552521943799096709372343\\\n" + // "9943475549906831683116791055225665627/2284671285987374648044782166659234642669413233343555899898341285496111418662257\\\n" // + // "4870902442510049863025667206258127311451949520409822391138243055993672121915936\\\n" + // "570990365106665813437806284123385754752042992343"); check("((3/7)^3)^3", // "19683/40353607"); check("Power((-x)^(1/2), 2)", // "-x"); check("Power((-x)^(1/3), 3)", // "-x"); check("( (-11)^(1/3))^3", // "-11"); check("(-(-89)^(1/3))^3-89", // "0"); check("Power(a,b,c,d) // FullForm", // "Power(a, Power(b, Power(c, d)))"); check("(I)^(-0.5)", // "0.707107+I*(-0.707107)"); check("(I)^(-1/2)", // "-(-1)^(3/4)"); check("Sqrt(-1)*(-1)^(1/10)", // "(-1)^(3/5)"); check("(-1)^(2/3)", // "(-1)^(2/3)"); check("1/2*Sqrt(2)", // "1/Sqrt(2)"); check("I*1/2*Sqrt(2)", // "I/Sqrt(2)"); check("E^(I*2/3*Pi)", // "-1/2+I*1/2*Sqrt(3)"); check("E^((-11/6)*I*Pi)", // "I*1/2+Sqrt(3)/2"); check("E^((3/4)*I*Pi)", // "(-1+I)/Sqrt(2)"); check("E^((7/6)*I*Pi)", // "-I*1/2-Sqrt(3)/2"); // check("TimeConstrained(1^3^3^3^3, 10)", // // "$Aborted"); // check("TimeConstrained(1^3^3^3, 10)", // // "1"); check("0^(-1)", // "ComplexInfinity"); check("Refine(Exp(I*k*Pi),Element(k,Integers))", // "(-1)^k"); check("Exp(2*I*43*Pi)", // "1"); check("Exp(I*43*Pi)", // "-1"); check("E^(I/2*Pi)", // "I"); check("(I)^(-1)", // "-I"); check("(I)^(-1+k)", // "I^(-1+k)"); check("2^(2/3)*(-5+3*Sqrt[3])^(2/3)", // "(2*(-5+3*Sqrt(3)))^(2/3)"); check("(-1095912791)^(2/3)", // "1062961*(-1)^(2/3)"); check("(-1062961)^(2/3)", // "1031*(-1)^(2/3)*1031^(1/3)"); check("(-27)^(2/3)", // "9*(-1)^(2/3)"); check("(-1)^(1/6)*9178829416159^(1/6)", // "(-9178829416159)^(1/6)"); check("(-(50!)/30!)^(1/6)", // "24*(-9178829416159)^(1/6)*Sqrt(2)*5^(5/6)*7^(2/3)*33^(1/3)"); check("(-27)^(2/3)", // "9*(-1)^(2/3)"); check("(-(50!))^(1/6)", // "604800*(-2756205443)^(1/6)*2^(5/6)*Sqrt(13)*33^(2/3)*52003^(1/3)"); check("604800^6* -621447116887301398870058090208==(-(50!)) ", // "True"); check("(-2)^(-11/4)", // "-(-1)^(1/4)/(4*2^(3/4))"); check("(-2)^(11/4)", // "4*(-2)^(3/4)"); check("(-2)^(4/3)", // "-2*(-2)^(1/3)"); check("1/(-8/27*(-2/3)^(2/5))", // "27/8*(-1)^(3/5)*(3/2)^(2/5)"); check("(-2/3)^(5/2)", // "I*4/9*Sqrt(2/3)"); check("(-2/3)^(17/5)", // "-8/27*(-2/3)^(2/5)"); check("(-2/3)^(-17/5)", // "27/8*(-1)^(3/5)*(3/2)^(2/5)"); check("(-1)^(8/5)", // "-(-1)^(3/5)"); check("(-1)^(12/5)", // "(-1)^(2/5)"); check("(-1)^(5/4)", // "-(-1)^(1/4)"); check("(-1)^(7/4)", // "-(-1)^(3/4)"); check("(-2/3)^(5/4)", // "-2/3*(-2/3)^(1/4)"); check("I^(5/2) - Sqrt(I^5)", // "-2*(-1)^(1/4)"); // github #114 check("Sqrt(1/(2*Surd(-Cos(9/20*Pi),3)))", // "Sqrt(-1/(2*Cos(9/20*Pi)^(1/3)))"); check("0^(13+n)/a", // "0^(13+n)/a"); check(" 2^(2*I) - 2^(-2*I) - 2*I*Sin(Log(4)) ", // "0"); check("2*Sqrt(2)", // "2*Sqrt(2)"); check("-2*Sqrt(2)", // "-2*Sqrt(2)"); check("(2/3)^(-m)", // "(3/2)^m"); check("(3/2)^(-m)", // "(3/2)^(-m)"); check("(-2/3)*(3/2)^m", // "-(2/3)^(1-m)"); check("(2/3)*(3/2)^m", // "(2/3)^(1-m)"); check("(-2/3)*(x)/(3/2)^m", // "-x/(3/2)^(1+m)"); check("(-2/3)*(x)*(3/2)^m", // "-(2/3)^(1-m)*x"); check("(2/3)*(x)/(3/2)^m", // "x/(3/2)^(1+m)"); check("(2/3)*(x)*(3/2)^m", // "(2/3)^(1-m)*x"); check("(2/3)^(1+m)*x", // "(2/3)^(1+m)*x"); check("Sqrt(Pi/b)", // "Sqrt(1/b)*Sqrt(Pi)"); check("(2*x*y)^n", // "2^n*(x*y)^n"); check("(0.3333*x*y)^n", // "0.3333^n*(x*y)^n"); check("(a*3/4*E*x*y)^n", // "(3/4*E)^n*(a*x*y)^n"); check("(a*42*(-Pi)*x*y)^n", // "(42*Pi)^n*(-a*x*y)^n"); check("(-Infinity)^(42.0)", // "Infinity"); check("(-Infinity)^(43.0)", // "-Infinity"); check("(-Infinity)^(-42.0)", // "0"); check("(-Infinity)^(-43.0)", // "0"); check("(-5/6)^(1/2)", // "I*Sqrt(5/6)"); check("(9/4)^(-3/8)", // "(2/3)^(3/4)"); check("4^(-3/8)", // "1/2^(3/4)"); check("5103^(1/3)", // "9*7^(1/3)"); check("4^(3/8)", // "2^(3/4)"); check("(-42)^Infinity", // "ComplexInfinity"); check("(-1)^Infinity", // "Indeterminate"); check("(-1/2)^Infinity", // "0"); check("(1/4)^Infinity", // "0"); check("(1)^Infinity", // "Indeterminate"); check("(42)^Infinity", // "Infinity"); check("(-42)^(-Infinity)", // "0"); check("(-1)^(-Infinity)", // "Indeterminate"); check("(-1/2)^(-Infinity)", // "ComplexInfinity"); check("(1/4)^(-Infinity)", // "Infinity"); check("(1)^(-Infinity)", // "Indeterminate"); check("(42)^(-Infinity)", // "0"); check("64^(2/3)", // "16"); check("81^(3/4)", // "27"); check("Sqrt(63/5)", // "3*Sqrt(7/5)"); check("Sqrt(9/2)", // "3/Sqrt(2)"); check("Sqrt(1/2)", // "1/Sqrt(2)"); check("1/Sqrt(2)-Sqrt(1/2)", // "0"); check("(2/3)^(-3/4)", // "(3/2)^(3/4)"); check("(y*1/z)^(-1.0)", // "z/y"); check("0^(3+I*4)", // "0"); check("4 ^ (1/2)", // "2"); check("4 ^ (1/3)", // "2^(2/3)"); check("3^123", // "48519278097689642681155855396759336072749841943521979872827"); check("(y ^ 2) ^ (1/2)", // "Sqrt(y^2)"); check("(y ^ 2) ^ 3", // "y^6"); check("4.0 ^ (1/3)", // "1.5874"); check("a /. x_ ^ n_. :> {x, n}", // "{a,1}"); check("(1.5 + 1.0*I) ^ 3.5", // "-3.68294+I*6.95139"); check("(1.5 + 1.0*I) ^ (3.5 + 1.5*I)", // "-3.19182+I*0.645659"); check("1/0", // "ComplexInfinity"); check("0 ^ -2", // "ComplexInfinity"); check("0 ^ (-1/2)", // "ComplexInfinity"); check("0 ^ -Pi", // "ComplexInfinity"); check("0 ^ I", // "Indeterminate"); check("0 ^ (2*I*E)", // "Indeterminate"); check("0 ^ - (Pi + 2*E*I)", // "ComplexInfinity"); check("0^0", // "Indeterminate"); check("Sqrt(-3+2.*I)", // "0.550251+I*1.81735"); check("Sqrt(-3+2*I)", // "Sqrt(-3+I*2)"); check("(3/2+1/2*I)^2", // "2+I*3/2"); check("I ^ I", // "I^I"); check("2 ^ 2.0", // "4.0"); check("Pi ^ 4.", // "97.40909"); check("a^b", // "a^b"); check("54^(1/3)", // "3*2^(1/3)"); check("Exp(y + Log(x))", // "E^y*x"); check("E^(2*(y+Log(x)))", // "E^(2*y)*x^2"); // don't change see issue #137 check("2^(3+x)", // "2^(3+x)"); check("I^(1/3)", // "(-1)^(1/6)"); check("I^(1/4)", // "(-1)^(1/8)"); check("I^(1/8)", // "(-1)^(1/16)"); check("I^(3/8)", // "(-1)^(3/16)"); check("I^(3/5)", // "(-1)^(3/10)"); check("(-I)^(1/2)", // "-(-1)^(3/4)"); check("(-I)^(1/3)", // "-(-1)^(5/6)"); check("(-I)^(3/5)", // "-(-1)^(7/10)"); check("(-I)^(21/32)", // "-(-1)^(43/64)"); check("(-I)^(32/21)", // "-(-1)^(5/21)"); check("(-I)^(1/4)", // "-(-1)^(7/8)"); check("(-I)^(1/5)", // "-(-1)^(9/10)"); check("(-I)^(1/6)", // "-(-1)^(11/12)"); check("(-I)^(1/24)", // "-(-1)^(47/48)"); check("(-I)^(64/7)", // "-(-1)^(3/7)"); check("(-I)^(71/7)", // "(-1)^(13/14)"); check("27^(1/3)", // "3"); check("5103^(1/3)", // "9*7^(1/3)"); check("5103^(1/2)", // "27*Sqrt(7)"); check("Sqrt(75/4)", // "5/2*Sqrt(3)"); check("0^(-1/2)", // "ComplexInfinity"); check("E^(x+2*Pi*I)", // "E^x"); check("E^(x+11*Pi*I)", // "-E^x"); check("E^(x+Sin(a)+2*Pi*I)", // "E^(x+Sin(a))"); check("(-9/5)*(3)^(-1/2)", // "-3/5*Sqrt(3)"); check("(-1/9)*3^(1/2)", // "-1/(3*Sqrt(3))"); check("3^(1/2)/9", // "1/(3*Sqrt(3))"); check("0^0", // "Indeterminate"); check("27^(1/3)", // "3"); check("(-27)^(1/3)", // "3*(-1)^(1/3)"); check("(-5)^(1/2)", // "I*Sqrt(5)"); check("(-5)^(-1/2)", // "-I/Sqrt(5)"); check("(-(2/3))^(-1/2)", // "-I*Sqrt(3/2)"); check("FullForm(a^b^c)", // "Power(a, Power(b, c))"); check("FullForm((a^b)^c)", // "Power(Power(a, b), c)"); check("(a*b)^3", // "a^3*b^3"); check("(a*b)^(1/2)", // "Sqrt(a*b)"); check("FullForm((a^b)^3)", // "Power(a, Times(3, b))"); check("{2,3,4,5}^3", // "{8,27,64,125}"); check("N(29^(1/3))", // "3.07232"); check("50!^(1/6)", // "604800*2^(5/6)*Sqrt(13)*33^(2/3)*52003^(1/3)*2756205443^(1/6)"); check("(z^(1/3))^3", // "z"); check("(z^3)^(1/3)", // "(z^3)^(1/3)"); check("Sqrt(x^2)", // "Sqrt(x^2)"); check("E^Log(x)", // "x"); check("E^(y+Log(x))", // "E^y*x"); check("E^(y+Log(x)-z)", // "E^(y-z)*x"); check("E^(y-Log(x)-z)", // "E^(y-z)/x"); check("E^(y+Log(x)-a*Log(v)*b*Log(u)-z)", // "E^(y-z-a*b*Log(u)*Log(v))*x"); check("E^(y-Log(x)+Log(y)-a*Log(v)*b*Log(u)-z)", // "(E^(y-z-a*b*Log(u)*Log(v))*y)/x"); check("Sqrt(1/a)", // "Sqrt(1/a)"); } @Test public void testPowerExpand() { check("PowerExpand(Log(4*(Im(z)^2+ Re(z)^2)))", // "2*Log(2)+Log(Im(z)^2+Re(z)^2)"); check("PowerExpand(Log(24/10)+Log(2))", // "3*Log(2)+Log(3)-Log(5)"); check("PowerExpand(Log(24/10)+Log(2)+Log(x/y))", // "3*Log(2)+Log(3)-Log(5)+Log(x)-Log(y)"); check("PowerExpand(Log(-13/350))", // "I*Pi-Log(2)-2*Log(5)-Log(7)+Log(13)"); check("PowerExpand(Log(24/175))", // "3*Log(2)+Log(3)-2*Log(5)-Log(7)"); check("PowerExpand(Log(12))", // "2*Log(2)+Log(3)"); check("PowerExpand(Log(-12))", // "I*Pi+2*Log(2)+Log(3)"); check("PowerExpand(ProductLog(y*Exp(y)))", // "y"); check("PowerExpand(Log(x/y))", // "Log(x)-Log(y)"); check("PowerExpand((x*y*z)^n)", // "x^n*y^n*z^n"); check("PowerExpand(Log(x*y))", // "Log(x)+Log(y)"); check("PowerExpand(Log(x^k))", // "k*Log(x)"); check("PowerExpand(Sqrt(-a))", // "I*Sqrt(a)"); check("PowerExpand(Sqrt(a^2))", // "a"); // check("PowerExpand(Sqrt(a/b))", "Sqrt(a)*Sqrt(1/b)"); check("PowerExpand((a ^ b) ^ c)", // "a^(b*c)"); check("PowerExpand((a * b) ^ c)", // "a^c*b^c"); check("PowerExpand((x ^ 2) ^ (1/2))", // "x"); check("PowerExpand(Log(a*b*c, d))", // "Log(d)/(Log(a)+Log(b)+Log(c))"); check("PowerExpand(Log(a*b*c))", // "Log(a)+Log(b)+Log(c)"); check("PowerExpand(Log(a*b^c,d))", // "Log(d)/(Log(a)+c*Log(b))"); check("PowerExpand(Log(a*b^c))", // "Log(a)+c*Log(b)"); check("PowerExpand(Log(a/b))", // "Log(a)-Log(b)"); check("-2^(1/2)*3^(1/2)", // "-Sqrt(6)"); check("Sqrt(x*y)", // "Sqrt(x*y)"); check("{Sqrt(x*y), Sqrt(x)*Sqrt(y)} /. {x -> -2, y -> -3}", // "{Sqrt(6),-Sqrt(6)}"); check("PowerExpand((a^b)^(1/2))", // "a^(b/2)"); check("Powerexpand((a*b)^(1/2))", // "Sqrt(a)*Sqrt(b)"); check("Powerexpand(Log((a^b)^c))", // "b*c*Log(a)"); check("Powerexpand({y*(a^b)^g, x+(a*b)^42,Log(a^b)})", // "{a^(b*g)*y,a^42*b^42+x,b*Log(a)}"); check("Powerexpand(Sqrt(x^2))", // "x"); check("Powerexpand(Log(1/z))", // "-Log(z)"); check("Powerexpand(2-Log(1/z^3))", // "2+3*Log(z)"); check("Powerexpand(Log(z^a))", // "a*Log(z)"); check("Powerexpand(Sqrt(a* b) + Sqrt(c*d))", // "Sqrt(a)*Sqrt(b)+Sqrt(c)*Sqrt(d)"); check("PowerExpand(Sqrt(x*y))", // "Sqrt(x)*Sqrt(y)"); check("PowerExpand(Log(z^a), Assumptions->True)", // "I*2*Pi*Floor((Pi-Im(a*Log(z)))/(2*Pi))+a*Log(z)"); check("PowerExpand((E^x)^(y), Assumptions->True)", // "E^(x*y+I*2*Pi*y*Floor((Pi-Im(x))/(2*Pi)))"); // "E^(x*y)*E^(I*2*Pi*y*Floor(1/2*(-Im(x)+Pi)*Pi^(-1)))"); check("PowerExpand((x*y)^(1/2), Assumptions->True)", // "E^(I*Pi*Floor(1/2-Arg(x)/(2*Pi)-Arg(y)/(2*Pi)))*Sqrt(x)*Sqrt(y)"); check("PowerExpand((a*b*c)^(1/3), Assumptions->True)", // "a^(1/3)*b^(1/3)*c^(1/3)*E^(I*2/3*Pi*Floor(1/2-Arg(a)/(2*Pi)-Arg(b)/(2*Pi)-Arg(c)/(\n" + "2*Pi)))"); } @Test public void testPowerMod() { // 2 is a primitive root for 13 check("PowerMod(2, Range(12), 13)", // "{2,4,8,3,6,12,11,9,5,10,7,1}"); // 3 is not a primitive root for 13 check("PowerMod(3, Range(12), 13)", // "{3,9,1,3,9,1,3,9,1,3,9,1}"); // check("PowerMod(6, 1/2, 10)", "1"); check("PowerMod(2, 10, 3)", // "1"); // similar to Java modInverse() check("PowerMod(3, -1, 7)", // "5"); // prints warning check("PowerMod(0, -1, 2)", // "PowerMod(0,-1,2)"); // prints warning check("PowerMod(5, 2, 0)", // "PowerMod(5,2,0)"); check("PowerMod(2, 10^9, 18)", // "16"); check("PowerMod(2, {10, 11, 12, 13, 14}, 5)", // "{4,3,1,2,4}"); check("PowerMod(147198853397, -1, 73599183960)", // "43827926933"); check("PowerMod(2, 10000000, 3)", // "1"); check("PowerMod(3, -2, 10)", // "9"); check("PowerMod(0, -1, 2)", // "PowerMod(0,-1,2)"); check("PowerMod(5, 2, 0)", // "PowerMod(5,2,0)"); } @Test public void testPreDecrement() { check("--5", // "--5"); check("a = 2", // "2"); check("--a", // "1"); check("a", // "1"); check("index = {1,2,3,4,5,6}", // "{1,2,3,4,5,6}"); check("--index[[2]]", // "1"); check("index", // "{1,1,3,4,5,6}"); } @Test public void testPreIncrement() { check("a = 2", // "2"); check("++a", // "3"); check("a", // "3"); check("index = {1,2,3,4,5,6}", // "{1,2,3,4,5,6}"); check("++index[[2]]", // "3"); check("index", // "{1,3,3,4,5,6}"); } @Test public void testPrepend() { check("Prepend(<|a->0,b:>1|>,<|a->0,b:>1|>)", // "<|a->0,b:>1|>"); check("Prepend(<|a->0,b:>1|>,<|b:>1,a->0|>)", // "<|b:>1,a->0|>"); check("$n=4;Prepend(Table(0,{$n +(-1)*1}),1)", // "{1,0,0,0}"); check("Prepend(1/Sqrt(5),<|x->y|>)", // "<|x->y^(1/Sqrt(5))|>"); check("Prepend(<|1 -> a, 2 -> b|>, {3 -> d, 4 -> e})", // "<|3->d,4->e,1->a,2->b|>"); check("Prepend(1/Sqrt(5),<|x->y|>)", // "<|x->y^(1/Sqrt(5))|>"); check("Prepend(Infinity,-I)", // "DirectedInfinity(-I,1)"); check("Prepend({2, 3, 4}, 1)", // "{1,2,3,4}"); check("Prepend(f(b, c), a)", // "f(a,b,c)"); check("Prepend({c, d}, {a, b})", // "{{a,b},c,d}"); check("Prepend(a, b)", // "Prepend(a,b)"); // operator form check("Prepend(a)[{c, d}]", // "{a,c,d}"); } @Test public void testPrependTo() { check("s = {1, 2, 4, 9}", // "{1,2,4,9}"); check("PrependTo(s, 0)", // "{0,1,2,4,9}"); check("s", // "{0,1,2,4,9}"); check("y = f(a, b, c)", // "f(a,b,c)"); check("PrependTo(y, x)", // "f(x,a,b,c)"); check("y", // "f(x,a,b,c)"); check("PrependTo({a, b}, 1)", // "PrependTo({a,b},1)"); check("PrependTo(a, b)", // "PrependTo(a,b)"); check("x = 1 + 2", // "3"); check("PrependTo(x, {3, 4}) ", // "PrependTo(x,{3,4})"); check("$l = {1, 2, 4, 9};PrependTo($l, 16)", // "{16,1,2,4,9}"); check("$l = {1, 2, 4, 9};PrependTo($l, 16);$l", // "{16,1,2,4,9}"); } @Test public void testPrimePi() { // iteration limit exceeded check("PrimePi(2147483647)", // "Hold(PrimePi(2147483647))"); check("PrimePi(0)", // "0"); check("PrimePi(3.5)", // "2"); check("PrimePi(100)", // "25"); check("PrimePi(-1)", "0"); check("PrimePi(3.5)" // , "2"); check("PrimePi(E)", // "1"); check("PrimePi(1)", // "0"); check("PrimePi(2)", // "1"); // check("PrimePi(1000000)", "78498"); check("PrimePi(10000)", // "1229"); check("PrimePi(5.2)", // "3"); check("PrimePi(997)", // "168"); check("Prime(168)", // "997"); } @Test public void testPrincipleComponents() { // message SparseArray: Input matrix contains an indeterminate entry. check("PrincipalComponents(SparseArray({{0,0},{0,0}},0) ^ (I*1/3*Pi))", // "PrincipalComponents(SparseArray(Number of elements: 4 Dimensions: {2,2} Default value: 0))"); check("PrincipalComponents({{0.25,0.33,0.45,0.01}},Method->\"Correlation\")", // "{{0.0,0.0,0.0,0.0}}"); check("PrincipalComponents({{0.25,0.33,0.01}} )", // "{{0.0,0.0,0.0}}"); check("PrincipalComponents({{ }})", // "{}"); check("PrincipalComponents({"// + "{90.0, 60, 90},"// + "{90, 90, 30},"// + "{60, 60, 60},"// + "{60, 60, 90},"// + "{30, 30, 30}"// + "})", // "{{34.37098,-13.66927,-10.38202},\n" // + " {9.98346,47.68821,1.47161},\n" // + " {-3.93481,-2.31599,3.89274},\n" // + " {14.69692,-25.24923,9.08167},\n" // + " {-55.11655,-6.45371,-4.06399}}"); check("PrincipalComponents({{-0.3,1.5},{-0.3,1.5} })", // "{{0.0,0.0},\n" // + " {0.0,0.0}}"); check("PrincipalComponents({"// + "{90.0, 60, 90},"// + "{90, 90, 30},"// + "{60, 60, 60},"// + "{60, 60, 90},"// + "{30, 30, 30}"// + "})", // "{{34.37098,-13.66927,-10.38202},\n" // + " {9.98346,47.68821,1.47161},\n" // + " {-3.93481,-2.31599,3.89274},\n" // + " {14.69692,-25.24923,9.08167},\n" // + " {-55.11655,-6.45371,-4.06399}}"); check("PrincipalComponents({{1.0, 2.0}, {2.0, 3.0}, {4.0, 10.0}})", // "{{3.27053,-0.285293},\n" // + " {1.99969,0.335165},\n"// + " {-5.27023,-0.0498715}}"); check("PrincipalComponents({{1.0, 2.0}, {3.0, 5.0}, {5.0, 6.0}})", // "{{3.06837,0.171857},\n" // + " {-0.481117,-0.461488},\n" // + " {-2.58726,0.289631}}"); check("PrincipalComponents({"// + "{90.0, 60, 90},"// + "{90, 90, 30},"// + "{60, 60, 60},"// + "{60, 60, 90},"// + "{30, 30, 30}"// + "}, Method -> \"Correlation\")", // "{{0.911826,-0.942809,0.440421},\n" // + " {1.38323,1.41421,-0.0309834},\n" // + " {-0.169031,0.0,-0.169031},\n" // + " {0.0666714,-0.942809,-0.404733},\n" // + " {-2.1927,0.471405,0.164326}}"); check( "PrincipalComponents({{1., 2., -1.}, {2., 3., 2.}, {4., 10., 9.}, {4., 5., 6.}}, Method -> \"Correlation\")", // "{{1.81962,0.226286,0.0503109},\n"// + " {0.873896,-0.0527284,-0.0788127},\n"// + " {-1.94708,0.412467,0.00116417},\n"// + " {-0.746438,-0.586024,0.0273376}}"); check("pc=PrincipalComponents( {{13.2, 200, 58, 21.2}," // + "{10, 263, 48, 44.5}," // + "{8.1, 294, 80, 31}," // + "{8.8, 190, 50, 19.5}," // + "{9, 276, 91, 40.6}," // + "{7.9, 204, 78, 38.7}," // + "{3.3, 110, 77, 11.1}," // + "{5.9, 238, 72, 15.8}," // + "{15.4, 335, 80, 31.9}," // + "{17.4, 211, 60, 25.8}})", // "{{33.21737,9.53712,-3.82769,2.93848},\n" // + " {-31.07601,23.87403,11.64669,-3.65609},\n" // + " {-62.33075,-7.21028,-3.4159,-2.71508},\n" // + " {43.95844,16.22527,-4.73401,-2.09407},\n" // + " {-46.27848,-18.29775,8.74335,0.369594},\n" // + " {26.1816,-9.56118,14.31321,0.292612},\n" // + " {122.6114,-15.97682,-2.36041,-1.13754},\n" // + " {-4.55805,-3.5664,-12.54463,-3.97383},\n" // + " {-103.2831,-4.01632,-7.32915,2.98506},\n" // + " {21.55756,8.99234,-0.491475,6.99086}}"); check("Variance(pc)", // "{4100.023,196.3743,75.84303,12.0943}"); check("Mean(pc) // Chop", // "{0,0,0,0}"); check("Correlation(pc)", // "{{1.0,0.0,0.0,0.0},\n" // + " {0.0,1.0,0.0,0.0},\n" // + " {0.0,0.0,1.0,0.0},\n" // + " {0.0,0.0,0.0,1.0}}"); check("PrincipalComponents( {{13.2, 200, 58, 21.2}," // + "{10, 263, 48, 44.5}," // + "{8.1, 294, 80, 31}," // + "{8.8, 190, 50, 19.5}," // + "{9, 276, 91, 40.6}," // + "{7.9, 204, 78, 38.7}," // + "{3.3, 110, 77, 11.1}," // + "{5.9, 238, 72, 15.8}," // + "{15.4, 335, 80, 31.9}," // + "{17.4, 211, 60, 25.8}}, Method -> \"Correlation\")", // "{{0.483183,1.18691,-0.415228,-0.148809},\n" // + " {-0.977884,1.02174,1.59196,0.250963},\n" // + " {-0.730655,-0.966191,-0.0518975,0.514159},\n" // + " {1.20901,1.07107,0.327703,0.407897},\n" // + " {-1.26624,-1.49626,0.107426,-0.405185},\n" // + " {-0.16975,-0.776364,0.700605,-0.745549},\n" // + " {2.74941,-0.959475,-0.138538,-0.340949},\n" // + " {0.967206,-0.600593,-0.31439,0.838019},\n" // + " {-1.9416,-0.0663725,-1.03767,0.267141},\n" // + " {-0.322683,1.58554,-0.769967,-0.637687}}"); check( "PrincipalComponents({{1., 2., -1.}, {2., 3., 2.}, {4., 10., 9.}, {4., 5., 6.}}, Method -> \"Correlation\")", // "{{1.81962,0.226286,0.0503109},\n"// + " {0.873896,-0.0527284,-0.0788127},\n"// + " {-1.94708,0.412467,0.00116417},\n"// + " {-0.746438,-0.586024,0.0273376}}"); } @Test public void testPrime() { check("Prime(10^6)", // "15485863"); check("Prime(10^7)", // "179424673"); // check("Prime(10^8)", "2038074743"); // check("Prime(103000000)", "2102429869"); // above the limit return Prime(...) // check("Prime(10^9)", "22801763489"); // check("Prime(10^10)", "252097800623"); // check("Prime(10^11)", "2760727302517"); check("Prime(1)", // "2"); check("Prime(167)", // "991"); } @Test public void testPrimeOmega() { check("PrimeOmega(-n)", // "PrimeOmega(n)"); check("PrimeOmega(0)", // "PrimeOmega(0)"); check("PrimeOmega(990)", // "5"); check("PrimeOmega(2010)", // "4"); check("PrimeOmega(2^2)", // "2"); check("PrimeOmega(3*2^2)", // "3"); check("PrimeOmega(50!)", // "108"); check("PrimeOmega({1,2,3,4,5,6,20})", // "{0,1,1,2,1,2,3}"); check("PrimeOmega({-1,-2,-3,-4,-5,-6,-20})", // "{0,1,1,2,1,2,3}"); } @Test public void testPrimePowerQ() { check("PrimePowerQ(0)", // "False"); check("PrimePowerQ(1)", // "False"); check("PrimePowerQ(-1)", // "False"); check("13^9", // "10604499373"); check("PrimePowerQ(10604499373)", // "True"); check("PrimePowerQ(-8)", // "True"); check("PrimePowerQ(9)", // "True"); check("PrimePowerQ(52142)", // "False"); check("PrimePowerQ(371293)", // "True"); check("PrimePowerQ(1)", // "False"); } @Test public void testPrimeQ() { check("PrimeQ({1,2,4})", // "{False,True,False}"); check("PrimeQ(<|a->1,b->2,c->4|>)", // "<|a->False,b->True,c->False|>"); // Gaussian primes // https://en.wikipedia.org/wiki/Gaussian_integer#Gaussian_primes check("PrimeQ(-3*I, GaussianIntegers->True)", // "True"); check("PrimeQ(-3*I, GaussianIntegers->False)", // "False"); check("PrimeQ(3*I, GaussianIntegers->True)", // "True"); check("PrimeQ(-3, GaussianIntegers->True)", // "True"); check("PrimeQ(-3)", "True"); check("PrimeQ({0,1,2,3,4,5,6,7,8,9,10,11}, GaussianIntegers->True)", // "{False,False,False,True,False,False,False,True,False,False,False,True}"); check("PrimeQ({-5-4*I,-5-4*I, -5-2*I, -5+2*I, -5+4*I, " // + "-4-5*I, -4-I, -4+I, -4+5*I, " // + "-3-2*I, -3, -3+2*I, " // + "-2-5*I, -2-3*I, -2-I, -2+I, -2+3*I, -2+5*I, " // + "-1-4*I, -1-2*I, -1-I, -1+I, -1+2*I, -1+4*I, " // + "-3*I, 3*I, 1-4*I, 1-2*I, 1-I, 1+I, 1+2*I, 1+4*I, 2-5*I, 2-3*I, 2-I, 2+I, 2+3*I, " // + "2+5*I, 3-2*I, 3, 3+2*I, 4-5*I, 4-I, 4+I, 4+5*I, 5-4*I, 5-2*I, 5+2*I, 5+4*I}, GaussianIntegers->True)", // "{True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True}"); // Mersenne Prime // https://en.wikipedia.org/wiki/Mersenne_prime check("PrimeQ(131071)", // "True"); check("PrimeQ(524287)", // "True"); check("PrimeQ(2147483647)", // "True"); check("PrimeQ(99999999999971)", // "True"); check("Select(Range(100), PrimeQ)", // "{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97}"); check("PrimeQ(Range(20))", // "{False,True,True,False,True,False,True,False,False,False,True,False,True,False,False,False,True,False,True,False}"); } @Test public void testPrimitiveRoot() { check("PrimitiveRoot(12)", // "PrimitiveRoot(12)"); // check("Select(Range(100), PrimitiveRoot(#) != {} &)", // // ""); } @Test public void testPrimitiveRootList() { check("PrimitiveRootList(-2147483648)", // "{}"); check("PrimitiveRootList(14)", // "{3,5}"); check("PrimitiveRootList(2*Prime(5))", // "{7,13,17,19}"); check("PrimitiveRootList(9)", // "{2,5}"); check("PrimitiveRootList(10)", // "{3,7}"); check("PrimitiveRootList(7)", // "{3,5}"); check("PrimitiveRootList(12)", // "{}"); check("PrimitiveRootList(19)", // "{2,3,10,13,14,15}"); check("PrimitiveRootList(43)", // "{3,5,12,18,19,20,26,28,29,30,33,34}"); check("PrimitiveRootList(127)", // "{3,6,7,12,14,23,29,39,43,45,46,48,53,55,56,57,58,65,67,78,83,85,86,91,92,93,96,\n" + "97,101,106,109,110,112,114,116,118}"); } @Test public void testPrint() { // in console simply print the styled text check("Print(Style(\"AbBbCc\", Red))", // ""); check("do(print(i0);if(i0>4,Return(toobig)), {i0,1,10})", // "toobig"); } @Test public void testPrintableASCIIQ() { check("PrintableASCIIQ(FromCharacterCode /@ Range(0, 127))", // "{False,False,False,False,False,False,False,False,False,False,False,False," // + "False,False,False,False,False,False,False,False,False,False,False,False," // + "False,False,False,False,False,False,False,False,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,False}"); check("PrintableASCIIQ(\"Symja\")", // "True"); check("PrintableASCIIQ({\"a\", \"b\", \"c\", \"¤\", \"d\", \"Ë©\"})", // "{True,True,True,False,True,False}"); check("PrintableASCIIQ(\"\")", // "True"); check("PrintableASCIIQ(\" \")", // "True"); check("PrintableASCIIQ(\"!\")", // "True"); check("PrintableASCIIQ(\"~\")", // "True"); check("PrintableASCIIQ(\"\\\"\")", // "True"); check("PrintableASCIIQ(FromCharacterCode(32))", // "True"); check("PrintableASCIIQ(FromCharacterCode /@ Range(0, 127))", // "{False,False,False,False,False,False,False,False,False,False,False,False," // + "False,False,False,False,False,False,False,False,False,False,False,False," // + "False,False,False,False,False,False,False,False,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,True,True,True,True,True," // + "True,True,True,True,True,True,True,False}"); } @Test public void testProductLog() { check("ProductLog(9/2*Sqrt(3)*Log(3))", // "3/2*Log(3)"); check("ProductLog(1/2*Sqrt(7)*Log(7))", // "Log(7)/2"); check("ProductLog(1/2*Sqrt(-7)*Log(-7))", // "ProductLog(I*1/2*Sqrt(7)*(I*Pi+Log(7)))"); // https://docs.sympy.org/latest/modules/functions/elementary.html#sympy.functions.elementary.exponential.LambertW check("ProductLog(1.2)", // "0.635564"); check("ProductLog(-1, 1.2)", // "-1.34748+I*(-4.41624)"); // -1/E < z < 0.0 check("ProductLog(-0.12)", // "-0.137718"); check("ProductLog(-1, -0.12)", // "-3.32033"); check("N(ProductLog(1/3), 100)", // "0.2576276530497367042829162016260977909096926475032044915339511440663191292752043724596398879341002505"); check("Table(ProductLog(k, 2.3), {k, -2, 2})", // "{-1.56175+I*(-10.85265),-0.696131+I*(-4.56093),0.918224,-0.696131+I*4.56093,-1.56175+I*10.85265}"); check("ProductLog(9/3*Sqrt(5)*Log(5))", // "ProductLog(3*Sqrt(5)*Log(5))"); check("ProductLog(3*E^3)", // "3"); check("ProductLog(-1, -3*E^(-3))", // "-3"); check("ProductLog(2*Log(2))", // "Log(2)"); check("ProductLog(-Log(2)/2)", // "-Log(2)"); check("ProductLog(1/Sqrt(5)) // N", // "0.323582"); check("ProductLog(-1, 0)", // "-Infinity"); check("ProductLog(-1, -(Pi/2))", // "-I*1/2*Pi"); check("ProductLog(-1, -(1/E))", // "-1"); check("Refine(ProductLog(k, 0), k>1)", // "-Infinity"); check("ProductLog(2.5 + 2*I)", // "1.05617+I*0.352561"); check("z == ProductLog(z) * E ^ ProductLog(z)", // "True"); check("ProductLog(0)", // "0"); check("ProductLog(E)", // "1"); String s = System.getProperty("os.name"); if (s.contains("Windows")) { // TODO fix apfloat output for "exponential" format check("ProductLog(-1.5)", // "-0.0327837+I*1.54964"); check("ProductLog({0.2, 0.5, 0.8})", // "{0.168916,0.351734,0.490068}"); check("ProductLog(2.5 + 2*I)", // "1.05617+I*0.352561"); check("N(ProductLog(4/10),50)", // "0.29716775067313854677972696224702134190445810155012"); check("N(ProductLog(-1),20)", // "-0.3181315052047641353+I*1.3372357014306894089"); } check("ProductLog(-Pi/2)", // "I*1/2*Pi"); check("ProductLog(-1/E)", // "-1"); check("ProductLog(Infinity)", // "Infinity"); check("ProductLog(-Infinity)", // "Infinity"); check("ProductLog(I*Infinity)", // "Infinity"); check("ProductLog(-I*Infinity)", // "Infinity"); check("ProductLog(ComplexInfinity)", // "Infinity"); check("ProductLog(0,a)", // "ProductLog(a)"); check("ProductLog(42,0)", // "-Infinity"); check("ProductLog(-1,(-1/2)*Pi)", // "-I*1/2*Pi"); check("ProductLog(-1,-E^(-1))", // "-1"); } @Test public void testProjection() { check("Projection({},{},Dot)", // "{}"); check("Projection({},{})", // "{}"); check("Projection({5, 6, 7}, {1, 0, 0})", // "{5,0,0}"); check("Projection({5, 6, 7}, {1, 1, 1})", // "{6,6,6}"); check("Projection({5, I, 7}, {1, 1, 1})", // "{4+I*1/3,4+I*1/3,4+I*1/3}"); check("Projection({x,y}, {a,b}, Dot)", // "{(a*(a*x+b*y))/(a^2+b^2),(b*(a*x+b*y))/(a^2+b^2)}"); check("Projection({x,y}, {a,b})", // "{(a*(x*Conjugate(a)+y*Conjugate(b)))/(a*Conjugate(a)+b*Conjugate(b)),(b*(x*Conjugate(a)+y*Conjugate(b)))/(a*Conjugate(a)+b*Conjugate(b))}"); check("ip(p1_, p2_) := Integrate(p1*p2, {x, -1, 1}); Projection(x^2, LegendreP(2, x), ip)", // "2/3*(-1/2+3/2*x^2)"); } @Test public void testProtect() { check("Protect(test1, test2, test3)", // "{test1,test2,test3}"); check("Attributes({test1,test2,test3,Plus,Times})", // "{{Protected},{Protected},{Protected},{Flat,Listable,NumericFunction,OneIdentity,Orderless,Protected},{Flat,Listable,NumericFunction,OneIdentity,Orderless,Protected}}"); // message Set: Symbol test1 is Protected. check("test=42", // "42"); // message SetDelayed: Symbol test1 is Protected. check("test1:=42", // "$Failed"); check("test1", // "test1"); check("Unprotect(test1, test2)", // "{test1,test2}"); check("Unprotect(test1, test2, test3)", // "{test3}"); check("test1=42", // "42"); check("test1", // "42"); } @Test public void testPutGet() { if (Config.FILESYSTEM_ENABLED) { check("Put(x + y, \"c:/temp/example_file1.m\"); Get(\"c:/temp/example_file1.m\")", // "x+y"); check( "Put(x + y, 2x^2 + 4z!, Cos(x) + I Sin(x), \"c:/temp/example_file2.m\");" + "Get(\"c:/temp/example_file2.m\")", // "Cos(x)+I*Sin(x)"); check("Put(47!, \"c:/temp/test.m\"); Get(\"c:/temp/test.m\")", // "258623241511168180642964355153611979969197632389120000000000"); } } @Test public void testRootReduce() { // TODO eliminate gcd check("RootReduce((-35-7*Sqrt(35))^-1)", // "1/490*(35-7*Sqrt(35))"); check("RootReduce((35-7*Sqrt(35))^-1)", // "1/490*(-35-7*Sqrt(35))"); check("RootReduce((35+7*Sqrt(35))^-1)", // "1/490*(-35+7*Sqrt(35))"); check("RootReduce((-35+7*Sqrt(35))^-1)", // "1/490*(35+7*Sqrt(35))"); check("RootReduce((-35-Sqrt(35))^-1)", // "1/1190*(-35+Sqrt(35))"); check("RootReduce((35-Sqrt(35))^-1)", // "1/1190*(35+Sqrt(35))"); check("RootReduce((35+Sqrt(35))^-1)", // "1/1190*(35-Sqrt(35))"); check("RootReduce((-35+Sqrt(35))^-1)", // "1/1190*(-35-Sqrt(35))"); } @Test public void testQuadraticIrrationalQ() { check("QuadraticIrrationalQ(5*Sqrt(11))", // "True"); check("QuadraticIrrationalQ((7*Sqrt(2) + 1)/11)", // "True"); check("QuadraticIrrationalQ(42)", // "False"); check("QuadraticIrrationalQ({Sqrt(2), Sqrt(3), Sqrt(4)})", // "{True,True,False}"); check("QuadraticIrrationalQ(n)", // "False"); check("QuadraticIrrationalQ(Sqrt(2)+Sqrt(7))", // "False"); } @Test public void testQuantile() { check("Quantile({},1/2)", // "Quantile({},1/2)"); check("Quantile({1,2,3,4,5,6,7},-1/2)", // "Quantile({1,2,3,4,5,6,7},-1/2)"); check("Quantile(WeibullDistribution(2, 5), N(1/4,25))", // "2.68180010651325822971629"); check("Quantile({10, 50, 10, 15, 20}, 3/4, {{1/2, 0}, {0, 1}})", // "55/2"); check("Quantile(NormalDistribution(m, s))", // "ConditionalExpression(m-Sqrt(2)*s*InverseErfc(2*#1),0<=#1<=1)&"); check("Quantile(NormalDistribution(m, s), q)", // "ConditionalExpression(m-Sqrt(2)*s*InverseErfc(2*q),0<=q<=1)"); check("Quantile({1, 2, 3, 4, 5, 6, 7}, 1/2)", // "4"); check("Quantile({1,2}, 0.5)", // "1"); check("Quantile({Sqrt(2), E, Pi, Sqrt(3)}, 1/4)", // "Sqrt(2)"); check("Quantile({Sqrt(2), E, Pi, Sqrt(3)}, 3/4)", // "E"); check("Quantile(N({E, Pi, Sqrt(2), Sqrt(3)}), 1/4)", // "1.41421"); check("Quantile({1, 2, 3, 4, 5, 6, 7}, 1/2)", // "4"); check("Quantile({1, 2, 3, 4, 5, 6, 7}, 1/4)", // "2"); check("Quantile({1, 2, 3, 4, 5, 6, 7}, {1/4, 3/4})", // "{2,6}"); check("Quantile({1.0, 2.0, 3.0, 4.0, 5, 6, 7}, {1/4, 3/4})", // "{2.0,6}"); check("Quantile({{1,2,3,4},{ E, Pi, Sqrt(2),Sqrt(3)}}, 0.75)", // "{E,Pi,3,4}"); check("Quantile({{1,2},{ E, Pi, Sqrt(2),Sqrt(3)}}, 0.75)", // "Quantile({{1,2},{E,Pi,Sqrt(2),Sqrt(3)}},0.75)"); // Quantile[{5, 10, 4, 25, 2, 1}, 1/5, {{1/2, 0}, {0, 1}}] check("Quantile({5, 10, 4, 25, 2, 1}, 1/5, {{1/2, 0}, {0, 1}})", // "17/10"); } @Test public void testQuartiles() { check("Quartiles({{-1,-2,3}},{{0,0},{0,0}}+1)", // "{{-1,-1,-1},{-2,-2,-2},{3,3,3}}"); // method 1 from Wikipedia check("Quartiles({6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49}, {{0, 0}, {1, 0}}) // N", // "{15.0,40.0,43.0}"); // method 3 from Wikipedia check("Quartiles({6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49}) // N", // "{20.25,40.0,42.75}"); check("Quartiles({-1, 5, 10, 4, 25, 2, 1}, {{0, 0}, {1, 0}})", // "{1,4,10}"); check("Quartiles(ExponentialDistribution(x))", // "{Log(4/3)/x,Log(2)/x,Log(4)/x}"); check("Quartiles({1, 3, 4, 2, 5, 6})", // "{2,7/2,5}"); check("Quartiles(N({Sin(1), 2, 3, 4},30))", // "{1.42073549240394825332625116081,2.5,3.5}"); } @Test public void testQuiet() { // message: Quiet: Quiet called with 3 arguments; 1 argument is expected. check("Quiet(a,b,c)", // "Quiet(a,b,c)"); check("Quiet(1/0)", // "ComplexInfinity"); check("1/0", // "ComplexInfinity"); } @Test public void testQuotient() { check("Table(Quotient(x + y*I, y + x*I), {x, -3.9,3.9,0.5}, {y, -3.9,3.9,0.5})", // "{{1,1,1,1,1-I,1-I,-I,-I,-I,-I,-1-I,-1-I,-1-I,-1,-1,-1},{1,1,1,1,1-I,1-I,-I,-I,-I,-I,-\n" + "1-I,-1-I,-1,-1,-1,-1},{1,1,1,1,1,1-I,1-I,-I,-I,-I,-1-I,-1-I,-1,-1,-1,-1},{1,1,1,\n" + "1,1,1,1-I,-I,-I,-I,-1-I,-1,-1,-1,-1,-1},{1+I,1+I,1,1,1,1,1-I,-I,-I,-1-I,-1,-1,-1,-\n" + "1,-1,-1+I},{1+I,1+I,1+I,1,1,1,1,1-I,-I,-1-I,-1,-1,-1,-1+I,-1+I,-1+I},{I,I,1+I,1+I,\n" + "1+I,1,1,1-I,-I,-1,-1,-1+I,-1+I,-1+I,-1+I,I},{I,I,I,I,I,1+I,1+I,1,-I,-1,-1+I,I,I,I,I,I},{I,I,I,I,I,I,I,I,\n" + "1,I,I,I,I,I,I,I},{I,I,I,I,-1+I,-1+I,-1,-1,-I,1,1+I,1+I,1+I,I,I,I},{-1+I,-1+I,-1+I,-\n" + "1+I,-1,-1,-1,-1-I,-I,1-I,1,1,1+I,1+I,1+I,1+I},{-1+I,-1+I,-1+I,-1,-1,-1,-1-I,-I,-I,\n" + "1-I,1,1,1,1,1+I,1+I},{-1+I,-1,-1,-1,-1,-1,-1-I,-I,-I,1-I,1-I,1,1,1,1,1},{-1,-1,-\n" + "1,-1,-1,-1-I,-1-I,-I,-I,-I,1-I,1,1,1,1,1},{-1,-1,-1,-1,-1,-1-I,-1-I,-I,-I,-I,1-I,\n" + "1-I,1,1,1,1},{-1,-1,-1,-1,-1-I,-1-I,-I,-I,-I,-I,1-I,1-I,1,1,1,1}}"); check("Table(Quotient(x + y*I, 3.0 - I*2.0), {x, -5, 5}, {y, -5, 5})", // "{{-I*2,-1-I*2,-1-I,-1-I,-1-I,-1-I,-1-I,-1,-2,-2,-2},{-I*2,-I*2,-I,-1-I,-1-I,-1-I,-\n" + "1,-1,-1,-2,-2+I},{-I*2,-I,-I,-I,-1-I,-1,-1,-1,-1,-1,-1+I},{-I,-I,-I,-I,-I,0,-1,-\n" + "1,-1,-1+I,-1+I},{1-I,-I,-I,-I,0,0,0,-1,-1+I,-1+I,-1+I},{1-I,1-I,-I,0,0,0,0,0,I,-\n" + "1+I,-1+I},{1-I,1-I,1-I,1,0,0,0,I,I,I,-1+I},{1-I,1-I,1,1,1,0,I,I,I,I,I},{1-I,1,1,\n" + "1,1,1,1+I,I,I,I,I*2},{2-I,2,1,1,1,1+I,1+I,1+I,I,I*2,I*2},{2,2,2,1,1+I,1+I,1+I,1+I,\n" + "1+I,1+I*2,I*2}}"); check("Quotient(4.56, 2.5)", // "1"); check("Quotient(E^E^E, Pi)", // "1214122"); check("Quotient(10.4 + I*8.0, 4.0 + I*5.0)", // "2"); check("Quotient(Sqrt(-113), 2)", // "I*5"); check("Quotient(42,Pi)", // "13"); check("Quotient(13, 0)", // "ComplexInfinity"); check("Quotient(-17, 7)", // "-3"); check("Quotient(15, -5)", // "-3"); check("Quotient(17, 5)", // "3"); check("Quotient(-17, -4)", // "4"); check("Quotient(-14, 7)", // "-2"); check("Quotient(19, -4)", // "-5"); } @Test public void testExpectation() { // TODO improve integration for piecewise functions // check("Expectation((x + 3)/(x + 5), Distributed(x, ExponentialDistribution(2)))", // // "Expectation((3+x)/(5+x),x\uF3D2ExponentialDistribution(2))"); check("Limit((-3*x)/(E^(x^2/2)*Sqrt(2*Pi))+4*Erf(x/Sqrt(2)), x -> -Infinity)", // "-4"); check("Expectation(2*x+3, x \\[Distributed] NormalDistribution() )", // "3"); check("Expectation(3*x^2 + 5, Distributed(x, NormalDistribution()))", // "8"); check("Expectation((#^3)&, {a,b,c})", // "1/3*(a^3+b^3+c^3)"); check("Expectation(2*x+3,Distributed(x,{a,b,c,d}))", // "1/4*(12+2*a+2*b+2*c+2*d)"); check("Expectation(f(x),Distributed(x,{a,b}))", // "1/2*(f(a)+f(b))"); // check("PDF( PoissonDistribution(m),x)", // // "Piecewise({{m^x/(E^m*x!),x>=0}},0)"); // check("Expectation(x^2+7*x+8,Distributed(x,PoissonDistribution(m)))", // // "8+8*m+m^2"); // check("Expectation(E^(2*x) + 3, Distributed( x, PoissonDistribution(l)))", // // ""); // // check("Expectation(x,Distributed(x, DiscreteUniformDistribution({4, 9})))", "13/2"); // check("Expectation(x,Distributed(x, DiscreteUniformDistribution({4, 10})))", "7"); // // check("Expectation(2*x+3,Distributed(x, DiscreteUniformDistribution({4, 9})))", "16"); // check("Expectation(2*x+3,Distributed(x, DiscreteUniformDistribution({4, 10})))", "17"); } @Test public void testQuotientRemainder() { check("QuotientRemainder(-5.1*Pi,Pi)", // "{-6,2.82743}"); check("QuotientRemainder(5-Pi,Pi)", // "{0,5-Pi}"); check("QuotientRemainder(-1/2+I*1/2, 1/2-I*1/2)", // "{-1,0}"); check("QuotientRemainder(-15/4-I*1/3.0, -1/3-2/33*I)", // "{11-I,-0.0227273}"); check("QuotientRemainder(-15/4-I*1/3, -1/3-2/33*I)", // "{11-I,-1/44}"); check("QuotientRemainder(-15/4-I*1/3.0, 2/33*I)", // "{-5+I*62,0.00757576+I*(-0.030303)}"); check("QuotientRemainder(-15/4+I*1/3.0, 2/33*I)", // "{5+I*62,0.00757576+I*0.030303}"); check("QuotientRemainder(-15/4-I*1/3, 2/33*I)", // "{-6+I*62,1/132+I*1/33}"); check("QuotientRemainder(-15/4+I*1/3, 2/33*I)", // "{6+I*62,1/132-I*1/33}"); check("QuotientRemainder(-15/4+I*1/3.0, 2/3)", // "{-6,0.25+I*0.333333}"); check("QuotientRemainder(-15/4+I*1/3, 2/3)", // "{-6,1/4+I*1/3}"); check("QuotientRemainder(26+120*I,37+226*I)", // "{1,-11-I*106}"); check("QuotientRemainder(13, 0)", // "QuotientRemainder(13,0)"); check("QuotientRemainder(-17, 7)", // "{-3,4}"); check("QuotientRemainder(15, -5)", // "{-3,0}"); check("QuotientRemainder(17, 5)", // "{3,2}"); check("QuotientRemainder(-17, -4)", // "{4,-1}"); check("QuotientRemainder(-14, 7)", // "{-2,0}"); check("QuotientRemainder(19, -4)", // "{-5,-1}"); } @Test public void testRamp() { check("Ramp(-1)", // "0"); check("Ramp(3.7)", // "3.7"); check("Ramp(Pi-E)", // "-E+Pi"); } @Test public void testRandom() { // RandomReal: The specification Infinity is not a random distribution recognized by the // system. check("RandomReal(Infinity)", // "RandomReal(Infinity)"); // set the seed to get always the same JUnit results check("SeedRandom[1234]; RandomReal[]", // "0.646582"); check("SeedRandom[1234]; RandomReal[]", // "0.646582"); check("SeedRandom[987654321]; RandomReal[]", // "0.30594"); check("RandomInteger({0,2147483647})", // "RandomInteger({0,2147483647})"); check("RandomReal(7,{5,4,2,3})", // "{{{{5.73144,0.319728,4.94061},{0.0679933,4.72926,0.116555}},{{0.773992,6.94591,2.30291},{3.52974,5.42991,1.12177}},{{3.32875,2.72358,6.15825},{0.697204,2.29928,5.89195}},{{1.10541,6.22831,2.3344},{4.18358,5.5935,0.736481}}},{{{1.67449,0.906546,6.79422},{6.84396,2.51322,5.9361}},{{5.04364,6.46733,4.64001},{1.04158,2.70263,0.215921}},{{3.81838,3.23419,6.47141},{4.44989,5.12608,3.21665}},{{5.41254,5.85401,5.62645},{1.58933,6.62786,4.3783}}},{{{1.72772,3.63391,0.568468},{2.48554,5.41832,1.25711}},{{0.335168,2.82838,6.24056},{3.03068,4.04821,1.75494}},{{2.38406,0.212825,0.430829},{4.4122,0.642352,1.1778}},{{2.16,0.679996,0.182249},{4.81619,4.29105,0.726369}}},{{{2.1253,2.19809,6.15916},{4.62626,4.83428,4.11445}},{{6.60144,5.23054,5.53491},{5.02889,3.12733,6.31147}},{{1.48409,5.48308,5.79296},{5.94312,1.32072,4.10319}},{{0.00705484,4.10168,0.503736},{0.053271,2.31095,0.590767}}},{{{2.85435,6.07331,2.33489},{4.61071,0.175366,1.12545}},{{2.63546,0.598288,4.72051},{0.151525,1.9658,5.36484}},{{1.93,6.51802,2.72058},{4.05592,5.33617,3.3918}},{{0.832009,4.04422,5.87361},{3.55061,3.27097,2.55045}}}}"); check("RandomReal({0,4},{5,4,2,3})", // "{{{{2.85922,1.70673,0.8738},{3.17883,0.0462446,2.3491}},{{3.44193,2.56976,2.43017},{2.51678,1.29868,3.99964}},{{0.507159,0.57407,2.82929},{1.91924,0.616029,2.25034}},{{0.295793,2.93624,0.0917664},{2.59264,1.17732,1.65084}}},{{{0.814614,3.99736,2.44831},{1.79291,3.5879,2.87252}},{{1.25318,1.87824,1.73488},{2.97028,1.7055,0.901991}},{{1.88688,1.5425,3.43454},{0.51331,3.14207,1.21088}},{{3.0212,1.66593,2.60619},{1.80588,0.610305,3.91522}}},{{{1.78368,2.41743,0.75524},{2.33301,0.369574,2.51342}},{{0.946016,0.437311,1.69956},{0.220327,1.29092,1.58481}},{{1.44784,1.72371,0.466719},{1.94973,0.119095,2.23436}},{{2.32171,1.5136,2.46327},{0.0793879,0.410682,3.41606}}},{{{3.14867,1.21575,2.26017},{2.56774,3.86094,1.82695}},{{1.30695,3.60202,2.45262},{1.65196,2.22244,0.0431879}},{{3.84996,0.308677,2.72992},{2.99436,1.1306,3.11259}},{{0.0412127,0.699323,3.5179},{3.75446,2.68401,0.00810998}}},{{{1.99472,2.68929,0.760376},{3.07714,2.82133,2.20191}},{{3.57165,3.56024,0.449397},{3.85303,1.06455,2.09794}},{{0.155784,1.3727,0.697554},{1.08796,1.17714,0.0565625}},{{2.0965,3.52074,1.20815},{2.33334,2.26257,2.08967}}}}"); check("RandomInteger(20,{10,3})", // "{{2,2,19},{8,2,1},{11,17,4},{9,8,13},{13,0,15},{14,11,13},{4,13,7},{18,19,2},{5,\n" + "8,0},{1,16,1}}"); check("RandomInteger(7,{5,4,2,3})", // "{{{{6,2,5},{3,7,1}},{{5,3,2},{1,3,1}},{{6,4,7},{6,6,3}},{{7,1,2},{6,5,3}}},{{{3,\n" + "1,1},{5,6,1}},{{0,0,4},{6,6,6}},{{7,1,1},{0,0,0}},{{6,0,7},{0,0,0}}},{{{3,3,7},{\n" + "3,3,3}},{{6,4,5},{6,0,4}},{{6,2,4},{7,1,3}},{{7,1,4},{4,2,6}}},{{{0,3,4},{1,0,1}},{{\n" + "1,6,4},{0,4,2}},{{6,6,1},{2,5,2}},{{6,1,1},{5,4,6}}},{{{7,3,1},{6,6,2}},{{1,6,2},{\n" + "3,5,5}},{{0,7,2},{0,1,4}},{{5,6,2},{0,6,5}}}}"); check("RandomInteger({0,4},{5,4,2,3})", // "{{{{0,4,2},{0,0,0}},{{3,4,3},{3,3,4}},{{3,4,3},{0,2,1}},{{0,1,0},{4,2,0}}},{{{3,\n" + "3,0},{0,1,1}},{{0,1,3},{3,1,4}},{{0,0,3},{0,2,1}},{{4,4,4},{2,2,4}}},{{{3,0,2},{\n" + "3,3,2}},{{0,0,0},{2,2,2}},{{0,2,0},{1,3,3}},{{3,1,0},{2,0,0}}},{{{3,3,3},{3,3,3}},{{\n" + "2,3,0},{3,0,2}},{{2,4,4},{2,0,2}},{{0,3,3},{1,4,2}}},{{{4,3,0},{3,3,4}},{{1,0,4},{\n" + "0,1,2}},{{0,4,4},{2,1,0}},{{1,4,4},{0,0,1}}}}"); check("RandomInteger()", // "1"); check("RandomInteger(-10)", // "-7"); check("RandomInteger(100)", // "91"); check("RandomReal()", // "0.441958"); String expected = String.join("\n", // " 1.53368 2.64244 0.603094 1.93993 0.757192 2.52053 3.6458 4.3667 0.0264575 1.62091 3.42147 ", // " 1.95564 3.8064 0.156164 2.52057 1.43282 3.08827 2.00007 2.09918 0.794163 1.28679 3.92551 ", // " 1.85792 1.60386 0.440516 3.06543 4.53076 0.156222 3.41509 2.07223 1.42567 1.66608 2.34519 ", // " 0.244549 1.42317 4.90009 1.99318 2.84108 3.10954 0.564542 4.05133 4.90708 3.39802 0.324629 ", // " 4.6692 0.202169 1.07454 4.54645 2.649 0.236909 0.193603 0.724548 4.81904 3.00081 1.14547 ", // " 1.08643 3.06911 0.695871 1.51773 2.05006 4.41148 0.677521 4.58214 0.0509575 1.21727 3.84864 ", // " 0.351929 2.75283 3.47041 4.95268 2.67536 1.80884 3.48008 4.56827 0.758013 3.15025 0.997234 "); check("RandomReal(5, {7, 11}) // TableForm", // expected); // distributions use org.hipparchus.random.RandomDataGenerator.RandomDataGenerator() which often // doesn't depend on java.util.Random where we set the seed. // check("RandomReal(ChiSquareDistribution(5),5)", // // "{6.88724,17.61347,4.88216,3.42269,1.84075}"); // check("RandomReal(WeibullDistribution(10,6),5)", // // "{6.04801,4.26361,5.57834,5.60149,5.86845}"); // check("RandomReal(CauchyDistribution(10,6),5)", // // "{25.46486,10.17115,9.24139,6.02044,-3.21386}"); // check("RandomReal(NormalDistribution(10,6),5)", // // "{15.39771,18.15348,3.84502,4.17546,13.37926}"); // message: RandomPrime: Positive integer value expected. check("RandomPrime(#2,{1,1,1,1})", // "RandomPrime(#2,{1,1,1,1})"); check("RandomPrime(-11)", // "RandomPrime(-11)"); // message: RandomPrime: There are no primes in the specified interval. check("RandomPrime(1)", // "RandomPrime(1)"); check("RandomPrime(2)", // "2"); // check("RandomPrime(100000000000000000000000000)", // // "87660272303062923753002687"); // } @Test public void testRandomChoice() { // check( // "RandomChoice({1, 10, 5} -> {a, b, c}, {3,3})", // // "{c,a,a,b,c,c,b,b,a,c,b,b,c,b,b,c,b,b,b,b}"); // check( // "RandomChoice({1, 10, 5} -> {a, b, c}, 20)", // // "{c,a,a,b,c,c,b,b,a,c,b,b,c,b,b,c,b,b,b,b}"); // check( // "RandomChoice({a,b,c}, {5,2})", // // "{{b,c},{c,c},{a,c},{a,c},{c,b}}"); // check("Table(StringJoin(RandomChoice(CharacterRange(\"a\", \"z\"), 5)), {10}) // InputForm", // // // "{\"jbuhp\",\"uneaw\",\"icixu\",\"vsrsy\",\"ycxsx\",\"atfvl\",\"kivvj\",\"xjllp\",\"xtwms\",\"ixwuk\"}"); // check("RandomChoice({1,2,3,4,5,6,7},11.0)", "{2,1,5,3,5,7,4,5,5,6,5}"); // check("RandomChoice({1,2,3,4,5,6,7},10)", "{3,7,3,6,2,7,4,1,1,4}"); // check("RandomChoice({False, True})", "True"); // check("RandomChoice({1,2,3,4,5,6,7})", "3"); } @Test public void testRandomComplex() { // check( // "RandomComplex(2+2I )", // // "1.07196+I*1.10905"); // check( // "RandomComplex( )", // // "0.313565+I*0.954076"); // check( // "RandomComplex({1+I, 2+2I}, {2,2,3})", // // // "{{{1.61894+I*1.62895,1.42982+I*1.64042,1.88055+I*1.24075},{1.27681+I*1.09553,1.29139+I*1.79987,1.47368+I*1.59429}},{{1.42116+I*1.54729,1.51395+I*1.05403,1.47495+I*1.7832},{1.79694+I*1.1428,1.93639+I*1.50855,1.51072+I*1.02286}}}"); // check("RandomComplex({2 + I, 10 + 20*I}, {3, 2})", // // "{{2.33543+I*15.51255,6.05421+I*7.19415},{4.84163+I*3.70955,8.92918+I*16.73326},{8.78651+I*5.42401,8.82129+I*15.18506}}"); // check("RandomComplex( )", // // "0.320015+I*0.506726"); // check("RandomComplex({-2-I,5+3*I})", // // "0.61304+I*(-0.482746)"); } @Test public void testRandomPermutation() { // check( // "RandomPermutation(10)", // // "Cycles({{1,2,7,3,8,10,5,9,4,6}})"); // check( // "RandomPermutation(10,3)", // // "{Cycles({{1,6,4,5,7,10,9,2,3,8}}),Cycles({{1,10,9,4,2,6,3,8,7,5}}),Cycles({{1,4,\n" // + "2,6,8,9,5,7,10,3}})}"); } @Test public void testRandomReal() { // check("RandomReal(WorkingPrecision -> 50)", // // "0.02914582860934237466618813817377889841321841114067"); check("NonNegative(RandomReal(-Sqrt(2)/2)*(-1.0))", // "True"); check("NonNegative(RandomReal({-Sqrt(2)/2,-1.0})*(-1.0))", // "True"); } @Test public void testRandomVariate() { // check("RandomVariate(HypergeometricDistribution(44,18,57), 10^2)", // // "{16,16,14,11,14,13,14,14,13,15,13,11,14,15,15,13,15,13,14,15,15,13,16,13,14,12,\r\n" + // "16,12,14,13,13,17,16,15,16,12,15,13,13,16,15,16,15,14,15,14,10,15,17,14,15,13,14,\r\n" + // "13,11,15,15,15,16,15,14,12,16,13,15,16,14,12,13,15,12,13,15,12,12,10,14,16,15,12,\r\n" + // "15,16,16,14,14,13,17,14,15,13,15,15,14,15,15,12,12,14,13,15}"); // check("RandomVariate(GammaDistribution(0.5,0.6), {2,3,4})", // // "{{{0.000793278,0.0921714,0.0523716,0.100137},"// // + "{0.104185,0.0459276,3.79475,0.247275},"// // + "{0.0363476,0.843459,0.662268,0.0752151}},"// // // // + "{{0.00037008,0.125594,0.0058051,0.158089}," // + "{0.573566,0.128191,0.00204638,0.819725},"// // + "{0.407606,0.00820377,0.0115433,0.107513}}}"); // check("RandomVariate(DiscreteUniformDistribution({1,15}), 10^1)", // // "{14,1,9,11,5,11,11,5,13,9}"); // check("RandomVariate(ExponentialDistribution(1), 10^1)", // // "{0.304049,0.242275,0.291415,1.28545,0.567106,1.02787,3.29483,4.40819,9.03388,0.375482}"); // // check("RandomVariate(BetaDistribution(0.25,0.75), 10^1)", // // "{0.0598983,0.109825,0.00899438,0.127621,0.000186889,0.00620042,0.213545,0.82361,0.0000629664,0.465407}"); // check("RandomVariate(UniformDistribution({0,2}), 10^1)", // // "{1.95015,1.42461,0.379616,0.828009,1.29886,1.74158,0.792286,0.651039,1.32392,1.71367}"); // check("RandomVariate(BinomialDistribution(100,0.25), 10^1)", // // "{28,25,30,25,25,26,29,17,33,20}"); // check("RandomVariate(BetaDistribution(0.5,0.6), {10})", // // "{0.651565,0.0687826,0.53907,0.511176,0.0419515,0.946387,0.995215,0.0896617,0.00242461,0.607517}"); // check("RandomVariate(FrechetDistribution(0.5,0.6), {10})", // // "{288.7521,2.9714,0.403198,2.0156,0.21531,0.0399206,0.665026,1.49444,434.9269,118.3019}"); // check("RandomVariate(GumbelDistribution(0.5,0.6), {10})", // // "{0.983572,1.01258,1.02586,0.351624,0.674945,0.549278,0.173217,0.464434,-0.335133,-0.151538}"); // check("RandomVariate(GammaDistribution(0.5,0.6), {10})", // // "{0.08716,0.39611,0.04844,0.03546,0.57366,0.02071,0.01487,1.65639,0.75104,0.05348}"); // check("RandomVariate(UniformDistribution({1,3}), {2})", // // "{1.95941,2.69658}"); // check("RandomVariate(NormalDistribution(), 10^1)", // // ""); // check("KolmogorovSmirnovTest({-0.79675,0.3841,-0.84567,0.3421,0.46447,-0.01124,-0.33517,0.82206,1.40563,0.48811}, // NormalDistribution())", // // "0.56794"); // check("KolmogorovSmirnovTest({-0.79675,0.3841,-0.84567,0.3421,0.46447,-0.01124,-0.33517,0.82206,1.40563,0.48811})", // // // "0.99446"); // check("KolmogorovSmirnovTest({-0.79675,0.3841,-0.84567,0.3421,0.46447,-0.01124,-0.33517,0.82206,1.40563,0.48811}," // + "{1.64433,-0.31318,1.27263,0.16141,0.21162,-1.01509,-0.76259,0.73259,0.2478,1.28021})", // // "0.7869"); // check("RandomVariate(BinomialDistribution(100,0.25), 10^1)", // // "{28,25,30,25,25,26,29,17,33,20}"); // check("RandomVariate(BernoulliDistribution(0.25), 10^1)", // // "{1,0,0,0,1,0,0,0,0,0}"); // check("RandomVariate(ExponentialDistribution(5.6), 10^1)", // // "{0.36309,0.10609,0.14096,0.11642,0.01146,0.11286,0.05236,0.00071,0.01648,0.0303}"); // check("RandomVariate(DiscreteUniformDistribution({50,1000}), 10^1)", // // "{468,989,156,353,469,91,399,304,700,137}"); // check("RandomVariate(PoissonDistribution(2.0), 10^1)", // // "{1,3,5,3,2,2,2,5,1,2}"); // check("RandomVariate(NormalDistribution(2,3), 10^1)", // // "{3.16579,3.4267,6.43772,4.53451,3.45249,6.51662,2.10209,-3.8462,3.87387,-4.47763}"); // check("RandomVariate(NormalDistribution(2,3))", // // "1.99583"); // check("RandomVariate(NormalDistribution())", // // "-0.56291"); // check("RandomVariate(DiscreteUniformDistribution({3,7}), {2})", "{3,7}"); // check("RandomVariate(DiscreteUniformDistribution({3,7}), {2,3})", "{{5,4,7},{5,7,3}}"); // check("RandomVariate(DiscreteUniformDistribution({3,7}), {2,3,4})", // "{{{4,5,5,3},{5,4,4,6},{6,3,4,7}},{{6,6,7,3},{4,6,5,6},{7,7,6,5}}}"); // check("RandomVariate(DiscreteUniformDistribution({3,7}), 10)", "{6,5,7,7,7,7,4,5,6,3}"); // check("RandomVariate(DiscreteUniformDistribution({1, 5}) )", "3"); } @Test public void testRandomSample() { // check("RandomSample(f(1,2,3,4,5),3)", // // "f(3,4,1)"); // check("RandomSample(f(1,2,3,4,5))", // // "f(3,4,5,1,2)"); } @Test public void testRange() { check("Range(a, b, (b - a)/4)", // "{a,a+1/4*(-a+b),a+1/2*(-a+b),a+3/4*(-a+b),b}"); byte[] b0Array = new byte[] {0}; ByteArrayExpr b0a = ByteArrayExpr.newInstance(b0Array); IAST range = F.Range(F.CNI, b0a, F.Quantity(F.num(1.2), F.stringx("m"))); check(range, // "{}"); check("Range(-Infinity,0.5)", // "Range(-Infinity,0.5)"); check("Range(a,b,ComplexInfinity)", // "a"); check("Range(a,b,-Infinity)", // "a"); check("Range(a,b,Infinity)", // "a"); check("Range(1,1.25,0)", // "Range(1,1.25,0)"); check("Range(1,-1 )", // "{}"); check("Range(1,-1,1/2)", // "{}"); check("Range(1,1+1/2,0)", // "Range(1,3/2,0)"); check("Range(1,1+1/2,1/2)", // "{1,3/2}"); check("Range(1,1.25,0.1)", // "{1.0,1.1,1.2}"); check("Range(5.0)", // "{1,2,3,4,5}"); check("Range(-5.0)", // "{}"); check("Range(0,10,Pi)", // "{0,Pi,2*Pi,3*Pi}"); check("x * Range(-1, 1, 1/5)", // "{-x,-4/5*x,-3/5*x,-2/5*x,-x/5,0,x/5,2/5*x,3/5*x,4/5*x,x}"); check("a + Range(0, 3, Pi/8)", // "{a,a+Pi/8,a+Pi/4,a+3/8*Pi,a+Pi/2,a+5/8*Pi,a+3/4*Pi,a+7/8*Pi}"); check("x^Range(n, n + 10, 2)", // "{x^n,x^(2+n),x^(4+n),x^(6+n),x^(8+n),x^(10+n)}"); check("Range(a, a + 12*n, 2*n)", // "{a,a+2*n,a+4*n,a+6*n,a+8*n,a+10*n,a+12*n}"); check("Range(5)", // "{1,2,3,4,5}"); check("Range(-3, 2)", // "{-3,-2,-1,0,1,2}"); check("Range(0, 2, 1/3)", // "{0,1/3,2/3,1,4/3,5/3,2}"); check("Range(1.2, 2.2, 0.15)", // "{1.2,1.35,1.5,1.65,1.8,1.95,2.1}"); check("Range(0)", // "{}"); check("Range(1)", // "{1}"); check("Range(-1)", // "{}"); check("Range(10)", // "{1,2,3,4,5,6,7,8,9,10}"); check("Range(1,10,2)", // "{1,3,5,7,9}"); check("Range(10,20,3)", // "{10,13,16,19}"); check("Range(10,1,-1)", // "{10,9,8,7,6,5,4,3,2,1}"); } @Test public void testRankedMax() { // message: RankedMax: Input {1,I,E} is not a vector of reals or integers. check("RankedMax({1, I, E}, 2)", // "RankedMax({1,I,E},2)"); check("RankedMax({12,13,11}, 2)", // "12"); check("RankedMax({Pi, Sqrt(3), 2.95, 3}, 3)", // "2.95"); check("RankedMax({12.99, 3.775, 25.33}, 2)", // "12.99"); check("RankedMax({2.5, E, 12, 15, 485}, -2)", // "E"); check("RankedMax({2.5, E, 12, 15, 485}, -4)", // "15"); check("RankedMax({2.5, E, 12, 15, 485}, -5)", // "485"); check("RankedMax({Infinity,5, Infinity, -Infinity}, 2)", // "Infinity"); check("RankedMax({Infinity,5, Infinity, -Infinity}, -1)", // "-Infinity"); } @Test public void testRankedMin() { check( "RankedMin({Quantity(1, \"Kilograms\"), Quantity(2, \"kg\"), Quantity(3, \"Kilograms\")}, 2)", // "2[kg]"); check("RankedMin({Quantity(1, \"kg\"), Quantity(2, \"kg\"), Quantity(3, \"kg\")}, 2)", // "2[kg]"); check("RankedMin(<|a -> 1, b -> 2, c -> 3, d -> 4|>, 2)", // "2"); // message: RankedMin: Input {1,I,E} is not a vector of reals or integers. check("RankedMin({1, I, E}, 2)", // "RankedMin({1,I,E},2)"); check("RankedMin({12,13,11}, 2)", // "12"); check("RankedMin({Pi, Sqrt(3), 2.95, 3}, 3)", // "3"); check("RankedMin({12.99, 3.775, 25.33}, 2)", // "12.99"); check("RankedMin({2.5, E, 12, 15, 485}, -2)", // "15"); check("RankedMin({2.5, E, 12, 15, 485}, -4)", // "E"); check("RankedMin({2.5, E, 12, 15, 485}, -5)", // "2.5"); } @Test public void testRational() { check("1.29600*10^-17", // "1.296*10^-17"); check("1.29600*^-17", // "1.296*10^-17"); check("6*^3", // "6000"); check("6*^-1", // "3/5"); check("6*^0", // "6"); check("Head(1/2)", // "Rational"); check("Rational(1, 2)", // "1/2"); check("-2/3", // "-2/3"); check("f(22/7, 201/64, x/y) /. Rational(n_, d_) :> d/n", // "f(7/22,64/201,x/y)"); } @Test public void testRationalize() { // check("Rationalize(0.1234567*^2)", // // "1234567/100000"); // // check("Rationalize(0.12345678*^2)", // // // "12.3457"); // check("Rationalize(0.123*^100)", // // "1.23*10^99"); // check("Rationalize(0.1*^-99)", // // "1.*10^-100"); // check("Rationalize(0.1*^-11)", // // "1.*10^-12"); // check("Rationalize(0.1*^-11)", // // "0"); // check("Rationalize(0.1*^-10)", // // "1/100000000000"); // check("Rationalize(0.123*^10)", // // "1230000000"); // check("Rationalize(0.202898)", // // "101449/500000"); // check("Rationalize(1.1/2147483647 *2.5,0)", // // "245850922/78256779"); check("Rationalize(0.000000000008854187817)", // "8.85419*10^-12"); check("Rationalize(N(Pi), 0)", // "884279719003555/281474976710656"); check("Rationalize(0.202898)", // "101449/500000"); check("Rationalize(Sin(3.0),0)", // "5084384125703515/36028797018963968"); check("Rationalize(N(Pi),0)", // "884279719003555/281474976710656"); check("Rationalize(x+E)", // "E+x"); check("Rationalize(E)", // "E"); check("Rationalize(E, 0.01)", // "19/7"); check("Rationalize(x+E, 0.01)", // "E+x"); check("Rationalize(x+y)", // "x+y"); check("Rationalize(x+0.3333*y)", // "x+3333/10000*y"); check("ArcCos(-Rationalize(0.5))", // "2/3*Pi"); check("Rationalize(0.202898)", // "101449/500000"); check("Rationalize(1.2 + 6.7*x)", // "6/5+67/10*x"); check("Rationalize(-1.2 - 6.7*x)", // "-6/5-67/10*x"); check("Rationalize(Exp(Sqrt(2)), 2^-12)", // "218/53"); check("Rationalize(6.75)", // "27/4"); check("Rationalize(-6.75)", // "-27/4"); check("Rationalize(Pi)", // "Pi"); check("Rationalize(Pi, .01)", // "22/7"); check("Rationalize(Pi, .001)", // "333/106"); } @Test public void testRe() { // check("Re(I*Arg(z) + Log(2) + (1/2)*Log(Im(z)^2 + Re(z)^2))", // "Log(2)+Re(Log(Im(z)^2+Re(z)^2))/2"); check("Re(I*Im(z)+x+y+Im(t)*I+Re(u))", // "Re(u+x+y)"); check("Re(Quantity(2,\"m\"))", // "2[m]"); check("Re(Quantity(a,\"m\"))", // "Re(a)[m]"); check("Re(I*Pi/4 )", // "0"); check("Re(E^(I*Pi/4))", // "1/Sqrt(2)"); check("Re(Sin(42)*Cos(43))", // "Cos(43)*Sin(42)"); check("Re(Sin(42))", // "Sin(42)"); check("Re(I*9*Sin(5))", // "0"); check("Re(3+4*I)", // "3"); check("Re(0.5 + 2.3*I)", // "0.5"); check("Im(0.5 + 2.3*I)", // "2.3"); check("Re(0)", // "0"); check("Re(I)", // "0"); check("Re(Indeterminate)", // "Indeterminate"); check("Re(Infinity)", // "Infinity"); check("Re(-Infinity)", // "-Infinity"); check("Re(ComplexInfinity)", // "Indeterminate"); } @Test public void testReIm() { check("ReIm(Exp(2*I*Pi/3))", // "{-1/2,Sqrt(3)/2}"); check("ReIm((-17)^(1/4))", // "{17^(1/4)/Sqrt(2),17^(1/4)/Sqrt(2)}"); check("ReIm(2*z)", // "{2*Re(z),2*Im(z)}"); check("ReIm(Gamma(-1/2))", // "{-2*Sqrt(Pi),0}"); check("ReIm({a, {b, c}})", // "{{Re(a),Im(a)},{{Re(b),Im(b)},{Re(c),Im(c)}}}"); check("ReIm(3+4*I)", // "{3,4}"); check("ReIm(0.5 + 2.3*I)", // "{0.5,2.3}"); check("ReIm({I, -I, 0})", // "{{0,1},{0,-1},{0,0}}"); check("ReIm(z) /. z -> {I, -I, 0}", // "{{0,0,0},{1,-1,0}}"); check("ReIm(SparseArray({{1} -> I, {3} -> a, {4} -> -Pi}, {5})) // MatrixForm", // "{{0,1},\n"// + " {0,0},\n"// + " {Re(a),Im(a)},\n"// + " {-Pi,0},\n"// + " {0,0}}"); } @Test public void testReal() { check("Head(1.5)", // "Real"); } @Test public void testRealDigits() { check("RealDigits(423.012345678*^-11)", // "{{4,2,3,0,1,2,3,4,5,6,7,8},-8}"); check("RealDigits(423.012345678*^9)", // "{{4,2,3,0,1,2,3,4,5,6,7,8},12}"); check("RealDigits(1.012345678*^-11)", // "{{1,0,1,2,3,4,5,6,7,8},-10}"); check("RealDigits(1.012345678*^9)", // "{{1,0,1,2,3,4,5,6,7,8},10}"); check("RealDigits(1.012345678*^-42)", // "{{1,0,1,2,3,4,5,6,7,8},-41}"); check("RealDigits(1.012345678*^123)", // "{{1,0,1,2,3,4,5,6,7,8},124}"); check("N(RealDigits(Pi+42),30)", // "{{4,5,1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6,2,6,4,3,3,8,3,2},2}"); check("RealDigits(-42)", // "{{4,2},2}"); check("RealDigits(123.33333)", // "{{1,2,3,3,3,3,3,3},3}"); } @Test public void testRealValuedNumberQ() { // TODO // check("RealValuedNumberQ(Overflow())", // // "True"); check("RealValuedNumberQ(10)", // "True"); check("RealValuedNumberQ(4.0)", // "True"); check("RealValuedNumberQ(1+I)", // "False"); check("RealValuedNumberQ(0*I)", // "True"); check("RealValuedNumberQ(0.0*I)", // "False"); check("RealValuedNumberQ(Infinity)", // "False"); } @Test public void testRealValuedNumericQ() { check("RealValuedNumericQ(10)", // "True"); check("RealValuedNumericQ(4.0)", // "True"); check("RealValuedNumericQ(1+I)", // "False"); check("RealValuedNumericQ(0*I)", // "True"); check("RealValuedNumericQ(0.0*I)", // "False"); check("RealValuedNumericQ(Infinity)", // "False"); // TODO fix Underflow(),Overflow() implementation check("TableForm(\n" // + " Table({x, RealValuedNumberQ(x), " // + " RealValuedNumericQ(x)}, {x, {1, 3/2, 1.5, 1 + I, E, Sin(1), Underflow(), Overflow(), Infinity}}))", // " 1 True True \n" // + " 3/2 True True \n" // + " 1.5 True True \n" // + " 1+I False False \n" // + " E False True \n" // + " Sin(1) False True \n" // + " Underflow() True True \n" // + " Overflow() True True \n" // + " Infinity False False "); } @Test public void testRealAbs() { check("xval = Solve(RealAbs(x) == 2, x)", // "{{x->-2},{x->2}}"); check("N(RealAbs(Pi - Catalan), 50)", // "2.2256270594125742234080398683471187734230200250934"); check("RealAbs(Indeterminate)", // "Indeterminate"); check("RealAbs(-Infinity)", // "Infinity"); check("RealAbs({1.2, 1.5, 0})", // "{1.2,1.5,0}"); check("RealAbs(Interval({-1, 2}))", // "Interval({0,2})"); check("D(RealAbs(x),x)", // "x/RealAbs(x)"); check("Integrate(RealAbs(x),x)", // "1/2*x*RealAbs(x)"); check("PiecewiseExpand(RealAbs(x))", // "Piecewise({{-x,x<0}},x)"); } @Test public void testRealSign() { check("RealSign(1.1)", // "1"); check("RealSign(RealSign(x))", // "RealSign(x)"); // TODO ? return -Abs(a)+Abs(b) check("Integrate(RealSign(x),{x,a,b})", // "-RealAbs(a)+RealAbs(b)"); check("Integrate(RealSign(x),x)", // "RealAbs(x)"); check("D(RealSign(x),x)", // "Piecewise({{0,x!=0}},Indeterminate)"); check("RealSign(-Infinity)", // "-1"); check("RealSign({3, -5, 2 + 5 I})", // "{1,-1,RealSign(2+I*5)}"); check("Sign({3, -5, 2 + 5 I})", // "{1,-1,(2+I*5)/Sqrt(29)}"); check("RealSign(0``200)", // "0"); check("RealSign({\n" // + " {1, u},\n" + " {v, -1}\n" + " })", // "{{1,RealSign(u)},{RealSign(v),-1}}"); check("PiecewiseExpand(RealSign(x))", // "Piecewise({{-1,x<0},{1,x>0}},0)"); } @Test public void testReap() { // Sow with no sourrounding Reap // prints the numbers on console check("Do(Sow(i);Print(i), {i, 4})", // ""); check( "depthFirstPreorder(expr_) := Module(\n" + " {stack = {expr, {}}, el = expr},\n" + " Reap(\n" + " While(stack =!= {},\n" + " {el, stack} = stack;\n" + " Sow(el);\n" + " If(Not(AtomQ(el)),\n" + " Do(stack = {el[[j]], stack}, {j, Length(el), 1, -1}));\n" + " );\n" + " )[[2, 1]]\n" + " )", // ""); check("depthFirstPreorder({{1, {2, 3}}, {4, 5}})", // "{{{1,{2,3}},{4,5}},{1,{2,3}},1,{2,3},2,3,{4,5},4,5}"); check("Reap(Sow(1); Sow(2); Sow(3))", // "{3,{{1,2,3}}}"); check("Reap(Sow(1, {x, x}); Sow(1); Sow(2); Sow(3, x) )", // "{3,{{1,1,3},{1,2}}}"); check("Reap(Sow(1, {x, x}); Sow(2, y); Sow(3, x) )", // "{3,{{1,1,3},{2}}}"); check("Reap(Sow(1, {x, x}); Sow(2, y); Sow(3, x), _ )", // "{3,{{1,1,3},{2}}}"); check("Reap(Sow(1, {x, x}); Sow(2, y); Sow(3, x), _, f )", // "{3,{f(x,{1,1,3}),f(y,{2})}}"); check("Reap(Sow(1, {x, x}); Sow(2, y); Sow(3, x), y, f )", // "{3,{f(y,{2})}}"); check("Reap(Sow(1, {x, x}); Sow(2); Sow(3, x), _, f )", // "{3,{f(x,{1,1,3}),f(None,{2})}}"); check("Reap(Sow(1, {x, x}); Sow(2,y); Sow(3, x), _, Rule )", // "{3,{x->{1,1,3},y->{2}}}"); check("Reap(x)", // "{x,{}}"); check("Reap(Sow(a); b; Sow(c); Sow(d); e)", // "{e,{{a,c,d}}}"); check("Reap(Sum(Sow(i0^2) + 1, {i0, 10}))", // "{395,{{1,4,9,16,25,36,49,64,81,100}}}"); } @Test public void testReleaseHold() { check("f(ReleaseHold(HoldForm()))", // "f()"); check("f(ReleaseHold(HoldComplete(1 + 1, Evaluate(1 + 2), Sequence(3, 4))))", // "f(2,3,3,4)"); check("ReleaseHold(f(HoldForm()))", // "f()"); check("ReleaseHold(f(HoldComplete(1 + 1, Evaluate(1 + 2), Sequence(3, 4))))", // "f(2,3,3,4)"); check("ReleaseHold(HoldComplete(1 + 1, Evaluate(1 + 2), Sequence(3, 4)))", // "Identity(2,3,3,4)"); check("x = 3;", // ""); check("Hold(x)", // "Hold(x)"); check("ReleaseHold(Hold(x))", // "3"); check("ReleaseHold(y)", // "y"); check("ReleaseHold(Hold(x)+y)", // "3+y"); check("ReleaseHold /@ {Hold(1 + 2), HoldForm(2 + 3), HoldComplete(3 + 4), HoldPattern(_*_)}", // "{3,5,7,_^2}"); check("ReleaseHold(f(Hold(1 + g(Hold(2 + 3)))))", // "f(1+g(Hold(2+3)))"); check("ReleaseHold(f(1 + g(Hold(2 + 3))))", // "f(1+g(5))"); } @Test public void testRepeated() { check("f(x: {{_, _} ..}) := Norm(N(x))", // ""); check("f({{1,1}, {1,2}, {1,3}})", // "4.07914"); check("f({{1,1,1}, {1,2}, {1,3}})", // "f({{1,1,1},{1,2},{1,3}})"); check("{{}, {a}, {a, a}, {a, a, a}} /. {Repeated(a, 2)} -> x", // "{{},x,x,{a,a,a}}"); check("{{}, {a}, {a, a}, {a, a, a}} /. {Repeated(a, {1})} -> x", // "{{},x,{a,a},{a,a,a}}"); check("{{}, {a}, {a, a}, {a, a, a}} /. {Repeated(a, {0, 2})} -> x", // "{x,x,x,{a,a,a}}"); check("{{}, {a}, {a, a}, {a, a, a}} /. {Repeated(a, {1, 2})} -> x", // "{{},x,x,{a,a,a}}"); check("Repeated(a)", // "a.."); check("Repeated(a) // FullForm", // "Repeated(a)"); check("{{1, 1}, {1}, {2, 1}} /. {(1) ..} -> x", // "{x,x,{2,1}}"); check("MatchQ({4, 5, 6}, {Repeated(x_Integer)})", // "False"); check("MatchQ({4, 4, 4}, {Repeated(x_Integer)})", // "True"); check("MatchQ({4, 5, 6}, {Repeated(_Integer)})", // "True"); } @Test public void testRepeatedNull() { check("{{}, {a}, {a, a}, {a, a, a}} /. {RepeatedNull(a, {0, 2})} -> x", // "{x,x,x,{a,a,a}}"); check("RepeatedNull(a)", // "a..."); check("RepeatedNull(a) // FullForm", // "RepeatedNull(a)"); } @Test public void testRefine() { // TODO // check("Refine((E)^(Pi*I*2*(1/4+x)), Element(x, Integers))", // // "I"); // check("Refine(Log(x)0)", // // "True"); // check("Refine((-1)^(x+y), Element(k/2, Integers))", // // "(-1)^y"); check("Refine(Sqrt(x^2 y^2), x>0&&y<-10)", // "-x*y"); check("Refine(Csc(Pi*(1/2+m)), Element(m, Integers))", // "I^(-1+2*(1/2+m))"); check("Refine(Csc(Pi*(-1/2+m)), Element(m, Integers))", // "I^(-1+2*(-1/2+m))"); check("Refine(Csc(Pi*(1/4+m)), Element(m, Integers))", // "Csc((1/4+m)*Pi)"); check("Refine(Csc(Pi*(-1/4+m)), Element(m, Integers))", // "Csc((-1/4+m)*Pi)"); check("Refine(Csc(x+k*Pi), Element(k, Integers))", // "(-1)^k*Csc(x)"); check("Refine(Sin(Pi*(1/2+m)), Element(m, Integers))", // "I^(-1+2*(1/2+m))"); check("Refine(Sin(Pi*(-1/2+m)), Element(m, Integers))", // "I^(-1+2*(-1/2+m))"); check("Refine(Sin(Pi*(1/4+m)), Element(m, Integers))", // "Sin((1/4+m)*Pi)"); check("Refine(Sin(Pi*(-1/4+m)), Element(m, Integers))", // "Sin((-1/4+m)*Pi)"); check("Refine(Sin(x+k*Pi), Element(k, Integers))", // "(-1)^k*Sin(x)"); check("Refine(Sin(k*Pi), Element(k, Integers))", // "0"); check("Sin(k*Pi)", // "Sin(k*Pi)"); check("Refine(Cos(x+k*Pi), Element(k, Integers))", // "(-1)^k*Cos(x)"); check("Refine(Re(Log(x)),x>0)", // "Log(x)"); check("Refine(Im(Log(x)),x>0)", // "0"); check("Refine(Re(Log(x)),x<0)", // "Log(-x)"); check("Refine(Im(Log(x)),x<0)", // "Pi"); check("Refine(Sqrt(x^2),Assumptions -> Re(x)>0)", // "x"); check("Refine(Sqrt(x^2),Assumptions -> Re(x)<0)", // "-x"); check("Refine((x^4)^(1/4),Assumptions -> Re(x)>0)", // "(x^4)^(1/4)"); check("Refine((x^3)^(1/3),Assumptions -> Re(x)>0)", // "(x^3)^(1/3)"); check("Refine(Abs(a^b),Element(b,Reals))", // "Abs(a)^b"); check("Refine(Abs(a^b), b<0)", // "Abs(a)^b"); check("Refine(Re(2*I*Pi*C(1) + Log(2)) ,Element(C(1) ,Reals))", // "Log(2)"); check("Refine(7+2*m+3*n>0)", // "2*m+3*n>-7"); check("Refine(Sqrt(x^2), x>0)", // "x"); check("Refine(2*Im(x)+3, x>3)", // "3"); check("Refine(x0)", // "False"); check("Refine(x>=x, x>0)", // "True"); check("Refine((-1)^(43*k), Element(k, Integers))", // "(-1)^k"); check("Refine((-1)^(42*k), Element(k, Integers))", // "1"); check("Refine((-1)^(2+k), Element(k, Integers))", // "(-1)^k"); check("Refine((-1)^(43+k), Element(k, Integers))", // "(-1)^(1+k)"); check("Refine((-1)^(-43+k), Element(k, Integers))", // "(-1)^(1+k)"); check("Refine((-1)^(4*k), Element(k, Integers))", // "1"); check("Refine(Log(-3/4), x < 0)", // "I*Pi-Log(4/3)"); check("Refine(Log(x), x < 0)", // "I*Pi+Log(-x)"); check("Refine(EvenQ(4*k), Element(k, Integers))", // "True"); // for EvenQ result is undetermined check("Refine(EvenQ(3*k), Element(k, Integers))", // "False"); // for OddQ we cann not determine if true/false check("Refine(OddQ(4*k), Element(k, Integers))", // "False"); check("Refine(OddQ(3*k), Element(k, Integers))", // "False"); check("Refine(a>0)", // "a>0"); check("Refine(MoebiusMu(p),Element(p, Primes))", // "-1"); // TODO // check("Refine((a^b)^c, -10, x>1)", // "True"); check("Refine(Log(x)<0, x<1&&x>0)", // "True"); check("Refine(Log(x)<0, x<1&&x>0)", // "True"); check("Refine(Log(x)<0, x<1&&x>=0)", // "Log(x)<0"); check("Refine(x^4<0,x<0)", // "False"); check("Refine(x^(1/2)>=0, x>=0)", // "Sqrt(x)>=0"); check("Refine(x^4>=0,Element(x, Reals))", // "True"); check("Refine(x^4>0,Element(x, Reals))", // "x^4>0"); check("Refine(x^3>=0,Element(x, Reals))", // "x^3>=0"); check("Refine(x^4<0,Element(x, Reals))", // "x^4<0"); check("Refine(x^4<0,x<0)", // "False"); check("Refine(-x^4<=0,Element(x, Reals))", // "True"); check("Refine(-x^4<0,Element(x, Reals))", // "x^4>0"); check("Refine(E^x>0,Element(x, Reals))", // "True"); check("Refine(DiscreteDelta(x),x>0)", // "0"); check("Refine(DiscreteDelta(x),x<-1)", // "0"); check("Refine(DiracDelta(x),x>0)", // "0"); check("Refine(DiracDelta(x),x<-1)", // "0"); check("Refine(UnitStep(-x),x>0)", // "0"); check("Refine(UnitStep(x),x>0)", // "1"); check("Refine(UnitStep(y,x), x>0&&y>0)", // "1"); check("Refine(Re(a+I*b), Element(a, Reals)&&Element(b, Reals))", // "a"); check("(x^3)^(1/3)", // "(x^3)^(1/3)"); check("Refine((x^3)^(1/3), x>=0)", // "x"); check("Refine(Sqrt(x^2), Element(x, Reals))", // "Abs(x)"); check("Refine(Sqrt(x^2), Assumptions -> Element(x, Reals))", // "Abs(x)"); check("Refine(Sqrt(x^2), Element(x, Integers))", // "Abs(x)"); check("Refine(Sqrt(x^2), x>=0)", // "x"); check("Refine(Power((-x)^(1/2), 2), Element(x, Reals))", // "-x"); check("Refine((x^3)^(1/3), x >= 0)", // "x"); check("Refine(Abs(x), x>0)", // "x"); check("Refine(Abs(x), Assumptions -> x>0)", // "x"); check("Refine(Abs(x), x>1)", // "x"); check("Refine(Abs(x)>=0, Element(x, Reals))", // "True"); check("Refine(x>0, x>0)", // "True"); check("Refine(x>=0, x>0)", // "True"); check("Refine(x<0, x>0)", // "False"); check("Refine(x>-1, x>0)", // "True"); check("Refine(x>=-1, x>0)", // "True"); check("Refine(x<-1, x>0)", // "False"); check("Refine(x<0, x<0)", // "True"); check("Refine(x<=0, x<0)", // "True"); check("Refine(x>0, x<0)", // "False"); check("Refine(x<-1, x<0)", // "x<-1"); check("Refine(x<=-1, x<0)", // "x<=-1"); check("Refine(x>-1, x<0)", // "x>-1"); check("Refine(x>-1, x>0)", // "True"); check("Refine(x>-1, x>=0)", // "True"); check("Refine(Log(-4), x<0)", // "I*Pi+Log(4)"); check("Refine(Floor(2*a + 1), Element(a, Integers))", // "1+2*a"); check("Floor(2*a + 1)", // "1+Floor(2*a)"); check("Refine(Element(x, Integers), Element(x, integers))", // "True"); check("Refine(Floor(x),Element(x,Integers))", // "x"); check("Refine(Arg(x), Assumptions -> x>0)", // "0"); check("Refine(Arg(x), Assumptions -> x<0)", // "Pi"); check("Refine(x==0)", // "x==0"); } @Test public void testRest() { check("Rest(<|1 :> a, 2 -> b, 3 :> c|>)", // "<|2->b,3:>c|>"); check("Rest(f(x))", // "f()"); check("Rest(E^(b*x))", // "b*x"); check("Rest(a + b + c + d)", // "b+c+d"); check("Rest(f(a, b, c, d))", // "f(b,c,d)"); check("NestList(Rest, {a, b, c, d, e}, 3)", // "{{a,b,c,d,e},{b,c,d,e},{c,d,e},{d,e}}"); check("Rest(1/b)", // "-1"); check("Rest({a, b, c})", // "{b,c}"); check("Rest(a + b + c)", // "b+c"); check("Rest(a)", // "Rest(a)"); } /** * If this test fails try a change in AbstractAST#isZERO(). * * 
   * public boolean AbstractAST#isZERO() {
   *     return PredicateQ.possibleZeroQ(this, EvalEngine.get());
   * }
   *
*/ @Test public void testResultant() { // https://math.stackexchange.com/a/542228 check("Resultant(x^5+a*x^4+b*x^3+c*x^2+d*x+e, y-(x^2+m*x+n), x)", // "-e^2+d*e*m-c*e*m^2+b*e*m^3-a*e*m^4+e*m^5-d^2*n+2*c*e*n+c*d*m*n-3*b*e*m*n-b*d*m^2*n+\n" // + "4*a*e*m^2*n+a*d*m^3*n-5*e*m^3*n-d*m^4*n-c^2*n^2+2*b*d*n^2-2*a*e*n^2+b*c*m*n^2-3*a*d*m*n^\n" // + "2+5*e*m*n^2-a*c*m^2*n^2+4*d*m^2*n^2+c*m^3*n^2-b^2*n^3+2*a*c*n^3-2*d*n^3+a*b*m*n^\n" // + "3-3*c*m*n^3-b*m^2*n^3-a^2*n^4+2*b*n^4+a*m*n^4-n^5+d^2*y-2*c*e*y-c*d*m*y+3*b*e*m*y+b*d*m^\n" // + "2*y-4*a*e*m^2*y-a*d*m^3*y+5*e*m^3*y+d*m^4*y+2*c^2*n*y-4*b*d*n*y+4*a*e*n*y-2*b*c*m*n*y+\n" // + "6*a*d*m*n*y-10*e*m*n*y+2*a*c*m^2*n*y-8*d*m^2*n*y-2*c*m^3*n*y+3*b^2*n^2*y-6*a*c*n^\n" // + "2*y+6*d*n^2*y-3*a*b*m*n^2*y+9*c*m*n^2*y+3*b*m^2*n^2*y+4*a^2*n^3*y-8*b*n^3*y-4*a*m*n^\n" // + "3*y+5*n^4*y-c^2*y^2+2*b*d*y^2-2*a*e*y^2+b*c*m*y^2-3*a*d*m*y^2+5*e*m*y^2-a*c*m^2*y^\n" // + "2+4*d*m^2*y^2+c*m^3*y^2-3*b^2*n*y^2+6*a*c*n*y^2-6*d*n*y^2+3*a*b*m*n*y^2-9*c*m*n*y^\n" // + "2-3*b*m^2*n*y^2-6*a^2*n^2*y^2+12*b*n^2*y^2+6*a*m*n^2*y^2-10*n^3*y^2+b^2*y^3-2*a*c*y^\n" // + "3+2*d*y^3-a*b*m*y^3+3*c*m*y^3+b*m^2*y^3+4*a^2*n*y^3-8*b*n*y^3-4*a*m*n*y^3+10*n^2*y^\n" // + "3-a^2*y^4+2*b*y^4+a*m*y^4-5*n*y^4+y^5"); check("Resultant(3/4,13,x)", // "1"); check("Resultant(3/4,13,Indeterminate)", // "Resultant(3/4,13,Indeterminate)"); check("Resultant(0, x^3+2*x, x)", // "0"); check("Resultant(f(x), 0, x)", // "0"); check("Resultant(1,a+x^2+c,x)", // "1"); check("Resultant(a+x^2+c, 1, x)", // "1"); // check("Resultant((x - a) (x - b), (x - c) (x - d) (x - e), x)",// // // "(a*b+(-(-a^2*b-a*b^2+a*b*c+a*b*d+a*b*e-c*d*e)*(-a-b-(-a^2*b-a*b^2+a*b*c+a*b*d+a*b*e-c*d*e)/(a^\n" // + // // "2+a*b+b^2-a*c-b*c-a*d-b*d+c*d-a*e-b*e+c*e+d*e)))/(a^2+a*b+b^2-a*c-b*c-a*d-b*d+c*d-a*e-b*e+c*e+d*e))*(a^\n" // + // "2+a*b+b^2-a*c-b*c-a*d-b*d+c*d-a*e-b*e+c*e+d*e)^2"); check("PolynomialRemainder(-2+x^2-2*x*y+y^2,-5+4*x-2*x^3+2*y+3*x^2*y,y)", "-2+x^2+(5-4*x+2*x^3)*((5-4*x+2*x^3)/(2+3*x^2)^2+(-2*x)/(2+3*x^2))"); check("Resultant((x-y)^2-2 , y^3-5, y)", // "17-60*x+12*x^2-10*x^3-6*x^4+x^6"); check("Resultant(x^2 - 2*x + 7, x^3 - x + 5, x)", // "265"); check("Resultant(x^2 + 2*x , x-c, x)", // "2*c+c^2"); check("Resultant(x^2 - 4, x^2 + 4*x + 4, x)", // "0"); // MMA -3807 - Sympy 3807 check("Resultant(3*x + 9, 6*x^3 - 3*x + 12, x)", // "3807"); // check("Resultant[a x^3 + b x^2 + c x + f, f x^3 + c x^2 + b x + a, // x]", ""); } @Test public void testReturn() { check("retother:=(Return();hello);retother", // ""); check("f(x_) := (If(x < 0, Return(0)); x)", // ""); check("f(-1)", // "0"); check("Do(If(i > 3, Return()); Print(i), {i, 10})", // ""); check("g(x_) := (Do(If(x < 0, Return(0)), {i, {2, 1, 0, -1}}); x)", // ""); check("g(-1)", // "-1"); check("h(x_) := (If(x < 0, Return()); x)", // ""); check("h(1)", // "1"); check("h(-1) // FullForm", "Null"); check("f(x_) := Return(x)", // ""); check("g(y_) := Module({}, z = f(y); 2)", // ""); check("g(1)", // "2"); check("$a(x_):=Return(1); $b(x_):=Module({},$c=$a(y);2); $b(1)", // "2"); check("$f(x_) := (If(x > 5, Return(a)); x + 3); $f(6)", // "a"); check("$g(x_) := (Do( If(x > 5, Return(a)), {3}); x); $g(6)", // "6"); check("$h(x_) := Catch(Do(If(x > 5, Throw(a)), {3}); x); $h(6)", // "a"); } @Test public void testReverse() { check("Reverse(<|U->1,V->2|>)", // "<|V->2,U->1|>"); check("Reverse({1, 2, 3})", // "{3,2,1}"); check("Reverse(x(a,b,c))", // "x(c,b,a)"); // check("Reverse({{1, 2}, {3, 4}}, 1)", ""); } @Test public void testRGBColor() { check("Yellow", // "RGBColor(1.0,1.0,0.0)"); check("Purple", // "RGBColor(0.5,0.0,0.5)"); } @Test public void testRightComposition() { check("Hold[f @ g@@h] // FullForm", // "Hold(Apply(f(g), h))"); check("RightComposition(f, g, h)[x, y]", // "h(g(f(x,y)))"); check("f /* g /* h@x", // "h(g(f(x)))"); check("(f /* g /* h)@x", // "h(g(f(x)))"); } @Test public void testRiffle() { check("Riffle({1, 2, 3, 4, 5, 6, 7, 8, 9}, x)", // "{1,x,2,x,3,x,4,x,5,x,6,x,7,x,8,x,9}"); check("Riffle({1, 2, 3, 4, 5, 6, 7, 8, 9}, {x, y})", // "{1,x,2,y,3,x,4,y,5,x,6,y,7,x,8,y,9}"); check("Riffle({1}, x)", // "{1}"); check("Riffle({a, b, c, d}, {x, y, z, w})", // "{a,x,b,y,c,z,d,w}"); } @Test public void testRogersTanimotoDissimilarity() { check("RogersTanimotoDissimilarity({1, 0, 1, 1, 0}, {1, 1, 0, 1, 1})", // "3/4"); check("RogersTanimotoDissimilarity({True, False, True}, {True, True, False})", // "4/5"); check("RogersTanimotoDissimilarity({1, 1, 1, 1}, {1, 1, 1, 1})", // "0"); check("RogersTanimotoDissimilarity({0, 0, 0, 0}, {1, 1, 1, 1})", // "1"); } @Test public void testRomanNumeral() { // zero as special case represented by 'N' check("RomanNumeral(0)", // "N"); check("RomanNumeral({4000,3267,3603,1929,2575,746,666,1457,3828})", // "{MMMM,MMMCCLXVII,MMMDCIII,MCMXXIX,MMDLXXV,DCCXLVI,DCLXVI,MCDLVII,MMMDCCCXXVIII}"); check("RomanNumeral({1, 2, 3, 4, 5, 10, 50, 60, 100, 250, 500, 1000, 1500, 2600})", // "{I,II,III,IV,V,X,L,LX,C,CCL,D,M,MD,MMDC}"); } @Test public void testRoot() { check("Root(EvenQ(#1)&,1009)", // "Root(EvenQ(#1)&,1009)"); check("Root((#^2 - 3*# - 1)&, 2)", // "3/2+Sqrt(13)/2"); check("Root((-3*#-1)&, 1)", // "-1/3"); } @Test public void testRoots() { check("(-EulerGamma)^(1/3)", // "(-EulerGamma)^(1/3)"); check("Roots(x^3==EulerGamma,x)", // "x==-(-EulerGamma)^(1/3)||x==EulerGamma^(1/3)||x==(-1)^(2/3)*EulerGamma^(1/3)"); check("Roots(a*x^2+b*x+c==0,2)", // "Roots(c+b*x+a*x^2==0,2)"); // check("Roots(a*x^3+b*x^2+c^2+d, x)", // "{(-b/2-Sqrt(b^2-4*a*c)/2)/a,(-b/2+Sqrt(b^2-4*a*c)/2)/a}"); check("Roots(x^2-2*x-3==0,x)", // "x==-1||x==3"); check("Roots(a*x^2+b*x+c==0, x)", // "x==(-b-Sqrt(b^2-4*a*c))/(2*a)||x==(-b+Sqrt(b^2-4*a*c))/(2*a)"); check("Roots(3*x^3-8*x^2+-11*x+10==0,x)", // "x==2/3||x==1-Sqrt(6)||x==1+Sqrt(6)"); check("Roots(3*x^3-5*x^2+5*x-2==0,x)", // "x==2/3||x==1/2*(1-I*Sqrt(3))||x==1/2*(1+I*Sqrt(3))"); check("Roots(x^3 - 5*x + 4==0,x)", // "x==1||x==1/2*(-1-Sqrt(17))||x==1/2*(-1+Sqrt(17))"); } @Test public void testRotateLeft() { check("RotateLeft({})", // "{}"); check("RotateLeft({a,b,c}, 5)", // "{c,a,b}"); check("RotateLeft({1, 2, 3})", // "{2,3,1}"); check("RotateLeft(Range(10),3)", // "{4,5,6,7,8,9,10,1,2,3}"); check("RotateLeft(x(a,b,c),2)", // "x(c,a,b)"); check("RotateLeft({1,2,3,4,5},2)", // "{3,4,5,1,2}"); } @Test public void testRotateRight() { check("RotateRight({})", // "{}"); check("RotateRight({a,b,c}, 5)", // "{b,c,a}"); check("RotateRight({1, 2, 3})", // "{3,1,2}"); check("RotateRight(Range(10),3)", // "{8,9,10,1,2,3,4,5,6,7}"); check("RotateRight(x(a,b,c),2)", // "x(b,c,a)"); check("RotateRight({1,2,3,4,5},2)", // "{4,5,1,2,3}"); } @Test public void testRound() { check("Round(Quantity(8.5, \"Meters\"))", // "8[Meters]"); check("Round(-1.235512, 0)", // "Indeterminate"); // message Round: Internal precision limit reached while evaluating // 1/E^(9223372036854775808/11). check("Round(3/2,1/E^(9223372036854775808/11))", // "Round(3/2,1/E^(9223372036854775808/11))"); check("Round(10+x)", // "Round(10+x)"); check("Round(-10+x)", // "-Round(10-x)"); check("Round(10+x,Pi)", // "Round(10+x,Pi)"); check("Round(Infinity, x)", // "Round(Infinity,x)"); check("Round(Infinity, Pi)", // "Infinity"); check("Round(-Infinity, Pi)", // "-Infinity"); check("Round(1+2*I, 2*I)", // "I*2"); check("Round(10, Pi)", // "3*Pi"); check("Round(-10, Pi)", // "-3*Pi"); check("Round(12, Pi)", // "4*Pi"); check("Round(-12, Pi)", // "-4*Pi"); check("Round(5.37 - 1.3*I)", // "5-I"); check("Round(DirectedInfinity(0))", // "ComplexInfinity"); check("Round(DirectedInfinity((1/2-I*1/2)*Sqrt(2)))", // "DirectedInfinity((1/2-I*1/2)*Sqrt(2))"); // github #145 // TODO add tests for big (Apfloat) numbers // Rationalize(2.1675 => 867/400 check("Round(Rationalize(867/400),10^(-3))", // "271/125"); check("Round(Rationalize(2.1675),10^(-3))", // "271/125"); check("Round(2.1675, 0.001)", // "2.168"); check("Round(2.1675, 1/1000)", // "271/125"); check("Round(500,10^(-3))", // "500"); check("Round(500, 10)", // "500"); check("Round(75.345677/7.56)", // "10"); check("Round(1.234512, 0.01)", // "1.23"); check("Round(-1.234512, 0.01)", // "-1.23"); check("Round(1.235512, 0.01)", // "1.24"); check("Round(-1.235512, 0.01)", // "-1.24"); check("Round(1.234512, -0.01)", // "1.23"); check("Round(-1.234512, -0.01)", // "-1.23"); check("Round(1.235512, -0.01)", // "1.24"); check("Round(-1.235512, -0.01)", // "-1.24"); check("Round(1.234512, 1/100)", // "123/100"); check("Round(-1.235512, 1/100)", // "-31/25"); check("Round(-1.235512, -100)", // "0"); check("Round(-1.235512, 0)", // "Indeterminate"); check("Refine(2/3*Round(x), Element(x,Integers))", // "2/3*x"); check("Round(226, 10)", // "230"); check("Round(226, -10)", // "230"); check("Round({12.5, 62.1, 68.3, 74.5, 80.7}, 5)", // "{10,60,70,75,80}"); check("Round({5, 15, 25, 35, 45}, 10)", // "{0,20,20,40,40}"); check("Round(75.345677/7.56)", // "10"); check("Table(Round(n), {n, {-5/3, 10/3, 13/2}})", // "{-2,3,6}"); check("Table(Round((GoldenRatio^k)/Sqrt(5)), {k, 15}) ==" + // "Table(Fibonacci(k), {k, 15})", // "True"); check("Round(Infinity)", // "Infinity"); check("Round(-Infinity)", // "-Infinity"); check("Round(Pi-E)", // "0"); check("Round(5.37-I)", // "5-I"); check("Round(4/(1+I))", // "2-I*2"); check("Round(3.4)", // "3"); check("Round(3.5)", // "4"); check("Round(3.6)", // "4"); check("Round(-3.4)", // "-3"); check("Round(-3.5)", // "-4"); check("Round(-3.6)", // "-4"); check("Round(N[0.03306158858189456, 30] * 100, 10^-2) // N", // "3.31"); } @Test public void testRussellRaoDissimilarity() { check("RussellRaoDissimilarity({1, 0, 1, 1, 0}, {1, 1, 0, 1, 1})", // "3/5"); check("RussellRaoDissimilarity({True, False, True}, {True, True, False})", // "2/3"); check("RussellRaoDissimilarity({1, 1, 1, 1}, {1, 1, 1, 1})", // "0"); check("RussellRaoDissimilarity({0, 0, 0, 0}, {1, 1, 1, 1})", // "1"); } @Test public void testRule() { check("a+b+c /. c->d", // "a+b+d"); check("{x,x^2,y} /. x->3", // "{3,9,y}"); // Rule called with 3 arguments; 2 arguments are expected. check("a /. Rule(1, 2, 3) -> t ", // "a"); } @Test public void testSameQUnsameQ() { // mathics #146 // check("a=N[2/9,3]; b=0.22222`5; {a,b,a==b, a===b}", // // "{0.222,0.22222,False,False}"); check("SameQ( )", // "True"); check("SameQ(abc)", // "True"); check("UnsameQ( )", // "True"); check("UnsameQ(abc)", // "True"); check("a===a", // "True"); check("SameQ(0.0, 0)", // "False"); check("UnsameQ(0.0, 0)", // "True"); check("$g(f(x))===v", // "False"); check("$g(f(x))===$g(f(x))", // "True"); check("$g(f(x))=!=v", // "True"); check("$g(f(x))=!=$g(f(x))", // "False"); check("Boole(Array(UnsameQ, {3, 3, 3}))", // "{{{0,0,0},{0,0,1},{0,1,0}},{{0,0,1},{0,0,0},{1,0,0}},{{0,1,0},{1,0,0},{0,0,0}}}"); } @Test public void testSawtoothWave() { check("SawtoothWave(-1.444444)", // "0.555556"); check("SawtoothWave({0, 5},{0.4, 1.2, 3.6})", // "{2.0,1.0,3.0}"); check("SawtoothWave(0.333)", // "0.333"); check("SawtoothWave(17.333)", // "0.333"); check("SawtoothWave(41/42)", // "41/42"); check("SawtoothWave(42/41)", // "1/41"); check("N(SawtoothWave(-1/47), 50)", // "0.97872340425531914893617021276595744680851063829787"); check("SawtoothWave({0.4, 1.2, 3.6})", // "{0.4,0.2,0.6}"); } @Test public void testScan() { // TODO e1 ~ e2 ~ e3 => e2[e1, e3] // check("(Print@#; #0 ~Scan~ #)& @ {{1, {2, 3}}, {4, 5}}", // // ""); // prints // 1 // 2 // 3 // {2,3} // {1,{2,3}} // 4 // 5 // {4,5} // {{1,{2,3}},{4,5}} check("Scan(Print,<|1 -> {{a}}, 2 -> b|>, 2)", // ""); check("Scan(Print,<|1 -> a, 2 -> b, 3 -> c|>)", // ""); check("expr = {{1, {2, 3}}, {4, 5}}; Scan(Print, expr, {0, -1})", // ""); check("Scan(Print)[{a, b, c}]", // ""); check("Scan(Print, {1, 2, 3}, Heads->True)", // ""); check("Scan(($u(#) = x) &, {55, 11, 77, 88});{$u(76), $u(77), $u(78)}", // "{$u(76),x,$u(78)}"); check("Map(If(# > 5, #, False) &, {2, 4, 6, 8})", // "{False,False,6,8}"); check("Catch(Map(If(# > 5, Throw(#)) &, {2, 4, 6, 8}))", // "6"); check("Catch(Scan(If(# > 5, Throw(#)) &, {2, 4, 6, 8}))", // "6"); check("Reap(Scan(\n" + " If(# > 0, Sow(#)) &, {1, {-2, Pi}, -Sqrt(3)},Infinity))[[2, 1]]", // "{1,Pi,3,1/2,Sqrt(3)}"); check("Scan(Return, {1, 2})", // "1"); check( "Reap(Scan(Sow, -(ArcTan((1 + 2*x)/Sqrt(3))/Sqrt(3)) + (1/3)*Log(1 - x) - (1/6)*Log(1 + x + x^2), {-1}))[[2, 1]]", // "{-1,3,-1/2,3,-1/2,1,2,x,1/3,1,-1,x,-1/6,1,x,x,2}"); } @Test public void testSec() { // check("Sec(8/15*Pi)", // // "-Csc(Pi/30)"); // check("Sec(4/15*Pi)", // // "-Csc(1/30*Pi)"); check("-Sec(Pi/4-x)", // "-Sec(Pi/4-x)"); check("-Sec(Pi/3-x)", // "-Sec(Pi/3-x)"); check("Sec(5/7*Pi+x)", // "-Csc(3/14*Pi+x)"); check("Sec(3/4*Pi+x)", // "-Csc(Pi/4+x)"); check("Sec(-3/4*Pi+x)", // "-Sec(Pi/4+x)"); check("Sec(e - Pi/2 + f*x)", // "Csc(e+f*x)"); check("Sec(e+f*x)^m*Tan(e+f*x)^2", // "Sec(e+f*x)^(2+m)*Sin(e+f*x)^2"); check("Sec(e+f*x)^m*Tan(e+f*x)", // "Sec(e+f*x)^(1+m)*Sin(e+f*x)"); check("Sec(Pi/2+Pi*n)", // "-Csc(n*Pi)"); check("Sec(0)", // "1"); check("Sec(1)", // "Sec(1)"); checkNumeric("Sec(1.)", // "1.8508157176809255"); check("Sec(Pi/2)", // "ComplexInfinity"); check("Sec(0)", // "1"); check("Sec(2/5*Pi)", // "1+Sqrt(5)"); check("Sec(23/12*Pi)", // "-Sqrt(2)+Sqrt(6)"); check("Sec(z+1/2*Pi)", // "-Csc(z)"); check("Sec(Pi)", // "-1"); check("Sec(33*Pi)", // "-1"); check("Sec(z+Pi)", // "-Sec(z)"); check("Sec(z+42*Pi)", // "Sec(z)"); check("Sec(x+y+z+43*Pi)", // "-Sec(x+y+z)"); check("Sec(z+42*a*Pi)", // "Sec(42*a*Pi+z)"); check("Sec(z+4/3*Pi)", // "-Sec(Pi/3+z)"); check("Sec(Sqrt(x^2))", // "Sec(x)"); } @Test public void testSech() { // gitbub #173 check("Sech(Log(5/3))", // "15/17"); check("Refine(Sech(x+I*k*Pi), Element(k, Integers))", // "(-1)^k*Sech(x)"); check("Refine(Sech(x-I*k*Pi), Element(k, Integers))", // "(-1)^k*Sech(x)"); check("Refine(Sech(x-42*I*k*Pi), Element(k, Integers))", // "Sech(x)"); check("Refine(Sech(x-43*I*k*Pi), Element(k, Integers))", // "(-1)^k*Sech(x)"); check("Sech(x)^m*Tanh(x)^2", // "Sech(x)^(2+m)*Sinh(x)^2"); check("Sech(0)", // "1"); checkNumeric("Sech(1.8)", // "0.3218048695065878"); check("Sech(-x)", // "Sech(x)"); check("D(Sech(x),x)", // "-Sech(x)*Tanh(x)"); } @Test public void testSelect() { check("Select({1,2,4,7,6,2},#1>2&,0)", // "{}"); check("Select({-3, 0}, #>10&)", // "{}"); check("Select(<|a -> 1, b -> 2, c -> 3, d -> 4|>, # > 6 &)", // "<||>"); check("Select(<|a -> 1, b -> 2, c -> 3, d -> 4|>, # > 2 &)", // "<|c->3,d->4|>"); check("Select(Accumulate(Table({1,Prime(x)},{x,900,1000})), PrimeQ( #[[2]] )& )", // "{{1,6997},{3,21011},{7,49139},{11,77447},{87,644377},{93,691333}}"); check("Select(# > 4 &) [{1, 2.2, 3, 4.5, 5, 6, 7.5, 8}]", // "{4.5,5,6,7.5,8}"); check("Cases(_Integer)@Select(# > 4 &)@{1, 2.2, 3, 4.5, 5, 6, 7.5, 8}", // "{5,6,8}"); check("Select({-3, 0, 1, 3, a}, #>0&)", // "{1,3}"); check("Select(f(a, 2, 3), NumberQ)", // "f(2,3)"); check("Select(a, True)", // "Select(a,True)"); check("Select({1, 2, 4, 7, 6, 2}, EvenQ)", // "{2,4,6,2}"); check("Select({1, 2, 4, 7, 6, 2}, # > 2 &)", // "{4,7,6}"); check("Select({1, 2, 4, 7, 6, 2}, # > 2 &, 1)", // "{4}"); check("Select({1, 2, 4, 7, x}, # > 2 &)", // "{4,7}"); check("Select(f(1, a, 2, b, 3), IntegerQ)", // "f(1,2,3)"); check("Select(Range(100), Mod(#, 3) == 1 && Mod(#, 5) == 1 &)", // "{1,16,31,46,61,76,91}"); } @Test public void testSelectFirst() { check("SelectFirst(<|1 -> \"a\", 2 -> \"b\", 3 -> c, 4 -> d|>,Head(#)==Symbol &)", // "c"); check("SelectFirst({-3, 0, 1, 3, a}, #>0 &)", // "1"); check("SelectFirst({-3, 0, 1, 3, a}, #>3 &)", // "Missing(NotFound)"); check("SelectFirst({1, 2, 4, 7, 6, 2}, EvenQ)", // "2"); check("SelectFirst({1, 2, 4, 7, 6, 2}, # > 2 &)", // "4"); check("SelectFirst({1, 3, 5}, EvenQ, x)", // "x"); check("SelectFirst({1, 3, 5, 6}, EvenQ, x)", // "6"); check("SelectFirst(EvenQ)[{1, 2, 4, 7, 6, 2}]", // "2"); check("SelectFirst({{1, y}, {2, z}, {3, x}, {4, y}, {5, x}}, MemberQ(#, x) &)", // "{3,x}"); check("SelectFirst(f(1, a, 2, b, 3), IntegerQ)", // "1"); check("SelectFirst({1, 2, 3}, StringQ, \"NoStrings\")", // "NoStrings"); } @Test public void testSequence() { check("Sequence(a,b,c)", // "Identity(a,b,c)"); check("{Sequence( ),a}", // "{a}"); check("f(a, Sequence( ),b,c)", // "f(a,b,c)"); check("{u, u, u} /. u -> Sequence(a, b, c)", // "{a,b,c,a,b,c,a,b,c}"); check("f(a, Sequence(b, c), d)", // "f(a,b,c,d)"); check("$u = Sequence(a, b, c)", // "Identity(a,b,c)"); check("$u = Sequence(a, b, c);{$u,$u,$u}", // "{a,b,c,a,b,c,a,b,c}"); check("f({{a, b}, {c, d}, {a}}) /. List -> Sequence", // "f(a,b,c,d,a)"); // message Identity: Identity called with 3 arguments; 1 argument is expected. check("f(a, b, c) /. f(x__) -> x", // "Identity(a,b,c)"); check("{a, Sequence(b), c, Identity(d)}", // "{a,b,c,d}"); // print message check("Head(Sequence(a,b))", // "b(Symbol)"); check("u->Sequence[a,b]", // "u->Sequence(a,b)"); check("myOpts(func_, target_) := {o1 -> thick, If(func === target, o2 -> 0, Sequence @@ {})}", // ""); check("myOpts(x^2,x^2)", // "{o1->thick,o2->0}"); check("myOpts(3*x,x^2)", // "{o1->thick}"); check("f(x, Sequence(a, b), y)", // "f(x,a,b,y)"); check("Attributes(Set)", // "{HoldFirst,Protected,SequenceHold}"); check("a = Sequence(b, c);", // ""); check("a", // "Identity(b,c)"); check("lst = {1, 2, 3};", // ""); check("f(Sequence @@ lst)", // "f(1,2,3)"); check("Hold(a, Sequence(b, c), d)", // "Hold(a,b,c,d)"); // If Sequence appears at a deeper level in Hold(), it is left unevaluated check("Hold({a, Sequence(b, c), d})", // "Hold({a,Sequence(b,c),d})"); } @Test public void testSet() { check("aVar=10", // "10"); // integer not allowed as header is (Protected) check("aVar(x_):={x}", // "$Failed"); // check("A = {{1, 2}, {3, 4}}", "{{1,2},{3,4}}"); // check("A[[;;, 2]] = {6, 7} ", "{6,7}"); // check("A", "{{1,6},{3,7}}"); // // check("B = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} ", "{{1,2,3},{4,5,6},{7,8,9}}"); // check("B[[1;;2, 2;;-1]] = {{t, u}, {y, z}}", "{{t,u},{y,z}}"); // check("B", "{{1,t,u},{4,y,z},{7,8,9}}"); check("foo=barf", // "barf"); check("foo(x)=1", // "1"); check("barf(x)=1", // "1"); check("a = 3", // "3"); check("a", // "3"); check("{a, b, c} = {10, 2, 3} ", // "{10,2,3}"); check("{a, b, {c, {d}}} = {1, 2, {{c1, c2}, {a}}} ", // "{1,2,{{c1,c2},{10}}}"); check("d", // "10"); check("a", // "1"); check("x = a", // "1"); check("a = 2", // "2"); check("x", // "1"); check("a = b = c = 2", // "2"); check("a == b == c == 2", // "True"); check("A = {{1, 2}, {3, 4}}", // "{{1,2},{3,4}}"); check("A[[1, 2]] = 5", // "5"); check("A", // "{{1,5},{3,4}}"); check("A[[;;, 2]] = {6, 7} ", // "{6,7}"); check("A", "{{1,6},{3,7}}"); check("B = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} ", // "{{1,2,3},{4,5,6},{7,8,9}}"); check("B[[1;;2, 2;;-1]] = {{t, u}, {y, z}}", // "{{t,u},{y,z}}"); check("B", // "{{1,t,u},{4,y,z},{7,8,9}}"); } @Test public void testSetAttributes() { check("SetAttributes({f, g}, {Flat, Orderless})", // ""); check("Attributes(f)", // "{Flat,Orderless}"); check("SetAttributes(h, Flat)", // ""); check("Attributes(h)", // "{Flat}"); } @Test public void testSetDelayed() { check("f(x_, nm : Association((_String -> _Integer) ..)) := {x,nm}", // ""); check("f(a,<|\"c\"->3, \"d\"->4|>)", // "{a,<|c->3,d->4|>}"); check("Attributes(SetDelayed) ", // "{HoldAll,Protected,SequenceHold}"); check("a = 1", // "1"); check("x := a", // ""); check("x", // "1"); check("a = 2", // "2"); check("x", // "2"); check("f(x_) := p(x) /; x>0", // ""); check("f(3)", // "p(3)"); check("f(-3)", // "f(-3)"); } @Test public void testSetDelayedOneIdentity() { check("SetAttributes(SUNIndex, {OneIdentity})", // ""); check("SetAttributes(SUNFIndex, {OneIdentity})", // ""); check( "SUNIndex(SUNFIndex(___)):= (Print(\"This error shouldn't be triggered here!\"); Abort())", // ""); check( "SUNFIndex(SUNIndex(___)):= (Print(\"This error shouldn't be triggered here!\"); Abort())", // ""); } @Test public void testShare() { check( "people = <|\n" + "236234 -> <|\"name\" -> \"bob\", \"age\" -> 18, \"sex\" -> \"M\"|>, \n" + "253456 -> <|\"name\" -> \"sue\", \"age\" -> 25, \"sex\" -> \"F\"|>, \n" + "323442 -> <|\"name\" -> \"ann\", \"age\" -> 18, \"sex\" -> \"F\"|>\n" + "|>", // "<|236234-><|name->bob,age->18,sex->M|>,253456-><|name->sue,age->25,sex->F|>,\n" + "323442-><|name->ann,age->18,sex->F|>|>"); check("Share(people)", // "2"); check("people", // "<|236234-><|name->bob,age->18,sex->M|>,253456-><|name->sue,age->25,sex->F|>,\n" + "323442-><|name->ann,age->18,sex->F|>|>"); check("sh= Table(j*(x + i), {i, 5}, {j, i}) ", // "{{1+x},{2+x,2*(2+x)},{3+x,2*(3+x),3*(3+x)},{4+x,2*(4+x),3*(4+x),4*(4+x)},{5+x,2*(\n" + "5+x),3*(5+x),4*(5+x),5*(5+x)}}"); check("Share(sh)", // "10"); check("sh", // "{{1+x},{2+x,2*(2+x)},{3+x,2*(3+x),3*(3+x)},{4+x,2*(4+x),3*(4+x),4*(4+x)},{5+x,2*(\n" + "5+x),3*(5+x),4*(5+x),5*(5+x)}}"); check("Share(Table(xi = x + i; Table(j*xi, {j, i}), {i, 5}))", // "0"); } @Test public void testShort() { check("Short(Expand((1 + x + y)^12))", // "1+12*x+66*x^2+220*x^3+495*<>10+12*y^\n" + "11+12*x*y^11+y^12"); } @Test public void testSignature() { check("Signature({1,2,3,4})", // "1"); check("Signature({1,4,3,2})", // "-1"); check("Signature({1,2,3,2})", // "0"); check("Signature({a,b,c})", // "1"); check("Signature({a,b,c,d})", // "1"); check("Signature({a,c,b})", // "-1"); check("Signature({a,c,b,d})", // "-1"); check("Signature({a,b,b})", // "0"); check("Select(Permutations({a,b,c,d}),Signature(#)==1&)", // "{{a,b,c,d},{a,c,d,b},{a,d,b,c},{b,a,d,c},{b,c,a,d},{b,d,c,a},{c,a,b,d},{c,b,d,a},{c,d,a,b},{d,a,c,b},{d,b,a,c},{d,c,b,a}}"); check("Array(Signature({##})&,{3,3,3})", // "{{{0,0,0},{0,0,1},{0,-1,0}},{{0,0,-1},{0,0,0},{1,0,0}},{{0,1,0},{-1,0,0},{0,0,0}}}"); } @Test public void testSign() { check("Sign(Sign(z))", // "Sign(z)"); check("Sign(Power(z, (-11)^(-1)))", // "1/Sign(z)^(1/11)"); check("Sign(Power(z, (13)^(-1)))", // "Sign(z)^(1/13)"); check("Sign(I^(2*Pi))", // "I^(2*Pi)"); check("Sign(a*b^(-3)*c^2)", // "(Sign(a)*Sign(c)^2)/Sign(b)^3"); // message Power: Infinite expression 1/0 encountered. check("Sign(1/0^(0.8+I*(-1.2)))", // "Indeterminate"); check("Sign(Sign(z))", // "Sign(z)"); check("Sign(Exp(z))", // "E^(I*Im(z))"); check("Sign(2+I)", // "(2+I)/Sqrt(5)"); check("Sign(1+I*Sqrt(3))", // "1/2*(1+I*Sqrt(3))"); check("Sign(Sqrt(3)+I)", // "1/2*(I+Sqrt(3))"); check("Sign(1.0+I)", // "0.707107+I*0.707107"); check("Sign(Indeterminate)", // "Indeterminate"); check("Sign(2.5)", // "1"); check("Sign(-2.5)", // "-1"); check("Sign(0.0)", // "0"); check("Sign({-2, -1, 0, 1, 2})", // "{-1,-1,0,1,1}"); check("Pi>E", // "True"); check("Pir})", // "r"); check("Simplify(Log(E^n))", // "Log(E^n)"); check("Simplify(Log(E^n),n>0)", // "n"); check("Simplify(0^x, x==0)", // "Indeterminate"); check("Simplify(0^x, x>0)", // "0"); check("Simplify(0^x, x<0)", // "ComplexInfinity"); check(" Simplify(y -> 1+Cot(x)^2)", // "y->Csc(x)^2"); // TODO ??? // check("Simplify(Sqrt(1+a*x)/Sqrt(1-a^2*x^2) )", // // "1/Sqrt(1-a*x)"); check("Together((-574-2*Sqrt(21))/(-476))", // "1/238*(287+Sqrt(21))"); check("Simplify(Abs(x)^2,Element(x,Reals))", // "x^2"); check("Simplify(Abs(x)^3,Element(x,Reals))", // "Abs(x)^3"); check("Simplify(1+Cot(x)^2)", // "Csc(x)^2"); check("Simplify(1+Tan(x)^2)", // "Sec(x)^2"); check("Simplify(E^(a1*a2*Log(f)+b+Log(g)))", // "E^b*f^(a1*a2)*g"); check("Simplify(E^(a1*a2*Log(f)*Log(h)+b+Log(g)))", // "E^(b+a1*a2*Log(f)*Log(h))*g"); check("Simplify(E^(a1*a2*Log(f)+Log(g)))", // "f^(a1*a2)*g"); check("Simplify((-a+c)*(-a+x))", // "(a-c)*(a-x)"); check("Simplify(Log(a*(a-b)*(a-c)-a^2*x+a*b*x+a*c*x-b*c*x))", // "Log((a-b)*(a-c)*(a-x))"); check("Simplify((2/3-a)^(-5/4)*(2/3+a)^(-5/4))", // "1/(4/9-a^2)^(5/4)"); check("Simplify((2-a)^(c)* (2+a)^(c))", // "(4-a^2)^c"); // FullSimplify tries more steps (even for the same expressions as in Simplify) check("FullSimplify((2/3-a)^(-5/4)*(2/3+a)^(-5/4))", // "1/(4/9-a^2)^(5/4)"); check("FullSimplify((2-a)^(c)* (2+a)^(c))", // "(4-a^2)^c"); // https://github.com/axkr/symja_android_library/issues/142 check("Simplify({{x+y+x*y==9},{x*y*(x+y)==20}})", // "{{x+y+x*y==9},{x*y*(x+y)==20}}"); check("Simplify(-3+2*x+x^2==0)", // "2*x+x^2==3"); check("Simplify({Im(Exp(I*Pi/5)* x), Im(2*x + I)}, x > 3)", // "{Im(E^(I*1/5*Pi)*x),1}"); // check("Simplify(1/((1+x)*(1/(2*x*(1+x))-ArcTan(Sqrt(x))/(2*x^(3/2)))))", // // "(-2*x^(3/2))/(-Sqrt(x) + (1 + x)*ArcTan(Sqrt(x)))"); // check("Simplify((-1/(Sqrt(x)*(1+x))+(-1-x)/(2*x^(3/2)*(1+x)))/(1+x))", // // "(-1 - 3*x)/(2*x^(3/2)*(1 + x)^2)"); // check("Simplify(1/(ArcTan(Sqrt(x))/(-1/(Sqrt(x)*(1+x)^2)-1/(2*x^(3/2)*(1+x))))", // // "(-2*x^(3/2)*(1 + x)^2*ArcTan(Sqrt(x)))/(1 + 3*x)"); // // check("Simplify((1+(-2*x*(d*Sqrt(-e/d)+e*x))/(d+e*x^2))/((d+e*x^2)*((-4*e*(d*Sqrt(-e/d)+e*x)*x^2)/(d+e*x^2)^2+(2*e*x)/(d+e*x^2)+(2*(d*Sqrt(-e/d)+e*x))/(d+e*x^2))))", // // // "(-d+2*d*Sqrt(-e/d)*x+e*x^2)/(2*d*(-d*Sqrt(-e/d)-2*e*x+e*Sqrt(-e/d)*x^2))");//"-Sqrt(-(e/d))/(2*e)"); check( "Simplify((x*(-Sqrt(-4+x^2)+x^2*Sqrt(-4+x^2)-4*Sqrt(-1+x^2)+x^2*Sqrt(-1+x^2)))/((4-5*x^2+x^4)*(x/Sqrt(-4+x^2)+x/Sqrt(-1+x^2))))", // "1"); check("Simplify((Cos(x)-I*Sin(x))/(I*Cos(x)-Sin(x)))", // "-I*Cos(2*x)-Sin(2*x)"); // -I*Cos(2*x)-Sin(2*x) check("Expand((-I*a+b)*(I*Cosh(x)+Sinh(x)))", // "a*Cosh(x)+I*b*Cosh(x)-I*a*Sinh(x)+b*Sinh(x)"); check("Factor(TrigToExp( a*Cosh(x)+I*b*Cosh(x)-I*a*Sinh(x)+b*Sinh(x) ))", // "((1/2+I*1/2)*(-I*a+b)*(I+E^(2*x)))/E^x"); check("Simplify((-I*a+b)*(I*Cosh(x)+Sinh(x)))", // "(a+I*b)*(Cosh(x)-I*Sinh(x))"); check("Simplify(Element(x, Reals), x>0)", // "True"); check("Simplify(Sin(n*Pi), Element(n, Integers))", // "0"); check("Simplify(Tan(x + Pi*n), Element(n, Integers))", // "Tan(x)"); check( "Simplify(a/((a-I*b)*(a/(a-I*b)+(-I*b)/(a-I*b)))+(b*Sinh(x))/((a-I*b)*(a/(a-I*b)+(-I*b)/(a-I*b))))", // "(a+b*Sinh(x))/(a-I*b)"); check("Simplify((a-I*b)*(a/(a-I*b)+(-I*b)/(a-I*b)))", // "a-I*b"); check("Simplify(-2*Log(2))", // "-Log(4)"); check("Simplify(Log(6)-Log(2))", // "Log(3)"); check("Simplify(a+Log(1/6)+Log(1/7)+z())", // "a-Log(42)+z()"); check("Simplify(a+Log(1/6)+Log(1/7)+Log(3/4)+z())", // "a-Log(56)+z()"); check("Simplify(a+Log(1/6)-2*Log(1/7)+7*Log(3/4)+z())", // "a+Log(35721/32768)+z()"); check("Simplify(1+n/2)", // "1/2*(2+n)"); check("Simplify((9-Sqrt(57))*x^2)", // "(9-Sqrt(57))*x^2"); check("Simplify(-a/(-b+a*c))", // "a/(b-a*c)"); check("Simplify(1/(Cos(x)+I*Sin(x))-(c+d*x)^n)", // "-(c+d*x)^n+Cos(x)-I*Sin(x)"); check("Simplify(1/(Cos(x)+I*Sin(x)))", // "Cos(x)-I*Sin(x)"); check("Expand((Sqrt(-d)*e+d*Sqrt(e)*Sqrt(-e/d))*(Sqrt(-d)*e-d*Sqrt(e)*Sqrt(-e/d)))", // "0"); check("Simplify((e*x^2)/(Sqrt(-d)*e-d*Sqrt(e)*Sqrt(-e/d)))", // "(e*x^2)/(Sqrt(-d)*e-d*Sqrt(e)*Sqrt(-e/d))"); check("Simplify((-b^12*x^456)/x^12+(x^12*(a+b*x^37)^12)/x^12)", // "-b^12*x^444+(a+b*x^37)^12"); check("Simplify(-Cos(x) +Sin(x)^2/(1-Cos(x)))", // "1"); check("Simplify(-Cos(x)/(1-Cos(x))+Sin(x)^2/(1-Cos(x))^2-1/(1-Cos(x)))", // "0"); check("Simplify(x^(5/2) - Sqrt(x^5), x>=0)", // "0"); check("Simplify(-136+40*Sqrt(17))", // "8*(-17+5*Sqrt(17))"); check("Simplify(Sqrt(17)/(5+Sqrt(17)))", // "1/8*(-17+5*Sqrt(17))"); // check("Simplify(Cos(b*x)/(-Cos(b*x)/x^2-CosIntegral(b*x)/x^2))", // // "(x^2*Cos(b*x))/(-Cos(b*x)-CosIntegral(b*x))"); check("Together(-Cos(b*x)/x^2+(-b*Sin(b*x))/x)", // "(-Cos(b*x)-b*x*Sin(b*x))/x^2"); check("Simplify(-Cos(b*x)/x^2+(-b*Sin(b*x))/x)", // "(-Cos(b*x)-b*x*Sin(b*x))/x^2"); check("Simplify(-(b/(2*Sqrt(c))+Sqrt(c)*x)^24+(a+b*x+c*x^2)^12)", // "-(b/(2*Sqrt(c))+Sqrt(c)*x)^24+(a+b*x+c*x^2)^12"); check("Simplify(-ArcTan((1+x)/Sqrt(2))/(2*Sqrt(2)))", // "-ArcTan((1+x)/Sqrt(2))/(2*Sqrt(2))"); check("Simplify(1 + 1/GoldenRatio - GoldenRatio)", // "0"); // check("Simplify(-15-6*x)/(3*(1+x+x^2))", ""); check("Simplify(Abs(x), x<0)", // "Abs(x)"); check("complexity(x_) := 2*Count(x, _Abs, {0, 10}) + LeafCount(x)", // ""); check("Simplify(Abs(x), x<0, ComplexityFunction->complexity)", // "-x"); check("Simplify(100*Log(2))", // "100*Log(2)"); check("Simplify(2*Sin(x)^2 + 2*Cos(x)^2)", // "2"); check("Simplify(f(x))", // "f(x)"); check("Simplify(a*x^2+b*x^2)", // "(a+b)*x^2"); check("Simplify(5*x*(6*x+30))", // "30*x*(5+x)"); check("Simplify(Sqrt(x^2), Assumptions -> x>0)", // "x"); check("Simplify(Sqrt(x^2), x>0)", // "x"); check("Together(2/(1/Tan(x) + Tan(x)))", // "2/(Cot(x)+Tan(x))"); check("Together(2*Tan(x)/(1 + Tan(x)^2))", // "(2*Tan(x))/(1+Tan(x)^2)"); check("Simplify(Sin(x)^2 + Cos(x)^2)", // "1"); check("Simplify((x - 1)*(x + 1)*(x^2 + 1) + 1)", // "x^4"); check("Simplify(3/(x + 3) + x/(x + 3))", // "1"); check("Simplify(2*Tan(x)/(1 + Tan(x)^2))", // "Sin(2*x)"); check( "Simplify((1/3+(1/3)*(-2)^(-1/3)*2^(-2/3)*(1+(0+1*I)*3^(1/2))+(1/6)*(-1)^(1/3)*(1+(0+-1*I)*3^(1/2)))^2)", // "1"); check( "Simplify((1/3+(1/3)*(-2)^(-1/3)*2^(-2/3)*(1+(0+-1*I)*3^(1/2))+(1/6)*(-1)^(1/3)*(1+(0+1*I)*3^(1/2)))^2)", // "0"); check("$Assumptions=(x>0);Simplify(0^x)", // "0"); } @Test public void testSimplifyBoolean() { check("Simplify((x+1)&&(x+1))", // "1+x"); check("Simplify(b&&b)", // "b"); check("Simplify(a && b && !b )", // "False"); check("Simplify((a || b) && (a || c) )", // "a||(b&&c)"); check("Simplify(a || ! a && b)", // "a||b"); check("Simplify( a || b || ! a || ! b)", // "True"); check("Simplify(a || (a && Infinity))", // "a"); check("Simplify((b || a) && (c || a))", // "a||(b&&c)"); check("Simplify((a || b || c || Not((a && b && c))))", // "True"); check("Simplify((a || b || c || Not((a && b && c && d))))", // "True"); check("Simplify( (a || b || c || d || Not((a && b && c))))", // "True"); check("Simplify((a || b || c || d || Not(a)))", // "True"); check("Simplify((az || b || cz || Not((ay && b && cy && dy))))", // "True"); check("Simplify( a || (a && b && c && d) )", // "a"); check("Simplify(d || (a && b && c && d))", // "d"); check("Simplify(d || e || (a && b && c && d) )", // "d||e"); check("Simplify(d || b || (a && b && c && d))", // "b||d"); check("Simplify(d || b || (a && b && c && d) || ! b)", // "True"); check("Simplify(foo(d || b || (a && b && c && d) || ! b))", // "foo(True)"); check("Simplify(d || e || (a && b && c))", // "d||e||(a&&b&&c)"); check("Simplify(z || z)", // "z"); check("Simplify(z || a || z)", // "a||z"); check("Simplify(a || a && b )", // "a"); check("Simplify(a || !a && b )", // "a||b"); check("Simplify(a || c || ! a && b )", // "a||b||c"); check("Simplify( a || c || ! a && ! c && b )", // "a||b||c"); check("Simplify(a || c || ! a && ! c && ! b)", // "a||!b||c"); check("Simplify(a || c || ! a && ! c && ! b && d )", // "a||c||(!b&&d)"); check("Simplify( c || a || Not(b))", // "c||a||!b"); check("Simplify(And(x1, a, x2, Not(Or(x3, a, x4)), x5))", // "False"); check("Simplify(And(x1, a, x2, Or(x3, a, x4), x5))", // "a&&x1&&x2&&x5"); check("Simplify(a&&b&&a)", // "a&&b"); } @Test public void testSin() { // check("Sin(4/15*Pi)", // // "Cos(7/30*Pi)"); check("trigs={Sin,Cos,Tan,Cot}", // "{Sin,Cos,Tan,Cot}"); check("trigs[[1]][10.0]", // "-0.544021"); check("Sin[SparseArray[{{2,3},{4,5}}]]//MatrixForm", // "{{Sin(2),Sin(3)},\n" + " {Sin(4),Sin(5)}}"); check("Sin(Interval({-Infinity,Infinity}))", // "Interval({-1,1})"); check("Sin({})", // "{}"); check("Sin(5*Pi/12)", // "(1+Sqrt(3))/(2*Sqrt(2))"); // check("Sin(Quantity(90,\"Degree\"))", // ""); check("Sin(-37/3*Pi+x)", // "-Cos(Pi/6+x)"); check("Sin(83/7*Pi+x)", // "-Cos(5/14*Pi+x)"); check("Refine(Sin(x+k*Pi), Element(k, Integers))", // "(-1)^k*Sin(x)"); check("Sin(3/4*Pi+x)", // "Cos(Pi/4+x)"); check("Sin(5/7*Pi+x)", // "Cos(3/14*Pi+x)"); check("Sin(-3/4*Pi+x)", // "-Sin(Pi/4+x)"); check("Sin({})", // "{}"); check("Sin(e - Pi/2 + f*x)", // "-Cos(e+f*x)"); check("Sin( -3/x+x )", // "-Sin(3/x-x)"); check("Sin((-3+x^2)/x)", // "Sin((-3+x^2)/x)"); check("Sin(-Pi/2+z)", // "-Cos(z)"); check("Sin(e-Pi/2+f*x)", // "-Cos(e+f*x)"); check("Sin(e-3/2*Pi+f*x)", // "Cos(e+f*x)"); check("Sin(e-1+f*x)", // "-Sin(1-e-f*x)"); check("Sin(ArcSin(x))", // "x"); check("Sin(ArcCos(x))", // "Sqrt(1-x^2)"); check("Sin(ArcTan(x))", // "x/Sqrt(1+x^2)"); check("Sin(ArcCot(x))", // "1/Sqrt(1+x^2)"); check("Sin(ArcCsc(x))", // "1/x"); check("Sin(ArcSec(x))", // "Sqrt(1-1/x^2)"); check("Sin(Pi/4)", // "1/Sqrt(2)"); check("Sin(0)", // "0"); checkNumeric("Sin(0.5)", // "0.479425538604203"); check("Sin(3*Pi)", // "0"); checkNumeric("Sin(1.0 + I)", // "1.2984575814159773+I*0.6349639147847361"); checkNumeric("Sin(1.1*Pi)", // "-0.30901699437494773"); checkNumeric("Sin({-0.5,9.1})", // "{-0.479425538604203,0.3190983623493521}"); checkNumeric("Sin({{0.5,1.1},{6.4,7.5}})", // "{{0.479425538604203,0.8912073600614354},\n" + " {0.11654920485049364,0.9379999767747389}}"); check("Sin({1,2})", // "{Sin(1),Sin(2)}"); check("Sin(z+1/4*Pi)", // "Sin(Pi/4+z)"); check("Sin(z+1/2*Pi)", // "Cos(z)"); check("Sin(z+1/3*Pi)", // "Sin(Pi/3+z)"); check("Sin(Pi)", // "0"); check("Sin(z+Pi)", // "-Sin(z)"); check("Sin(z+42*Pi)", // "Sin(z)"); check("Sin(x+y+z+43*Pi)", // "-Sin(x+y+z)"); check("Sin(z+42*a*Pi)", // "Sin(42*a*Pi+z)"); } @Test public void testSinc() { checkNumeric("Sinc(3.5)", // "-0.10022377933989138"); checkNumeric("N(Sinc(35/10),50)", // "-0.10022377933989138517724822858389588145285192455445"); checkNumeric("Sinc(1 + 3.5*I)", // "3.413480749977026+I*(-3.009162956293193)"); checkNumeric("N(Sinc(1+35/10*I),50)", // "3.4134807499770263967370518627588410722367885846662+I*(-3.0091629562931933945895646489407216870241346727697)"); check("Sinc(-x)", // "Sinc(x)"); check("Table(Sinc(n*Pi/3), {n, 0, 6})", // "{1,3/2*Sqrt(3)/Pi,3/4*Sqrt(3)/Pi,0,-3/8*Sqrt(3)/Pi,-3/10*Sqrt(3)/Pi,0}"); check("Sinc(3.5)", // "-0.100224"); check("Sinc(1.0+3.5*I)", // "3.41348+I*(-3.00916)"); check("(2*Sqrt(2))/Pi", // "(2*Sqrt(2))/Pi"); check("2+(-Sqrt(5))/8", // "2-Sqrt(5)/8"); check("Sinc(0)", // "1"); check("Sinc(1/6*Pi)", // "Pi/3"); check("Sinc(1/4*Pi)", // "(2*Sqrt(2))/Pi"); check("Sinc(1/3*Pi)", // "3/2*Sqrt(3)/Pi"); check("Sinc(1/2*Pi)", // "2/Pi"); check("Sinc(Pi)", // "0"); check("Sinc(5/12*Pi)", // "3/5*(Sqrt(2)*(1+Sqrt(3)))/Pi"); check("Sinc(Pi/5)", // "(5*Sqrt(5/8-Sqrt(5)/8))/Pi"); check("Sinc(Pi/12)", // "(3*Sqrt(2)*(-1+Sqrt(3)))/Pi"); check("Sinc(Pi/10)", // "5/2*(-1+Sqrt(5))/Pi"); check("Sinc(2/5*Pi)", // "5/2*Sqrt(5/8+Sqrt(5)/8)/Pi"); check("Sinc(3/10*Pi)", // "5/6*(1+Sqrt(5))/Pi"); check("Sinc(I)", // "Sinh(1)"); check("Sinc(ArcSin(x))", // "x/ArcSin(x)"); check("Sinc(ArcCos(x))", // "Sqrt(1-x^2)/ArcCos(x)"); check("Sinc(ArcTan(x))", // "x/(Sqrt(1+x^2)*ArcTan(x))"); check("Sinc(I*Infinity)", // "Infinity"); check("Sinc(ComplexInfinity)", // "Indeterminate"); } @Test public void testSinh() { check("Sinh(Pi*I+x)", // "-Sinh(x)"); check("Sinh(10*Pi*I+x)", // "Sinh(x)"); check("Sinh(43*Pi*I+x)", // "-Sinh(x)"); check("Sinh(0)", // "0"); check("Sinh(42*I*Pi)", // "0"); check("Sinh(3/2*I*Pi)", // "-I"); check("Sinh(5/3*Pi*I)", // "-I*1/2*Sqrt(3)"); check("Sinh(Infinity)", // "Infinity"); check("Sinh(ComplexInfinity)", // "Indeterminate"); } @Test public void testSinIntegral() { checkNumeric("SinIntegral(-3.1)", // "-1.8516593076745196"); check("SinIntegral(-3/4*I*x)", // "-I*SinhIntegral(3/4*x)"); check("SinIntegral(Infinity)", // "Pi/2"); check("SinIntegral(-Infinity)", // "-Pi/2"); check("SinIntegral(I*Infinity)", // "I*Infinity"); check("SinIntegral((-I)*Infinity)", // "-I*Infinity"); check("SinIntegral(I*1/2*x)", // "I*SinhIntegral(x/2)"); checkNumeric("SinIntegral(2.8)", // "1.8320965890813223"); check("Table(SinIntegral(x), {x,-4.0, 4.0, 1/4})", // "{-1.7582,-1.80123,-1.83313,-1.85011,-1.84865,-1.82564,-1.77852,-1.70546,-1.60541,-1.47823,-1.32468,-1.14645," // + "-0.946083,-0.726954,-0.493107,-0.249134,0.0,0.249134,0.493107,0.726954,0.946083,1.14645,1.32468," // + "1.47823,1.60541,1.70546,1.77852,1.82564,1.84865,1.85011,1.83313,1.80123,1.7582}"); check("Table(SinIntegral(x+I), {x,-4.0, 4.0, 1/4})", // "{-1.81528+I*(-0.231827),-1.89116+I*(-0.195138),-1.95531+I*(-0.14116),-2.00247+I*(-0.0705645),-2.02772+I*0.0152109," // + "-2.02661+I*0.114003,-1.99549+I*0.222995,-1.93158+I*0.338819,-1.83321+I*0.457692,-1.6999+I*0.575567," // + "-1.53242+I*0.688309,-1.33279+I*0.791868,-1.10422+I*0.882454,-0.851043+I*0.956708,-0.578517+I*1.01185," // + "-0.292658+I*1.04579,I*1.05725,0.292658+I*1.04579,0.578517+I*1.01185,0.851043+I*0.956708,1.10422+I*0.882454," // + "1.33279+I*0.791868,1.53242+I*0.688309,1.6999+I*0.575567,1.83321+I*0.457692,1.93158+I*0.338819,1.99549+I*0.222995," // + "2.02661+I*0.114003,2.02772+I*0.0152109,2.00247+I*(-0.0705645),1.95531+I*(-0.14116),1.89116+I*(-0.195138)," + "1.81528+I*(-0.231827)}"); } @Test public void testSinhIntegral() { checkNumeric("SinhIntegral(-3.1)", // "-5.318897351437731"); check("SinhIntegral(93/13*I*x)", // "I*SinIntegral(93/13*x)"); check("SinhIntegral(-x)", // "-SinhIntegral(x)"); check("SinhIntegral(Infinity)", // "Infinity"); check("SinhIntegral(-Infinity)", // "-Infinity"); check("SinhIntegral(I*Infinity)", // "I*1/2*Pi"); check("SinhIntegral(-I*Infinity)", // "-I*1/2*Pi"); check("SinhIntegral(I*1/2*x)", // "I*SinIntegral(x/2)"); checkNumeric("SinhIntegral(2.8)", // "4.348076508127191"); check("Table(SinhIntegral(x), {x,-4.0, 4.0, 1/4})", // "{-9.81733,-8.26122,-6.96616,-5.88341,-4.97344,-4.20414,-3.54934,-2.98767,-2.50157,-2.07657,-1.70065," // + "-1.36373,-1.05725,-0.773837,-0.506997,-0.25087,0.0,0.25087,0.506997,0.773837,1.05725,1.36373," // + "1.70065,2.07657,2.50157,2.98767,3.54934,4.20414,4.97344,5.88341,6.96616,8.26122,9.81733}"); check("Table(SinhIntegral(x+I), {x,-4.0, 4.0, 1/4})", // "{-7.40401+I*6.13828,-6.29879+I*5.11278,-5.36892+I*4.27784,-4.58248+I*3.59748,-3.91346+I*3.04277," // + "-3.34061+I*2.59043,-2.84649+I*2.22177,-2.4168+I*1.92172,-2.03968+I*1.67824,-1.70531+I*1.48166," // + "-1.40546+I*1.3243,-1.13315+I*1.20006,-0.882454+I*1.10422,-0.648183+I*1.03315,-0.425752+I*0.984193," // + "-0.210992+I*0.955523,I*0.946083,0.210992+I*0.955523,0.425752+I*0.984193,0.648183+I*1.03315," // + "0.882454+I*1.10422,1.13315+I*1.20006,1.40546+I*1.3243,1.70531+I*1.48166,2.03968+I*1.67824," // + "2.4168+I*1.92172,2.84649+I*2.22177,3.34061+I*2.59043,3.91346+I*3.04277,4.58248+I*3.59748," // + "5.36892+I*4.27784,6.29879+I*5.11278,7.40401+I*6.13828}"); } @Test public void testSixJSymbol() { // check("SixJSymbol({1, 2, 1}, {4,5,Pi})", // // "0"); // check("SixJSymbol({1, 2, 1}, {4,5,12})", // // "0"); // // TODO implement for half-integers // // check("SixJSymbol({1/2, 1/2, 1}, {5/2,7/2,3})", // // // "SixJSymbol({1/2,1/2,1},{5/2,7/2,3})"); // // check("SixJSymbol({1, 1, 2}, {5,7,6})", // // "1/Sqrt(65)"); // check("SixJSymbol({1, 2, 1}, {2,3,2})", // // "1/(5*Sqrt(21))"); // check("SixJSymbol({1, 2, 3}, {2, 1, 2})", // // "1/(5*Sqrt(21))"); // check("SixJSymbol({1, 2, 3}, {1,2,2})", // // "1/15"); } @Test public void testSkewness() { check("Skewness(WeibullDistribution(n,m))", // "(2*Gamma(1+1/n)^3-3*Gamma(1+1/n)*Gamma(1+2/n)+Gamma(1+3/n))/(-Gamma(1+1/n)^2+Gamma(\n" + // "1+2/n))^(3/2)"); check("Skewness(UniformDistribution())", // "0"); check("Skewness(StudentTDistribution(n ))", // "Piecewise({{0,n>3}},Indeterminate)"); check("Skewness(PoissonDistribution(n ))", // "1/Sqrt(n)"); check("Skewness(NormalDistribution(n,m))", // "0"); check("Skewness(NakagamiDistribution(n,m))", // "(Pochhammer(n,1/2)*(1/2-2*(n-Pochhammer(n,1/2)^2)))/(n-Pochhammer(n,1/2)^2)^(3/2)"); check("Skewness(LogNormalDistribution(n,m))", // "(2+E^m^2)*Sqrt(-1+E^m^2)"); check("Skewness(GumbelDistribution(n,m))", // "(-12*Sqrt(6)*Zeta(3))/Pi^3"); check("Skewness(GeometricDistribution(n))", // "(2-n)/Sqrt(1-n)"); check("Skewness(GammaDistribution(n,m))", // "2/Sqrt(n)"); check("Skewness(FrechetDistribution(n,m))", // "Piecewise({{(Gamma(1-3/n)-3*Gamma(1-2/n)*Gamma(1-1/n)+2*Gamma(1-1/n)^3)/(Gamma(1-\n" + "2/n)-Gamma(1-1/n)^2)^(3/2),n>3}},Infinity)"); check("Skewness(FRatioDistribution(n,m))", // "Piecewise({{(2*Sqrt(2)*Sqrt(-4+m)*(-2+m+2*n))/((-6+m)*Sqrt(n)*Sqrt(-2+m+n)),m>6}},Indeterminate)"); check("Skewness(ExponentialDistribution(n))", // "2"); check("Skewness(ErlangDistribution(n,m))", // "2/Sqrt(n)"); check("Skewness(DiscreteUniformDistribution({n,m}))", // "0"); check("Skewness(BinomialDistribution(n,m))", // "(1-2*m)/Sqrt((1-m)*m*n)"); check("Skewness(BernoulliDistribution(a))", // "(1-2*a)/Sqrt((1-a)*a)"); check("Skewness(ChiSquareDistribution(a))", // "2*Sqrt(2)*Sqrt(1/a)"); check("Skewness({1.1, 1.2, 1.4, 2.1, 2.4})", // "0.407041"); } @Test public void testSlot() { // check("x^2+x", "x+x^2"); check("f(#1, X) &[ ]", // "f(#1,X)"); check("(# &)[a, b, c]", // "a"); check("f = If(#1 == 1, 1, #1*#0(#1 - 1)) &", // "If(#1==1,1,#1*#0[-1+#1])&"); check("f(10)", // "3628800"); check("# &[1, 2, 3]", // "1"); check("#1 &[1, 2, 3]", // "1"); check("g(#0) &[x]", // "g(g(#0)&)"); // check("#1^2+#1", "#1^2+#1"); // check("#1+#1^7", "#1"); check("#", // "#1"); check("#42", // "#42"); } @Test public void testSlotSequence() { check("f(##1, X, ##2, Y, ##3, Z, ##4, W, ##5) &[a, b, c, d]", // "f(a,b,c,d,X,b,c,d,Y,c,d,Z,d,W)"); check("(## &)[a, b, c]", // "Identity(a,b,c)"); check("(##2 &)[a, b, c]", // "Identity(b,c)"); check("(##4 &)[a, b, c]", // "Identity()"); check("(##5 &)[a, b, c]", // "##5"); check("(##-1 &)[a, b, c]", // "-1+a+b+c"); check("(##2-7 &)[a, b, c]", // "-7+b+c"); check("##", // "##1"); check("##42", // "##42"); check("f(x, ##, y, ##) &[a, b, c, d]", // "f(x,a,b,c,d,y,a,b,c,d)"); check("f(##2) &[a, b, c, d]", // "f(b,c,d)"); check("{##2} &[a, b, c]", // "{b,c}"); } @Test public void testSokalSneathDissimilarity() { check("SokalSneathDissimilarity({1, 0, 1, 1, 0}, {1, 1, 0, 1, 1})", // "3/4"); check("SokalSneathDissimilarity({True, False, True}, {True, True, False})", // "4/5"); check("SokalSneathDissimilarity({1, 1, 1, 1}, {1, 1, 1, 1})", // "0"); check("SokalSneathDissimilarity({0, 0, 0, 0}, {1, 1, 1, 1})", // "1"); } @Test public void testSort() { check("Sort({f(1,2,3), f(1,4)})", // "{f(1,4),f(1,2,3)}"); check("Sort(<|a -> 4, b -> 1, c -> 3, e :> 2, d -> 2|>)", // "<|b->1,e:>2,d->2,c->3,a->4|>"); check("Sort(<|a -> 4, b -> 1, c -> 3, d :> 2, e -> 2|>, Greater)", // "<|a->4,c->3,d:>2,e->2,b->1|>"); check("Sort({2.1,1.1-I,2.1-I,I*E^(I*x)})", // "{1.1+I*(-1.0),2.1,2.1+I*(-1.0),I*E^(I*x)}"); check("Sort({2,1-I,2-I,I*E^(I*x)})", // "{1-I,2-I,2,I*E^(I*x)}"); check("Sort(StringJoin /@ Tuples({\"a\",\"A\",\"b\",\"B\"},2))", // "{aa,aA,Aa,AA,ab,aB,Ab,AB,ba,bA,Ba,BA,bb,bB,Bb,BB}"); check("Sort({a,A,a,b,B})", // "{a,a,A,b,B}"); check("Sort@{ 1+x^2,2+x^2,x(x),-x,x,Cos(x^2),Sin(x^2)}", // "{-x,x,1+x^2,2+x^2,Cos(x^2),Sin(x^2),x(x)}"); check("Sort@{x,1+x^2,1+x^2+y^3+z^4,Cos(x^2),Sin(x^2)}", // "{x,1+x^2,1+x^2+y^3+z^4,Cos(x^2),Sin(x^2)}"); check("Sort({E,a,D,d,N,b,c, Adele, enigma})", // "{a,adele,b,c,d,D,E,enigma,N}"); check("Sort({d, b, c, a})", // "{a,b,c,d}"); check("Sort({4, 1, 3, 2, 2}, Greater)", // "{4,3,2,2,1}"); check("Sort({4, 1, 3, 2, 2}, #1 > #2 &)", // "{4,3,2,2,1}"); check("Sort({{a, 2}, {c, 1}, {d, 3}}, #1[[2]] < #2[[2]] &)", // "{{c,1},{a,2},{d,3}}"); check("Sort({4, 1.0, a, 3+I})", // "{1.0,3+I,4,a}"); } @Test public void testSortBy() { check("SortBy({{5, 1}, {10, -1}}, Last)", // "{{10,-1},{5,1}}"); check("SortBy(Total)[{{5, 1}, {10, -9}}]", // "{{10,-9},{5,1}}"); } @Test public void testSow() { check("Reap(Do(If(GCD(num, den) == 1, Sow(num)), {den, 1, 20}, {num, 1, den-1}) )[[2, 1]] ", // "{1,1,2,1,3,1,2,3,4,1,5,1,2,3,4,5,6,1,3,5,7,1,2,4,5,7,8,1,3,7,9,1,2,3,4,5,6,7,8,9,\n" + // "10,1,5,7,11,1,2,3,4,5,6,7,8,9,10,11,12,1,3,5,9,11,13,1,2,4,7,8,11,13,14,1,3,5,7,\n" + // "9,11,13,15,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1,5,7,11,13,17,1,2,3,4,5,6,7,8,\n" + // "9,10,11,12,13,14,15,16,17,18,1,3,7,9,11,13,17,19}"); check("Reap(Sow(1, x); Sow(2, y); Sow(3, x); Sow(4, y))", // "{4,{{1,3},{2,4}}}"); check("Reap(Sow(a); b; Sow(c); Sow(d); e)", // "{e,{{a,c,d}}}"); check("Reap(Sum(Sow(i0^2) + 1, {i0, 10}))", // "{395,{{1,4,9,16,25,36,49,64,81,100}}}"); } @Test public void testSphericalBesselJ() { check("SphericalBesselJ(2.5,-5)", // "I*0.204488"); checkNumeric("SphericalBesselJ(1,5.2)", // "-0.12277149950214108"); checkNumeric("BesselJ(2.5,-5)", // "I*0.24037720111131736"); checkNumeric("SphericalBesselJ(2.5,-5)", // I*0.20448758430717914 "I*0.20448758430717917"); checkNumeric("SphericalBesselJ(2.0,-5)", // "0.13473121008883018"); checkNumeric("SphericalBesselJ(-0.5,1)", // "0.9590330784042026"); checkNumeric("SphericalBesselJ(2.0+I,5.0+I)", // "0.14163924534491812+I*0.005070099110737425"); } @Test public void testSphericalBesselY() { // TODO improve this value check("SphericalBesselY(2.5,-5)", // "-0.613462+I*0.122973"); checkNumeric("SphericalBesselY(1,5.5)", // "0.10485295921809935"); checkNumeric("BesselY(2.5,-5)", // "I*(-0.2943723749617925)"); checkNumeric("SphericalBesselY(-0.5,1)", // "0.11061370096805949"); checkNumeric("SphericalBesselY(2.0+I,5.0+I)", // "0.15456969798535916+I*(-0.05055787979478312)"); checkNumeric("SphericalBesselY(2.0,-5)", // "-0.16499545760108916"); } @Test public void testSphericalHarmonicY() { check("SphericalHarmonicY(0,0,t,p)", // "1/(2*Sqrt(Pi))"); check("SphericalHarmonicY(a,0,0,p)", // "Sqrt(1+2*a)/(2*Sqrt(Pi))"); check("SphericalHarmonicY(1,2,t,p)", // "0"); check("SphericalHarmonicY(1,1,t,p)", // "-1/2*E^(I*p)*Sqrt(3/2*1/Pi)*Sin(t)"); check("SphericalHarmonicY(n,-n-1,t,p)", // "0"); } @Test public void testSplice() { check("Splice({a,b,c})", // "Splice({a,b,c})"); check("Splice(12)", // "Splice(12)"); check("{1,2,Splice({x,x,x}),2,4,3}", // "{1,2,x,x,x,2,4,3}"); check("{a, b, c, Splice({ }), d, e}", // "{a,b,c,d,e}"); check("h(a, b, c, Splice({1, 2, 3}), d, e)", // "h(a,b,c,Splice({1,2,3}),d,e)"); check("{a, b, c, Splice[{1, 2, 3}], d, e}", // "{a,b,c,1,2,3,d,e}"); check("{a, b, c, Splice[{1, 2, 3},h], d, e}", // "{a,b,c,Splice({1,2,3},h),d,e}"); check("h(a, b, c, Splice({1, 2, 3}, h), d, e)", // "h(a,b,c,1,2,3,d,e)"); check("h(a, b, c, Splice({{1,1},{2,2}}, h), d, e)", // "h(a,b,c,{1,1},{2,2},d,e)"); check("f(1, 2, 3, Splice({x, y}, f | g), 4, 5)", // "f(1,2,3,x,y,4,5)"); check("f(a)[1, 2, 3, Splice({x, y}, _f), 4, 5]", // "f(a)[1,2,3,x,y,4,5]"); } @Test public void testSplit() { check("Split({x, x, x, y, x, y, y, z})", // "{{x,x,x},{y},{x},{y,y},{z}}"); check("Split({x, x, x, y, x, y, y, z}, x)", // "{{x},{x},{x},{y},{x},{y},{y},{z}}"); check("Split({1, 5, 6, 3, 6, 1, 6, 3, 4, 5, 4}, Less)", // "{{1,5,6},{3,6},{1,6},{3,4,5},{4}}"); check("Split({1, 5, 6, 3, 6, 1, 6, 3, 4, 5, 4}, Greater)", // "{{1},{5},{6,3},{6,1},{6,3},{4},{5,4}}"); check("Split({x -> a, x -> y, 2 -> a, z -> c, z -> a}, First(#1) === First(#2) &)", // "{{x->a,x->y},{2->a},{z->c,z->a}}"); check("Split({})", // "{}"); } @Test public void testSplitBy() { check("SplitBy(Range(1, 3, 1/3), Round)", // "{{1,4/3},{5/3,2,7/3},{8/3,3}}"); check("SplitBy({1, 2, 1, 1.2}, {Round, Identity})", // "{{{1}},{{2}},{{1},{1.2}}}"); check("Tuples({1, 2}, 3)", // "{{1,1,1},{1,1,2},{1,2,1},{1,2,2},{2,1,1},{2,1,2},{2,2,1},{2,2,2}}"); check("SplitBy(Tuples({1, 2}, 3), First)", // "{{{1,1,1},{1,1,2},{1,2,1},{1,2,2}},{{2,1,1},{2,1,2},{2,2,1},{2,2,2}}}"); } @Test public void testSqrt() { check("Sqrt(-Sqrt(3))", // "I*3^(1/4)"); check("Sqrt(Sqrt(3))", // "3^(1/4)"); check("Sqrt((1-a)*a)", // "Sqrt((1-a)*a)"); check("(-3/4)/Sqrt(-3/4)", // "I*1/2*Sqrt(3)"); check("(3/4)/Sqrt(3/4)", // "Sqrt(3)/2"); check("(-3)/Sqrt(-3)", // "I*Sqrt(3)"); check("3/Sqrt(3)", // "Sqrt(3)"); check("Sqrt(4)", // "2"); check("Sqrt(5)", // "Sqrt(5)"); check("Sqrt(5) // N", // "2.23607"); check("Sqrt(a)^2", // "a"); check("Sqrt(-4)", // "I*2"); check("I == Sqrt(-1)", // "True"); // TODO use ExprParser#getReal() if apfloat problems are fixed // check("N(Sqrt(2), 50)", // "1.41421356237309504880168872420969807856967187537694"); } @Test public void testSquareFreeQ() { check("SquareFreeQ(-45+28*I)", // "False"); check("SquareFreeQ(6+7*I)", // "True"); // message: SquareFreeQ: Currently not supported: number of variables in expression (2) unequals // number of user variables (1). check("SquareFreeQ(x*y^2, x)", // "SquareFreeQ(x*y^2,x)"); check("SquareFreeQ(x*y^2, y)", // "SquareFreeQ(x*y^2,y)"); check("SquareFreeQ(5/6)", // "True"); check("SquareFreeQ(3/4)", // "False"); check("SquareFreeQ(9)", // "False"); check("SquareFreeQ(5)", // "True"); check("SquareFreeQ(9)", // "False"); check("SquareFreeQ(20)", // "False"); check("SquareFreeQ(10)", // "True"); check("SquareFreeQ(12)", // "False"); check("SquareFreeQ(105)", // "True"); check("SquareFreeQ(x^4-1)", // "True"); check("SquareFreeQ(x^4 - 2*x^2 + 1)", // "False"); check("SquareFreeQ(x^2+1)", // "True"); check("SquareFreeQ(9 + 6*x + x^2)", // "False"); check("SquareFreeQ(x^2 + 1, Modulus -> 2)", // "False"); check("SquareFreeQ(6+6*x+x^2)", // "True"); } @Test public void testSquaredEuclideanDistance() { check("SquaredEuclideanDistance({-7, 5.0}, {1, 1})", // "80.0"); check("SquaredEuclideanDistance({-1, -1}, {1.5, 1})", // "10.25"); check("SquaredEuclideanDistance({-7, 5}, {1, 1})", // "80"); check("SquaredEuclideanDistance({-1, -1}, {1, 1})", // "8"); } @Test public void testSpan() { check("OddQ^(n) && n > 0;;", // "(OddQ^n&&n>0);;All"); check("Infinity[[2;;4]]", // "Infinity[[2;;4]]"); check("FullForm(1;;4;;2)", // "Span(1, 4, 2)"); check("{a, b, c, d, e, f, g, h}[[2 ;; -3]]", // "{b,c,d,e,f}"); check("FullForm( ;; )", // "Span(1, All)"); check("FullForm(1;;4;;2)", // "Span(1, 4, 2)"); check("FullForm(2;;-2)", // "Span(2, -2)"); check("FullForm(;;3)", // "Span(1, 3)"); // check("a ;; b ;; c ;; d", "(1;;d) (a;;b;;c)"); check("{a, b, c, d, e, f, g, h}[[2 ;; -3]]", // "{b,c,d,e,f}"); check("{a, b, c, d, e, f, g, h}[[2 ;; 5]]", // "{b,c,d,e}"); check("{a, b, c, d, e, f, g, h}[[2 ;; All]]", // "{b,c,d,e,f,g,h}"); } @Test public void testStandardize() { check("Standardize(N(Range(5)), Mean, 1 &)", // "{-2.0,-1.0,0.0,1.0,2.0}"); check("Standardize(N(Range(5)), Median, InterquartileRange)", // "{-0.8,-0.4,0.0,0.4,0.8}"); check("Standardize( Range(5) )", // "{-2*Sqrt(2/5),-Sqrt(2/5),0,Sqrt(2/5),2*Sqrt(2/5)}"); check("Standardize(SparseArray({{a,b},{c,d}}))", // "{{(Sqrt(2)*(a+1/2*(-a-c)))/Sqrt((a-c)*(Conjugate(a)-Conjugate(c))),(Sqrt(2)*(b+1/\n" // + "2*(-b-d)))/Sqrt((b-d)*(Conjugate(b)-Conjugate(d)))},{(Sqrt(2)*(1/2*(-a-c)+c))/Sqrt((a-c)*(Conjugate(a)-Conjugate(c))),(Sqrt(\n" + "2)*(1/2*(-b-d)+d))/Sqrt((b-d)*(Conjugate(b)-Conjugate(d)))}}"); check("Standardize({6.5, 3.8, 6.6, 5.7, 6.0, 6.4, 5.3})", // "{0.75705,-1.99453,0.85896,-0.0582346,0.247497,0.655139,-0.465877}"); check("Standardize({{a,b},{c,d}})", // "{{(Sqrt(2)*(a+1/2*(-a-c)))/Sqrt((a-c)*(Conjugate(a)-Conjugate(c))),(Sqrt(2)*(b+1/\n" // + "2*(-b-d)))/Sqrt((b-d)*(Conjugate(b)-Conjugate(d)))},{(Sqrt(2)*(1/2*(-a-c)+c))/Sqrt((a-c)*(Conjugate(a)-Conjugate(c))),(Sqrt(\n"// + "2)*(1/2*(-b-d)+d))/Sqrt((b-d)*(Conjugate(b)-Conjugate(d)))}}"); } @Test public void testSquaresR() { // TODO // check("TimeConstrained(SquaresR({3},2147483647),3)", // // ""); // message: $RecursionLimit: Recursion depth of 512 exceeded during evaluation of // SquaresR(2147483647,11). check("SquaresR(2147483647,11)", // "Hold(SquaresR(2147483647,11))"); check("Table(SquaresR(2, n), {n, 100})", // "{4,4,0,4,8,0,0,4,4,8,0,0,8,0,0,4,8,4,0,8,0,0,0,0,12,8,0,0,8,0,0,4,0,8,0,4,8,0,0,\n" // + "8,8,0,0,0,8,0,0,0,4,12,0,8,8,0,0,0,0,8,0,0,8,0,0,4,16,0,0,8,0,0,0,4,8,8,0,0,0,0,\n" // + "0,8,4,8,0,0,16,0,0,0,8,8,0,0,0,0,0,0,8,4,0,12}"); check("Sum(SquaresR(2, k), {k, 0, 20^2})", // "1257"); check("sierpinski(n_) := Sum(SquaresR(2, k)/k, {k, n})-Pi * Log(n);", // ""); check("N(sierpinski(10000))", // "2.58509"); } @Test public void testPowersRepresentations() { // Message check("PowersRepresentations(2147483647,1,{0})", // "PowersRepresentations(2147483647,1,{0})"); check("PowersRepresentations(8174, 6, 3)", // "{{0,0,4,10,13,17},{0,3,6,7,9,19},{0,7,10,12,12,15},{1,1,1,11,14,16},{1,3,5,12,13,\n" // + "16},{1,4,5,5,10,19},{1,5,6,10,10,18},{2,3,4,6,10,19},{3,3,3,4,13,18},{3,5,9,10,\n" // + "13,16},{4,5,6,13,13,15},{4,9,12,12,12,13},{5,9,9,13,13,13},{7,7,10,10,14,14}}"); check("PowersRepresentations(100, 1, 2)", // "{{10}}"); check("PowersRepresentations(1729, 0, 3)", // "{}"); check("PowersRepresentations(1729, 2, 3)", // "{{1,12},{9,10}}"); check("PowersRepresentations(102, 3, 2)", // "{{1,1,10},{2,7,7}}"); check("PowersRepresentations(100, 2, 2)", // "{{0,10},{6,8}}"); check("PowersRepresentations(87539319, 2, 3)", // "{{167,436},{228,423},{255,414}}"); check("PowersRepresentations(6963472309248, 2, 3)", // "{{2421,19083},{5436,18948},{10200,18072},{13322,16630}}"); } @Test public void testStack() { // print: {f,g,CompoundExpression,Print} check("f(g(1, Print(Stack()); 2))", // "f(g(1,2))"); check("f(g(1, Print(Stack(_)); 2))", // "f(g(1,2))"); } @Test public void testStackBegin() { // print: {Plus,Times,g,CompoundExpression,Print} check("1 + x + f(StackBegin(2 + x*g(Print(Stack( )); 2)))", // "1+x+f(2+x*g(2))"); check("1 + x + f(StackBegin(2 + x*g(Print(Stack(_)); 2)))", // "1+x+f(2+x*g(2))"); } @Test public void testStandardDeviation() { check("StandardDeviation({1, 2, 3})", // "1"); check("StandardDeviation({7, -5, 101, 100})", // "Sqrt(13297)/2"); check("StandardDeviation({a, a})", // "0"); check("StandardDeviation({{1, 10}, {-1, 20}})", // "{Sqrt(2),5*Sqrt(2)}"); check("StandardDeviation({1.21, 3.4, 2, 4.66, 1.5, 5.61, 7.22})", // "2.27183"); check("StandardDeviation(LogNormalDistribution(0, 1))", // "Sqrt((-1+E)*E)"); } @Test public void testStieltjesGamma() { check("StieltjesGamma(8,Indeterminate)", // "Indeterminate"); check("StieltjesGamma(0)", // "EulerGamma"); check("StieltjesGamma(0,a)", // "-PolyGamma(0,a)"); } @Test public void testStirlingS1() { // message Maximum AST dimension 20834 exceeded check("StirlingS1(10007,11)", // "StirlingS1(10007,11)"); check("StirlingS1(9,6)", // "-4536"); check("StirlingS1(0,0)", // "1"); check("StirlingS1(1,1)", // "1"); check("StirlingS1(0,1)", // "0"); check("StirlingS1(1,0)", // "0"); check("StirlingS1(50,1)", // "-608281864034267560872252163321295376887552831379210240000000000"); check("StirlingS1({2,4,6},2)", // "{1,11,274}"); check("Table(StirlingS1(12, m), {m, 5})", // "{-39916800,120543840,-150917976,105258076,-45995730}"); check( "Table(Sum( StirlingS1(m, l)*StirlingS2(l, n), {l, 0, Max(n, m) + 1}), {n, 0, 5}, {m, 0, 5})", // "{{1,0,0,0,0,0},{0,1,0,0,0,0},{0,0,1,0,0,0},{0,0,0,1,0,0},{0,0,0,0,1,0},{0,0,0,0,\n" + "0,1}}"); } @Test public void testStirlingS2() { check("StirlingS2(1317624576693539401,4)", // "StirlingS2(1317624576693539401,4)"); check("StirlingS2(-1,-3)", // "StirlingS2(-1,-3)"); check("StirlingS2(6,10)", // "0"); check("StirlingS2(10,6)", // "22827"); check("StirlingS2(0,0)", // "1"); check("StirlingS2(1,1)", // "1"); check("StirlingS2(0,1)", // "0"); check("StirlingS2(1,0)", // "0"); check("StirlingS2(10,11)", // "0"); check("Table(StirlingS2(10, m), {m, 10})", // "{1,511,9330,34105,42525,22827,5880,750,45,1}"); check("StirlingS2({2, 4, 6}, 2)", // "{1,7,31}"); check("StirlingS2(10,4)", // "34105"); check("StirlingS2(1000, 500)", "11897164077580438091910055658742826<>", // 35); check("StirlingS2(2000, 199)", "12783663313027805423901972026528914<>", // 35); } @Test public void testStruveH() { // message "BigInteger bit length 60600 exceeded" check( "StruveH(1009,-9223372036854775807/9223372036854775808-I*9223372036854775808/9223372036854775807)", // "StruveH(1009,-9223372036854775807/9223372036854775808-I*9223372036854775808/\n" + "9223372036854775807)"); // https://github.com/paulmasson/math/issues/9 check("StruveH(0, 50.0)", // "-0.0853377"); check("StruveH(0, 30.0)", // "-0.0960984"); check("StruveH(0, 5.2)", // "-0.212448"); check("StruveH(0, 4.0)", // "0.135015"); check("StruveH(7/3 + I, 4.5 - I)", // "2.35765+I*(-1.40054)"); check("StruveH(1,{0.5, 1.0, 1.5})", // "{0.0521737,0.198457,0.410288}"); check("StruveH(1.5, 3.5)", // "1.13192"); check("StruveH(I,0)", // "0"); check("StruveH(-1+I,0)", // "Indeterminate"); check("StruveH(-2+I,0)", // "ComplexInfinity"); check("StruveH(1/2,x)", // "Sqrt(2/Pi)*Sqrt(1/x)*(1-Cos(x))"); System.out.print("."); check("StruveH(-1/2,x)", // "Sqrt(2/Pi)*Sqrt(1/x)*Sin(x)"); check("StruveH(a,-x)", // "(-(-x)^a*StruveH(a,x))/x^a"); // TODO values > 30 check("Table(StruveH(0,x), {x, 0, 30.0})", // "{0.0,0.568657,0.790859,0.574306,0.135015,-0.185217,-0.184555,0.063383,0.301988,0.319876,0.118744,-0.111421,-0.172534," + "-0.0295133,0.172443,0.247724,0.135449,-0.0553148,-0.152291,-0.076104,0.0943937,0.20045,0.148766,-0.00835413,-0.126354," + "-0.101825,0.0364942,0.158762,0.154544,0.0314077,-0.0960984}"); // } @Test public void testStruveL() { check("StruveL(0, 5.0)", // "27.10592"); check("StruveL(0, 2.5)", // "3.01121"); check("StruveL(1.5, 3.5)", // "4.41126"); check("StruveL(0, 4.0)", // "11.13105"); check("StruveL(7/3 + I, 4.5 - I)", // "-0.977295+I*(-10.82588)"); check("StruveL(1,{0.5, 1.0, 1.5})", // "{0.0539422,0.226764,0.553857}"); check("StruveL(I,0)", // "0"); check("StruveL(-1+I,0)", // "Indeterminate"); check("StruveL(-2+I,0)", // "ComplexInfinity"); check("StruveL(1/2,x)", // "Sqrt(2/Pi)*Sqrt(1/x)*(-1+Cosh(x))"); check("StruveL(-1/2,x)", // "Sqrt(2/Pi)*Sqrt(1/x)*Sinh(x)"); check("StruveL(a,-x)", // "(-(-x)^a*StruveL(a,x))/x^a"); check("StruveL(1/2, ComplexInfinity)", // "Indeterminate"); check("Table(StruveL(0,x), {x, 0, 5,0.25})", // "{0.0,0.160263,0.327241,0.507986,0.710243,0.942845,1.21616,1.54264,1.93743,2.41923,3.01121," // + "3.7423,4.64869,5.77582,7.18085,8.9357,11.13105,13.88131,17.33089,21.66224,27.10592}"); } @Test public void testSubdivide() { // print: $IterationLimit: Iteration limit of 500 exceeded. // TODO // check( // "Subdivide(3/4,Quantity(1.2,\"m\"),11)", // // "{3/4+0[m],0,0,0,0,0,0,0,0,0,0,1.2[m]}"); // message: Subdivide: The number of subdivisions given in position 3 of Subdivide(a,b,-1) // should be a positive machine-sized integer. check("Subdivide(a,b,-1)", // "Subdivide(a,b,-1)"); check("N@Subdivide(-5, 5, 6)", // "{-5.0,-3.33333,-1.66667,0.0,1.66667,3.33333,5.0}"); // TODO result should be {{x,y,z},{a/2+x/2,a/2+y/2,a/2+z/2},a} check("Subdivide({x,y,z}, a, 2)", // "{{x,y,z},{a/2+x/2,a/2+y/2,a/2+z/2},{a,a,a}}"); check("Subdivide(N(E,21),E^(Pi*I*1/3),4)", // "{2.71828182845904523536," // + "2.16371137134428392652+I*0.21650635094610966169," + "1.60914091422952261768+I*0.43301270189221932338," + "1.05457045711476130884+I*0.64951905283832898507," + "0.5+I*0.866025403784438646763}"); check("Subdivide(10, 4)", // "{0,5/2,5,15/2,10}"); check("Subdivide({10,5}, 4)", // "{0,{5/2,5/4},{5,5/2},{15/2,15/4},{10,5}}"); check("Subdivide({10,5}, {5,15}, 4)", // "{{10,5},{35/4,15/2},{15/2,10},{25/4,25/2},{5,15}}"); check("Subdivide({10,5}, 3, 4)", // "{{10,5},{33/4,9/2},{13/2,4},{19/4,7/2},{3,3}}"); check("Subdivide({10,5}, {1,5,15}, 4)", // "Subdivide({10,5},{1,5,15},4)"); check("Subdivide(5)", // "{0,1/5,2/5,3/5,4/5,1}"); check("Subdivide(10,15,5)", // "{10,11,12,13,14,15}"); check("Subdivide(10,15,4)", // "{10,45/4,25/2,55/4,15}"); check("Subdivide(-1, -4, 3)", // "{-1,-2,-3,-4}"); check("Subdivide(10, 5, 4)", // "{10,35/4,15/2,25/4,5}"); check("Subdivide(5, 15, 4)", // "{5,15/2,10,25/2,15}"); check("Subdivide(10)", // "{0,1/10,1/5,3/10,2/5,1/2,3/5,7/10,4/5,9/10,1}"); check("Subdivide(10, 5)", // "{0,2,4,6,8,10}"); check("Subdivide(-1,2, 5)", // "{-1,-2/5,1/5,4/5,7/5,2}"); check("Subdivide(-1.,1., 8)", // "{-1.0,-0.75,-0.5,-0.25,0.0,0.25,0.5,0.75,1.0}"); check("Subdivide(E,Pi, 4)", // "{E,3/4*E+Pi/4,E/2+Pi/2,E/4+3/4*Pi,Pi}"); check("Subdivide(a, b, 6)", // "{a,5/6*a+b/6,2/3*a+b/3,a/2+b/2,a/3+2/3*b,a/6+5/6*b,b}"); check("Subdivide(N(E,21),N(Pi,21), 4)", // "{2.71828182845904523536,2.82410953474173223613,2.92993724102441923691,3.03576494730710623768,3.14159265358979323846}"); } @Test public void testSubfactorial() { check("Subfactorial(0)", // "1"); check("Subfactorial(12)", // "176214841"); check("Subfactorial(n)", // "Subfactorial(n)"); check("Table(Subfactorial(n), {n, 10})", // "{0,1,2,9,44,265,1854,14833,133496,1334961}"); // The only number equal to the sum of subfactorials of its digits: check("148349 == Total(Subfactorial({1, 4, 8, 3, 4, 9}))", // "True"); checkNumeric("Table(Subfactorial(x+I*y), {x,-2,2,0.5}, {y,-2 ,2,0.5})", // "{{-9.227084993591351+I*226.34804545754852,-3.60341368902144+I*57.52215812828752,-1.4981325243711963+I*15.10153257973711,-0.6594078761887109+I*4.109712417378417,-0.30282511676493395+I*1.1557273497909215,-0.14180973765939986+I*0.3301098233309934,-0.06578326936162285+I*0.09168075208986826,-0.02922777135324635+I*0.022366556059606305,-0.011937189234760486+I*0.003341706779474045},{-224.51199155103046+I*33.783138994311265,-57.42494014380803+I*9.344563804698737,-15.326014503799536+I*2.5908324907783915,-4.324154363255359+I*0.6889085300780474,-1.3040986643465844+I*0.15231802765107366,-0.42007108938336646+I*0.008720205463217,-0.1410130398831403+I*(-0.02117096465428944),-0.04657979136378597+I*(-0.02005229004488879),-0.0135786899199037+I*(-0.012819770339213575)},{-73.56847961607632+I*(-207.89387547036583),-21.43112760840351+I*(-52.11703759475536),-6.541027528670962+I*(-13.603400055365915),-2.0962132960874325+I*(-3.780008479284061),-0.6971748832350662+I*(-1.1557273497909215),-0.23112475035685875+I*(-0.40101469216069335),-0.06911140099201767+I*(-0.15746402145149108),-0.013305353757292544+I*(-0.06620821308947582),0.003386332944104408+I*(-0.027216085248995023)},{179.82227376413772+I*(-103.3592419198595),42.72931577895212+I*(-29.85265017649355),10.25383974267816+I*(-9.11009437436893),2.506531446666703+I*(-2.9928544643766957),0.6520493321732921+I*(-1.0761590138255368),0.20567544196007476+I*(-0.4222752237740537),0.09167748459585957+I*(-0.1736414758197678),0.05336833074922617+I*(-0.06882683304436397),0.03242888563837901+I*(-0.0226149374019086)},{119.70390458403307+I*147.13695923215263,33.1422220977232+I*32.146691412605264,9.537292577413355+I*6.541027528670962,2.9204731413233214+I*1.0481066480437162,1.0,0.4083869224311086+I*(-0.11556237517842935),0.20067793971526335+I*(-0.06911140099201767),0.10829561065534317+I*(-0.019958030635938814),0.05629961322969803+I*0.006772665888208815},{-116.80734695765014+I*124.1674870365595,-23.414317375264265+I*32.29747973318128,-3.98317450302985+I*8.331805702916647,-0.24316150885499624+I*2.060784425443652,0.3260246660866461+I*0.4619204930872316,0.31397533286706414+I*0.09957968544377245,0.21948021811769758+I*0.048070664949747925,0.12992441494115906+I*0.0546223706227867,0.0614443176230067+I*0.055417745307511694},{-121.51383247642643+I*(-92.27084993591352),-29.95551927322514+I*(-17.566641733979523),-7.062372526694953+I*(-2.9962650487423925),-1.3659509156201723+I*(-0.41212992261794434),0.0,0.25828853366956134+I*0.08863108603712493,0.22657542244350878+I*0.1315665387232457,0.12924936558812197+I*0.14248538534707594,0.0408868387215724+I*0.11937189234760487},{73.12395363664382+I*(-115.62573105462519),13.324743536875513+I*(-27.750082827187917),2.357043948371871+I*(-6.65980957537445),0.6656499494393316+I*(-1.5977199883723756),0.4890369991299692+I*(-0.30711926036915266),0.4211731565787101+I*0.09847761824842886,0.28114966222679844+I*0.24837229727854723,0.11295306647755851+I*0.2678368873247892,-0.01866901418051335+I*0.20414781047557296},{107.92229070008487+I*58.48596508102584,25.05677734243667+I*9.799995441878664,6.0196825306469695+I*1.0698424292101683,1.8725105884160347+I*(-0.14128438742580243),1.0,0.6801411006713222+I*0.3064064389090305,0.36479822442754406+I*0.4897084998900002,0.053753944176759445+I*0.47884481907633486,-0.15510266452035695+I*0.3205174621383546}}"); // check("Subfactorial(10000)", "Subfactorial(10000)"); } @Test public void testSubsetQ() { check("SubsetQ(f(b,a,b,c), f(c, c, c))", // "True"); check("SubsetQ(f(b,a,b,c), f(a, b, d))", // "False"); // same as ContainsAll check("SubsetQ({b,a,b,c}, {a, b})", // "True"); check("SubsetQ({b,a,b,c}, {c, c, c})", // "True"); check("SubsetQ({b,a,b,c}, {a, b, d})", // "False"); check("SubsetQ({b, a, d}, {a, b, c})", // "False"); check("SubsetQ({ }, {a, b, c})", // "False"); check("SubsetQ({ },{ })", // "True"); check("SubsetQ({a, b, c},{ })", // "True"); check("SubsetQ(1, {1,2,3})", // "SubsetQ(1,{1,2,3})"); check("SubsetQ({1,2,3}, 4)", // "SubsetQ({1,2,3},4)"); check("SubsetQ({1.0,2.0}, {1,2,3})", // "False"); check("SubsetQ({1.0,2.0}, {1,2,3}, SameTest->Equal)", // "False"); check("SubsetQ({1,2,3}, {1.0,2.0})", // "False"); check("SubsetQ({1,2,3}, {1.0,2.0}, SameTest->Equal)", // "True"); } @Test public void testSubsets() { // check( // "Subsets({a,b,c})", // // "{{},{a},{b},{c},{a,b},{a,c},{b,c},{a,b,c}}"); check("Subsets({},{2})", // "{}"); check("Subsets(Infinity,All)", // "{ComplexInfinity,Infinity}"); check("Subsets(Infinity,Infinity)", // "{ComplexInfinity,Infinity}"); check("Subsets(Infinity,-Infinity)", // "Subsets(Infinity,-Infinity)"); // https://oeis.org/A018900 - Sum of two distinct powers of 2 check("Union(Total/@Subsets(2^Range(0, 10), {2}))", // "{3,5,6,9,10,12,17,18,20,24,33,34,36,40,48,65,66,68,72,80,96,129,130,132,136,144,\n" + "160,192,257,258,260,264,272,288,320,384,513,514,516,520,528,544,576,640,768,1025,\n" + "1026,1028,1032,1040,1056,1088,1152,1280,1536}"); check("Subsets()", // "Subsets()"); check("Subsets({})", // "{{}}"); check("Subsets({a,b,c})", // "{{},{a},{b},{c},{a,b},{a,c},{b,c},{a,b,c}}"); check("Subsets({a,b,c},2)", // "{{},{a},{b},{c},{a,b},{a,c},{b,c}}"); check("Subsets({a,b,c},{2})", // "{{a,b},{a,c},{b,c}}"); check("Subsets({a,b,c,d},{2})", // "{{a,b},{a,c},{a,d},{b,c},{b,d},{c,d}}"); } @Test public void testSubtract() { check("a - x + z", // "a-x+z"); check("5 - 3", // "2"); check("a - b // FullForm", // "Plus(a, Times(-1, b))"); check("a - b - c", // "a-b-c"); check("a - (b - c)", // "a-b+c"); } @Test public void testSubtractFrom() { check("a = 10", // "10"); check("a -= 2", // "8"); check("a", // "8"); check("index={1,2,3,4,5,6,7,8,9}", // "{1,2,3,4,5,6,7,8,9}"); check("index[[3]]-=y", // "3-y"); check("index", // "{1,2,3-y,4,5,6,7,8,9}"); } @Test public void testSurd() { checkNumeric("N(Surd(-2, 5),25)", // "-1.148698354997035006798626"); checkNumeric("N(Surd({-3, -2, -1, 0, 1, 2, 3}, 7))", // "{-1.169930812758687,-1.1040895136738123,-1.0,0.0,1.0,1.1040895136738123,1.169930812758687}"); check("Surd(EulerGamma,3)", // "EulerGamma^(1/3)"); check("Surd(EulerGamma,-7)", // "1/EulerGamma^(1/7)"); check("Table(E^(n*I*Pi/3),{n,{0,2,-2}})", // "{1,-1/2+I*1/2*Sqrt(3),-1/2-I*1/2*Sqrt(3)}"); check("Table(Surd(EulerGamma,3)*E^(n*I*Pi/3),{n,{0,2,-2}})", // "{EulerGamma^(1/3),(-1/2+I*1/2*Sqrt(3))*EulerGamma^(1/3),(-1/2-I*1/2*Sqrt(3))*EulerGamma^(\n" + "1/3)}"); check("Refine((-x)^(1/3),x<0)", // "(-x)^(1/3)"); check("Refine(Surd(x,3),x<0)", // "-(-x)^(1/3)"); check("Refine(Surd(x,-7),x<0) // FullForm", // "Times(-1, Power(Times(-1, x), Rational(-1,7)))"); check("Surd(x,3)^14", // "x^4*Surd(x,3)^2"); check("Surd(x,3)^(-14)", // "1/(x^4*Surd(x,3)^2)"); check("Surd(x,3)^13", // "x^4*Surd(x,3)"); check("Surd(x,3)^(-13)", // "1/(x^4*Surd(x,3))"); check("Surd(x,5)^15", // "x^3"); check("Surd(x,5)^(-15)", // "1/x^3"); check("Surd(x,6)^23", // "Surd(x,6)^23"); check("Surd(x,6)^(-23)", // "1/Surd(x,6)^23"); check("Surd(x,7)^23", // "x^3*Surd(x,7)^2"); check("Surd(x,7)^(-23)", // "1/(x^3*Surd(x,7)^2)"); check("Surd(x,7)^8", // "x*Surd(x,7)"); check("Surd(x,7)^11", // "x*Surd(x,7)^4"); check("Surd(x,-1)", // "1/x"); // print: Surd: Integer expected at position 2 in Surd(-4.5,1/3). check("Surd(-4.5, 1/3)", // "Surd(-4.5,1/3)"); check("Surd(-4.5, 3)", // "-1.65096"); check("Power(-4.5, 1/3)", // "0.825482+I*1.42978"); check("Surd(-16.0,2)", // "Indeterminate"); checkNumeric("Surd(-3,3)", // "-3^(1/3)"); checkNumeric("N((-3)^(1/3))", // "0.7211247851537042+I*1.2490247664834064"); checkNumeric("Surd(-3,3)-(-3)^(1/3)", // "-(-3)^(1/3)-3^(1/3)"); checkNumeric("Surd(-3.,3)-(-3)^(1/3)", // "-2.1633743554611122+I*(-1.2490247664834064)"); checkNumeric("Surd(-3,3)", // "-3^(1/3)"); checkNumeric("Surd(-3.,3)", // "-1.4422495703074083"); checkNumeric("N(Surd(-3,3))", // "-1.4422495703074083"); checkNumeric("1/9 * 3^(4/3)", // "1/3^(2/3)"); // checkNumeric("1/9 * 3^(7/4)", "1/3^(1/4)"); checkNumeric("1/9 * 3^(3/4)", // "1/(3*3^(1/4))"); checkNumeric("1/9 * 3^(-1/2)", // "1/(9*Sqrt(3))"); checkNumeric("1/9 * 3^(1/2)", // "1/(3*Sqrt(3))"); checkNumeric("2^(1/4)*2^(-3)", // "1/(4*2^(3/4))"); checkNumeric("2^(-3)", // "1/8"); checkNumeric("2^(-3/4)", // "1/2^(3/4)"); // checkNumeric("Trace((2^(1/4))/8)", ""); checkNumeric("Surd(2,4)/8-(1/(4*2^(1/4.0)))", // "-0.061573214438088525"); checkNumeric("1/(4*2^(1/4.0))", // "0.21022410381342865"); checkNumeric("Surd(2,4)", // "2^(1/4)"); checkNumeric("Surd(2,4)/8", // "1/(4*2^(3/4))"); checkNumeric("Surd(-2.,5)", // "-1.148698354997035"); // checkNumeric("(-2.0)^(1/5)", "-1.148698354997035"); check("Surd(-16.0,2)", // "Indeterminate"); checkNumeric("Surd(-2.,5)", // "-1.148698354997035"); check("Surd(-3,2)", // "Indeterminate"); check("Surd(-3,-2)", // "Indeterminate"); check("Surd(I,2)", // "Surd(I,2)"); check("Surd({-3, -2, -1, 0, 1, 2, 3}, 7)", // "{-3^(1/7),-2^(1/7),-1,0,1,2^(1/7),3^(1/7)}"); } @Test public void testSurvivalFunction() { check("SurvivalFunction(GeometricDistribution(1/3), x)", // "1-Piecewise({{1-(2/3)^(1+Floor(x)),x>=0}},0)"); check("SurvivalFunction(NormalDistribution(), {0.2, 0.3})", // "{0.42074,0.382089}"); check("SurvivalFunction(BetaDistribution(1/2,1/2), {{0.0, 0.0}, {0.2, 0.2}, {0.3, 0.3}})", // "{{1.0,1.0},{0.704833,0.704833},{0.63099,0.63099}}"); check("SurvivalFunction(NormalDistribution(0, 1), x)", // "1-Erfc(-x/Sqrt(2))/2"); check("CDF(NormalDistribution(0, 1), x)", // "Erfc(-x/Sqrt(2))/2"); } @Test public void testSwitch() { check("Switch(2, 1, x, 2, y, 3, z)", // "y"); check("Switch(5, 1, x, 2, y)", // "Switch(5,1,x,2,y)"); check("Switch(5, 1, x, 2, y, _, z)", // "z"); check("Switch(2, 1)", // "Switch(2,1)"); check("$f(b_) := switch(b, True, 1, False, 0, _, -1);{$f(True), $f(False), $f(x)}", // "{1,0,-1}"); } @Test public void testSymbol() { check("Head(x)", // "Symbol"); check("Symbol(\"x\") + Symbol(\"x\")", // "2*x"); check("i\\[CapitalGamma]j(hjgg)", // "iγj(hjgg)"); check("i\\[Alpha]j=10;i\\[Alpha]j", // "10"); } @Test public void testSymbolName() { check("Context(x)", // "Global`"); check("SymbolName(x)", // "x"); // TODO allow contexts // check("SymbolName(a`b`x)", "x"); } @Test public void testSymbolQ() { check("SymbolQ(a)", // "True"); check("SymbolQ(1)", // "False"); check("SymbolQ(a+b)", // "False"); } @Test public void testSyntaxQ() { check("SyntaxQ(\"Integrate(f(x),{x,0,10})\")", // "True"); check("SyntaxQ(\"Integrate(f(x),{x,0,10)\")", // "False"); } @Test public void testTable() { EvalEngine.resetModuleCounter4JUnit(); check("Table(n, {n, 2147483647, 2147483647 , 1})", // "{2147483647}"); check("Table(n, {n, 2147483643, 2147483647 , 2})", // "{2147483643,2147483645,2147483647}"); check("Table(n, {n, -2147483640, -2147483648 , -1})", // "{-2147483640,-2147483641,-2147483642,-2147483643,-2147483644,-2147483645,-\n" + "2147483646,-2147483647,-2147483648}"); check("Table(n, {n, -2147483640, -2147483655 , -1})", // "{-2147483640,-2147483641,-2147483642,-2147483643,-2147483644,-2147483645,-\n" + "2147483646,-2147483647,-2147483648,-2147483649,-2147483650,-2147483651,-\n" + "2147483652,-2147483653,-2147483654,-2147483655}"); check("Table(n, {n, -2147483640, -2147483655 , -3})", // "{-2147483640,-2147483643,-2147483646,-2147483649,-2147483652,-2147483655}"); check("Table(n, {n, 2147483640, 2147483650})", // "{2147483640,2147483641,2147483642,2147483643,2147483644,2147483645,2147483646,\n" + "2147483647,2147483648,2147483649,2147483650}"); check("Table(n, {n, 2147483640, 2147483650,3})", // "{2147483640,2147483643,2147483646,2147483649}"); check( "Module({i}, Table({{1,2},{1,2},{1,2},{1,2}}[[ i,{{1,2},{1,2},{1,2},{1,2}}[[i]] ]], {i,2}))", // "{{1,2},{1,2}}"); check("Table(101,{-2})", // "{}"); check("Table(z, {z,-2.0,2.0,0.1})", // "{-2.0,-1.9,-1.8,-1.7,-1.6,-1.5,-1.4,-1.3,-1.2,-1.1,-1.0,-0.9,-0.8,-0.7,-0.6,-0.5,-0.4,-0.3,-0.2,-0.1," + "6.38378*10^-16,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.1,1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2.0}"); // message nliter check("s={x,1,10};Table(f(x),s)", // "Table(f(x),s)"); check("Table(Sum(k^n, {k, 0, m}), {n, 1, 5, 1})", // "{1/2*m*(1+m),m/6+m^2/2+m^3/3,m^2/4+m^3/2+m^4/4,-m/30+m^3/3+m^4/2+m^5/5,-m^2/12+5/\n" + "12*m^4+m^5/2+m^6/6}"); check("Table(f(x), {x, a, a+1})", // "{f(a),f(1+a)}"); check("s=0;Table(s=i+s, {i, 0, 7})", // "{0,1,3,6,10,15,21,28}"); check("Table(a + dx, {dx, 0, 3, Pi/8})", // "{a,a+Pi/8,a+Pi/4,a+3/8*Pi,a+Pi/2,a+5/8*Pi,a+3/4*Pi,a+7/8*Pi}"); check("Table(0.0^x, {x, -1.0, 1.0, 0.25})", // "{ComplexInfinity,ComplexInfinity,ComplexInfinity,ComplexInfinity,Indeterminate,0.0,0.0,0.0,0.0}"); check("Table(0^x, {x,-1, 1,1/4})", // "{ComplexInfinity,ComplexInfinity,ComplexInfinity,ComplexInfinity,Indeterminate,0,\n" + // "0,0,0}"); check("Table(x, {4})", // "{x,x,x,x}"); check("n=0", "0"); check("Table(n= n + 1, {5})", // "{1,2,3,4,5}"); check("Table(i, {i, 4})", // "{1,2,3,4}"); check("Table(i, {i, 2, 5})", // "{2,3,4,5}"); check("Table(i, {i, 2, 6, 2})", // "{2,4,6}"); check("Table(i, {i, Pi, 2*Pi, Pi / 2})", // "{Pi,3/2*Pi,2*Pi}"); check("Table(x^2, {x, {a, b, c}})", // "{a^2,b^2,c^2}"); check("Table({i, j}, {i, {a, b}}, {j, 1, 2})", // "{{{a,1},{a,2}},{{b,1},{b,2}}}"); check("Table(x, {x,0,1/3})", // "{0}"); check("Table(x, {x, -0.2, 3.9})", // "{-0.2,0.8,1.8,2.8,3.8}"); // check("Timing(Length(Table(i, {i, 1, 10000})))", "{0.159,10000}"); check("Table(x,10)", // "{x,x,x,x,x,x,x,x,x,x}"); check("Table(x,-1)", // "{}"); check("Table(0,{4-1})", // "{0,0,0}"); check("$a=10;Table($a^2, {$a, 10})", // "{1,4,9,16,25,36,49,64,81,100}"); check("Table(f(a), {a, 0, 20, 2})", // "{f(0),f(2),f(4),f(6),f(8),f(10),f(12),f(14),f(16),f(18),f(20)}"); check("Table(x, {10})", // "{x,x,x,x,x,x,x,x,x,x}"); check("Table(10*a + j, {a, 4}, {j, 3})", // "{{11,12,13},{21,22,23},{31,32,33},{41,42,43}}"); check("Table(f(a), {a, 10, -5, -2})", // "{f(10),f(8),f(6),f(4),f(2),f(0),f(-2),f(-4)}"); check("Table(Sqrt(x), {x, {1, 4, 9, 16}})", // "{1,2,3,4}"); check("Table(100*a + 10*j + k, {a, 3}, {j, 2}, {k, 4})", // "{{{111,112,113,114},{121,122,123,124}},{{211,212,213,214},{221,222,223,224}},{{\n" + "311,312,313,314},{321,322,323,324}}}"); check("Table(j^(1/a), {a, {1, 2, 4}}, {j, {1, 4, 9}})", // "{{1,4,9},{1,2,3},{1,Sqrt(2),Sqrt(3)}}"); check("Table(2^x + x, {x, a, a + 5*b, b})", // "{2^a+a,2^(a+b)+a+b,2^(a+2*b)+a+2*b,2^(a+3*b)+a+3*b,2^(a+4*b)+a+4*b,2^(a+5*b)+a+5*b}"); check("Table(a, {a, Pi, 2*Pi, Pi / 2})", // "{Pi,3/2*Pi,2*Pi}"); check( "b := 3 ; a := 1+b ; Length(Table(a*x^2,{x,-1.0,1.0605456,0.060606062},{y,-a+b^2,a+b^2,0.160606062}))", // "34"); check("x=2;Table(x^2,{x,0,10,1})", // "{0,1,4,9,16,25,36,49,64,81,100}"); } @Test public void testTableForm() { // check( // "TableForm({{a, b}, {c, d}, {e, f}}, TableHeadings -> {None, {\"c1\", \"c2\"}})", // // ""); String expected = String.join("\n", // " 1 ", // " 1 2 ", // " 1 2 3 ", // " 1 2 3 4 ", // " 1 2 3 4 5 "); check("TableForm({{1},{1,2},{1,2,3},{1,2,3,4},{1,2,3,4,5}})", // expected); expected = String.join("\n", // " 1 ", // " 1 2 ", // " a ", // " b ", // " c ", // " 1 2 3 ", // " 1 2 3 4 ", // " 1 2 3 4 5 "); check("TableForm({{1},{1,2},a,b,c,{1,2,3},{1,2,3,4},{1,2,3,4,5}})", // expected); expected = String.join("\n", // " a ", // " b ", // " 3 "); check("TableForm({a,b,3})", // expected); expected = String.join("\n", // " a "); check("TableForm(a)", // expected); expected = String.join("\n", // " a(1) ", // " a(2) "); check("TableForm(SparseArray(Array(a, {2})))", // expected); expected = String.join("\n", // " a(1,1) a(1,2) ", // " a(2,1) a(2,2) "); check("TableForm(SparseArray(Array(a, {2,2})))", // expected); expected = String.join("\n", // " a(1) ", // " a(2) "); check("TableForm(Array(a, {2}))", // expected); expected = String.join("\n", // " a(1,1) a(1,2) ", // " a(2,1) a(2,2) "); check("TableForm(Array(a, {2,2}))", // expected); // check("TableForm(RandomReal(5, {3, 4}))", // // "3.3966021212581032 0.37386691098759195 3.3714636398631437 4.888805919349176 \n" + // "3.977341548616806 0.7908229654057569 0.4052451831886883 1.455709563360077 \n" + // "1.0028599118204118 1.2764414981301953 4.024172644043268 1.3404548410990742"); } @Test public void testTake() { check("Take(SparseArray(Range(1000)), {100, 105})", // "{100,101,102,103,104,105}"); check("Take(<|1 -> a, 2 -> b, 3 -> c|>, {2})", // "<|2->b|>"); check("Take(<|1 -> a, 2 -> b, 3 -> c, 4 -> d|>, {2, -1})", // "<|2->b,3->c,4->d|>"); check("Take(x^2,{8,2,-1})", // "Take(x^2,{8,2,-1})"); check("Take({a, b, c, d}, -2)", // "{c,d}"); check("Take({a, b, c, d}, 3)", // "{a,b,c}"); check("Take({a, b, c, d}, -2)", // "{c,d}"); check("Take({a, b, c, d, e}, {2, -2})", // "{b,c,d}"); check("A = {{a, b, c}, {d, e, f}}", // "{{a,b,c},{d,e,f}}"); check("Take(A, 2, 2)", // "{{a,b},{d,e}}"); check("Take(A, All, {2})", // "{{b},{e}}"); check("Take(Range(10), {8, 2, -1})", // "{8,7,6,5,4,3,2}"); check("Take(Range(10), {-3, -7, -2})", // "{8,6,4}"); check("Take(Range(6), {-5, -2, -2})", // "Take({1,2,3,4,5,6},{-5,-2,-2})"); check("Take(l, {-1})", // "Take(l,{-1})"); check("Take({1, 2, 3, 4, 5}, {-1, -2})", // "{}"); check("Take({1, 2, 3, 4, 5}, {0, -1})", // "{}"); check("Take({1, 2, 3, 4, 5}, {1, 0})", // "{}"); check("Take({1, 2, 3, 4, 5}, {2, 1})", // "{}"); check("Take({1, 2, 3, 4, 5}, {1, 0, 2})", // "{}"); check("Take({1, 2, 3, 4, 5}, {1, 0, -1})", // "Take({1,2,3,4,5},{1,0,-1})"); check("Take({a, b, c, d, e, f}, All)", // "{a,b,c,d,e,f}"); check("Take({a, b, c, d, e, f}, 4)", // "{a,b,c,d}"); check("Take({a, b, c, d, e, f}, -3)", // "{d,e,f}"); check("Take({a, b, c, d, e, f}, {2,4})", // "{b,c,d}"); check("Take({{11, 12, 13}, {21, 22, 23},{31, 32, 33}}, 2, 2)", // "{{11,12},{21,22}}"); check("Take({{11, 12, 13}, {21, 22, 23},a,{31, 32, 33}}, 3, 2)", // "Take({{11,12,13},{21,22,23},a,{31,32,33}},3,2)"); check("Take({a, b, c, d, e, f}, None)", // "{}"); } @Test public void testTakeLargest() { check("TakeLargest(Prime(Range(10)), 3)", // "{29,23,19}"); check("TakeLargest({1, 3, 5, None, Indeterminate, Missing()}, 2)", // "{5,3}"); check("TakeLargest(<|a -> 1, b -> 2, c -> 3, d -> 4|>, 2)", // "<|d->4,c->3|>"); check("TakeLargest(3) @ {1, 3, 5, 4, 2}", // "{5,4,3}"); } @Test public void testTakeLargestBy() { // check("TakeLargestBy({-1.5+I*0.8660254037844386,-1.5+I*(-0.8660254037844386),-1.0},Abs,3)", // // // "{-1.5+I*0.8660254037844386,-1.5+I*(-0.8660254037844386),-1.0}"); checkNumeric("Abs(254/315+(14954373125000+I*7875000*Sqrt(9477810222))^(1/3)/31500+\n" // + " 1215035/63*2^(1/3)/(29908746250000+I*15750000*Sqrt(9477810222))^(1/3))//N", // "2.3710652374514223"); check("TakeLargestBy({254/315+(14954373125000+I*7875000*Sqrt(9477810222))^(1/3)/31500+\n" // + " 1215035/63*2^(1/3)/(29908746250000+I*15750000*Sqrt(9477810222))^(1/3),254/315+\n" // + " 1215035/63*(-1+I*Sqrt(3))/(2^(2/3)*(29908746250000+I*15750000*Sqrt(9477810222))^(\n" // + " 1/3))+((-1-I*Sqrt(3))*(29908746250000+I*15750000*Sqrt(9477810222))^(1/3))/(63000*\n" // + " 2^(1/3))},Abs,2)", // "{254/315+(14954373125000+I*7875000*Sqrt(9477810222))^(1/3)/31500+1215035/63*2^(1/\n"// + "3)/(29908746250000+I*15750000*Sqrt(9477810222))^(1/3),254/315+1215035/63*(-1+I*Sqrt(\n"// + "3))/(2^(2/3)*(29908746250000+I*15750000*Sqrt(9477810222))^(1/3))+((-1-I*Sqrt(3))*(\n"// + "29908746250000+I*15750000*Sqrt(9477810222))^(1/3))/(63000*2^(1/3))}"); // print message check("TakeLargestBy({2.0383668,3.96078,4.5547},Abs, 4)", // "TakeLargestBy({2.03837,3.96078,4.5547},Abs,4)"); check("TakeLargestBy({1, 3, 5, None, Indeterminate, Missing(),a,b}, Abs, 2)", // "TakeLargestBy({1,3,5,None,Indeterminate,Missing(),a,b},Abs,2)"); check("TakeLargestBy({2.0383668,3.96078,4.5547},Abs, 3)", // "{4.5547,3.96078,2.03837}"); check("TakeLargestBy(Prime(Range(10)),Mod(#,7)&, 3)", // "{13,5,19}"); check("TakeLargestBy(Prime(Range(10)),Mod(#,7)&, 3)", // "{13,5,19}"); check("TakeLargestBy({-5, -2, 4, 3, 1, 9, 2, -4}, Abs, 4)", // "{9,-5,4,-4}"); check("TakeLargestBy(<|a -> \"\", b -> \"xxx\", c -> \"xx\"|>, StringLength, 2)", // "<|b->xxx,c->xx|>"); } @Test public void testTakeSmallest() { // print message check("TakeSmallest({1, 3, 5, None, Indeterminate, Missing(),a,b}, 2)", // "TakeSmallest({1,3,5,None,Indeterminate,Missing(),a,b},2)"); check("TakeSmallest(Prime(Range(10)), 3)", // "{2,3,5}"); check("TakeSmallest({1, 3, 5, None, Indeterminate, Missing()}, 2)", // "{1,3}"); check("TakeSmallest(<|a -> 1, b -> 2, c -> 3, d -> 4|>, 2)", // "<|a->1,b->2|>"); check("TakeSmallest(3) @ {1, 3, 5, 4, 2}", // "{1,2,3}"); } @Test public void testTakeSmallestBy() { check("TakeSmallestBy({254/315+(14954373125000+I*7875000*Sqrt(9477810222))^(1/3)/31500+\n" // + " 1215035/63*2^(1/3)/(29908746250000+I*15750000*Sqrt(9477810222))^(1/3),254/315+\n" // + " 1215035/63*(-1+I*Sqrt(3))/(2^(2/3)*(29908746250000+I*15750000*Sqrt(9477810222))^(\n" // + " 1/3))+((-1-I*Sqrt(3))*(29908746250000+I*15750000*Sqrt(9477810222))^(1/3))/(63000*\n" // + " 2^(1/3))},Abs,2)", // "{254/315+1215035/63*(-1+I*Sqrt(3))/(2^(2/3)*(29908746250000+I*15750000*Sqrt(\n" + "9477810222))^(1/3))+((-1-I*Sqrt(3))*(29908746250000+I*15750000*Sqrt(9477810222))^(\n" + "1/3))/(63000*2^(1/3)),254/315+(14954373125000+I*7875000*Sqrt(9477810222))^(1/3)/\n" + "31500+1215035/63*2^(1/3)/(29908746250000+I*15750000*Sqrt(9477810222))^(1/3)}"); // print message check("TakeSmallestBy({1, 3, 5, None, Indeterminate, Missing(),a,b}, Abs, 2)", // "TakeSmallestBy({1,3,5,None,Indeterminate,Missing(),a,b},Abs,2)"); check("TakeSmallestBy(Prime(Range(10)),Mod(#,7)&, 3)", // "{7,29,2}"); check("TakeSmallestBy({-5, -2, 4, 3, 1, 9, 2, -4}, Abs, 4)", // "{1,-2,2,3}"); check("TakeSmallestBy(<|a -> \"\", b -> \"xxx\", c -> \"xx\"|>, StringLength, 2)", // "<|a->,c->xx|>"); } @Test public void testTakeWhile() { check("TakeWhile({2, 4, 6, 1, 2, 3}, EvenQ)", // "{2,4,6}"); check("TakeWhile(h(1, 1, 2, 3, a, 8, 13, b, c, d), IntegerQ)", // "h(1,1,2,3)"); check("TakeWhile({1, 1, 2, 3, 5, 8, 13, 21}, #1 < 10 &)", // "{1,1,2,3,5,8}"); check("Take({1, 1, 2, 3, 5, 8, 13, 21}, LengthWhile({1, 1, 2, 3, 5, 8, 13, 21}, #1 < 10 &))", // "{1,1,2,3,5,8}"); check("TakeWhile({1, 2, 3, 10, 5, 8, 42, 11}, # < 10 &)", // "{1,2,3}"); } @Test public void testTally() { check("Tally({{a, b}, {w, x, y, z}, E, {w, x, y, z}, E}, Head(#1) === Head(#2) &)", // "{{{a,b},3},{E,2}}"); check("Tally({a,a,b,a,c,b,a})", // "{{a,4},{b,2},{c,1}}"); check("Tally({b,a,b,a,c,b,a})", // "{{b,3},{a,3},{c,1}}"); check("Tally({{a, b}, {w, x, y, z}, E, {w, x, y, z}, E})", // "{{{a,b},1},{{w,x,y,z},2},{E,2}}"); check("str=\"The quick brown fox jumps over the lazy dog\";", // ""); check("Tally(Characters(str)) // InputForm", // "{{\"T\",1},{\"h\",2},{\"e\",3},{\" \",8},{\"q\",1},{\"u\",2},{\"i\",1},{\"c\",1},{\"k\",1},{\"b\",1},{\"r\",2},{\"o\",4},{\"w\",1},{\"n\",1},{\"f\",1},{\"x\",1},{\"j\",1},{\"m\",1},{\"p\",1},{\"s\",1},{\"v\",1},{\"t\",1},{\"l\",1},{\"a\",1},{\"z\",1},{\"y\",1},{\"d\",1},{\"g\",1}}"); check("Sort(Tally({b,a,c,b,a,c,b,a}))", // "{{a,3},{b,3},{c,2}}"); check("Map({#, Count({b, a, c, b, a, c, b, a}, #)} &,Union({b, a, c, b, a, c, b, a}))", // "{{a,3},{b,3},{c,2}}"); check("Counts({b, a, c, b, a, c, b, a})", // "<|a->3,b->3,c->2|>"); check("tb(list_, f_) := Tally(list, f(#) === f(#2) &)", // ""); check("tb({1, 2, 3, 2, 1, 1}, EvenQ)", // "{{1,4},{2,2}}"); // check("Tally(RandomInteger(10, 100))", // // "{{1,13},{7,11},{9,6},{0,12},{2,8},{8,7},{10,8},{4,6},{6,10},{3,11},{5,8}}"); } @Test public void testTagSet() { check("x /: g(h(x)) = 3", // "3"); check("f/:format(f)=0", // "0"); check("f/:format(f)/:0", // "Syntax error in line: 1 - Operator: '/:' not created properly (no grouping defined)\n" + // "f/:format(f)/:0\n" + // " ^"); check("f/: Format(f) = \"TagSet test\"", // "TagSet test"); check("Format(f)", // "TagSet test"); } @Test public void testTagSetDelayed() { check("g /: f(a,g,z_)/;True := {z}", // ""); check("f(a,g,test)", // "{test}"); check("g /: f(g(x_)) := fg(x)", // ""); check("{f(g(2)) , f(h(2)) }", // "{fg(2),f(h(2))}"); } @Test public void testTagSetDelayed02() { check("TagSetDelayed(g,0,\"TagSetDelayed test\")", // ""); check("g/: Format(a_,g(x)) := \"TagSetDelayed test\"", // ""); // check("Definition(g)", // // "TagSet test"); check("Format(f,g(x))", // "TagSetDelayed test"); } @Test public void testTan() { // check("Tan(8/15*Pi)", // // "-Cot(Pi/30)"); check("Tan(Pi / 2.0)", // "1.63312*10^16"); // TODO // check("Tan(z-Pi/3)", // // "-Cot(Pi/6+z)"); check("Tan(e-Pi/2+f*x)", // "-Cot(e+f*x)"); check("Tan(e+Pi/2+f*x)", // "-Cot(e+f*x)"); check("Tan(Pi/2+Pi*n)", // "-Cot(n*Pi)"); check("Tan(ArcSin(x))", // "x/Sqrt(1-x^2)"); check("Tan(ArcCos(x))", // "Sqrt(1-x^2)/x"); check("Tan(ArcTan(x))", // "x"); check("Tan(ArcCot(x))", // "1/x"); check("Tan(ArcCsc(x))", // "1/(Sqrt(1-1/x^2)*x)"); check("Tan(ArcSec(x))", // "Sqrt(1-1/x^2)*x"); check("Tan(0)", // "0"); check("Tan(Pi / 2)", // "ComplexInfinity"); checkNumeric("Tan(0.5*Pi)", // "1.633123935319537E16"); check("Tan(Pi/2)", // "ComplexInfinity"); check("Tan(1/6*Pi)", // "1/Sqrt(3)"); check("Tan(Pi)", // "0"); check("Tan(z+Pi)", // "Tan(z)"); check("Tan(z+42*Pi)", // "Tan(z)"); check("Tan(z+42*a*Pi)", // "Tan(42*a*Pi+z)"); check("Tan(z+1/2*Pi)", // "-Cot(z)"); check("Tan(Pi)", // "0"); check("Tan(33*Pi)", // "0"); check("Tan(z+Pi)", // "Tan(z)"); check("Tan(z+42*Pi)", // "Tan(z)"); check("Tan(x+y+z+43*Pi)", // "Tan(x+y+z)"); check("Tan(z+42*a*Pi)", // "Tan(42*a*Pi+z)"); check("Tan(z+4/3*Pi)", // "Tan(Pi/3+z)"); } @Test public void testTanh() { check("Tanh(0)", // "0"); } @Test public void testTautologyQ() { // https://en.wikipedia.org/wiki/Tautology_(logic) check("TautologyQ(a || !a)", // "True"); check("TautologyQ((a || b) && (! a || ! b))", // "False"); check("TautologyQ((a || b) || (! a && ! b))", // "True"); check("TautologyQ((a || b) && (! a || ! b), {a, b})", // "False"); check("TautologyQ((a || b) || (! a && ! b), {a, b})", // "True"); } @Test public void testTaylor() { check("Taylor(f(x),{x,a,2})", // "f(a)+(-a+x)*f'(a)+1/2*(-a+x)^2*f''(a)"); check("Taylor(ArcSin(x),{x,0,10})", // "x+x^3/6+3/40*x^5+5/112*x^7+35/1152*x^9"); check("Limit(ArcSin(x)/x,x->0)", // "1"); check("(-0^2+1)^(-1/2)", // "1"); } @Test public void testTextString() { check("TextString(10) // InputForm", // "\"10\""); } @Test public void testThread() { check("Thread(Tuples({0, 1}, 2) -> {a, b, c, d})", // "{{0,0}->a,{0,1}->b,{1,0}->c,{1,1}->d}"); check("Thread(f({a, b, c},{d,e}))", // "f({a,b,c},{d,e})"); check("Thread(f({}))", // "{}"); check("Thread(x^2)", // "x^2"); check("Thread(f(x^2))", // "f(x^2)"); check("Thread(f({a, b, c}))", // "{f(a),f(b),f(c)}"); check("Thread(f({a, b, c}, {x, y, z}))", // "{f(a,x),f(b,y),f(c,z)}"); check("Thread(Log(x == y), Equal)", // "Log(x)==Log(y)"); check("Thread(f({a, b, c}))", // "{f(a),f(b),f(c)}"); check("Thread(f({a, b, c}, t))", // "{f(a,t),f(b,t),f(c,t)}"); check("Thread(f(a + b + c), Plus)", // "f(a)+f(b)+f(c)"); check("{a, b, c} + {d, e, f} + g", // "{a+d+g,b+e+g,c+f+g}"); check("Thread(f({a, b, c}, h, {x, y, z}))", // "{f(a,h,x),f(b,h,y),f(c,h,z)}"); } @Test public void testThreeJSymbol() { check("ThreeJSymbol({2, 0}, {6, 0}, {4, 0})", // "Sqrt(5/143)"); check("ThreeJSymbol({3/2, -3/2}, {3/2, 3/2}, {1, 0})", // "Sqrt(3/5)/2"); check("ThreeJSymbol({5, 0}, {4, 0}, {1, 0})", // "-Sqrt(5/11)/3"); check("ThreeJSymbol({6, 0}, {4, 0}, {2, 0})", // "Sqrt(5/143)"); check("ThreeJSymbol({2, 1}, {2, 2}, {4, -3})", // "-1/(3*Sqrt(2))"); check("ThreeJSymbol({1/2, -1/2}, {1/2, -1/2}, {1, 1})", // "-1/Sqrt(3)"); check("{j1, j2} = {3, 2};\n" // + "Table(Sum(\n" // + " If(Abs(m1 + m2) > j || Abs(m1 + m2) > ji, 0, \n" // + " Sqrt((2 j + 1) (2 ji + 1))*ThreeJSymbol({j1, m1}, {j2, \n" // + " m2}, {j, -(m1 + m2)})*ThreeJSymbol({j1, m1}, {j2, \n" // + " m2}, {ji, -(m1 + m2)})), {m1, -j1, j1}, {m2, -j2, j2}), {j, \n" // + " Abs(j1 - j2), j1 + j2}, {ji, Abs(j1 - j2), j1 + j2})", // "{{3,0,0,0,0},{0,5,0,0,0},{0,0,7,0,0},{0,0,0,9,0},{0,0,0,0,11}}"); } @Test public void testThrough() { check("s1 = {\"t\", \"o\", \"d\", \"a\", \"y\"}", // "{t,o,d,a,y}"); check("Through({StringJoin, Length}[#])& @ s1", // "{today,5}"); check("s2 = {{\"h\", \"e\", \"l\", \"l\", \"o\"}, {\"d\", \"a\", \"y\"}}", // "{{h,e,l,l,o},{d,a,y}}"); check("Thread@ MapThread(# /@ s2 &, {{StringJoin, Length}})", // "{{hello,5},{day,3}}"); check("{StringJoin(##), Length({##})} & @@@ s2", // "{{hello,5},{day,3}}"); check("Through({StringJoin, Length}({##})) & @@@ s2", // "{{hello,5},{day,3}}"); check("Through(p(f, g)[])", // "p(f(),g())"); check("Through(p(f,g)[x])", // "p(f(x),g(x))"); check("Through(p(f,g)[])", // "p(f(),g())"); check("Through(f()[x])", // "f()"); check("Through(p(f,g))", // "p(f,g)"); check("Through(p(f,g)[x,y])", // "p(f(x,y),g(x,y))"); check("Through(f(g)[x])", // "f(g(x))"); check("NestList(Through, f(a)[b][c][d], 3)", // "{f(a)[b][c][d],f(a)[b][c(d)],f(a)[b(c(d))],f(a(b(c(d))))}"); check("Through( ((D(#, x) &) + (D(#, x, x) &))[f(x)] )", // "f'(x)+f''(x)"); check("Through((f*g)[x,y],Plus)", // "(f*g)[x,y]"); check("Through((f+g+h)[x,y],Plus)", // "f(x,y)+g(x,y)+h(x,y)"); } @Test public void testTimeConstrained() { if (!Config.TIMECONSTRAINED_NO_THREAD) { // Config.FUZZ_TESTING = true; try { check("TimeConstrained( Beta(I*1/2,1.5707963267948966,2147483647), 2)", // "$Aborted"); check("TimeConstrained(Do(i^2, {i, 10000000}), 1)", // "$Aborted"); check("TimeConstrained(Pause(1); t=TimeRemaining(); Print(t);t>1&&Head(t)==Real, 10)", // "True"); } finally { // Config.FUZZ_TESTING = false; } } } @Test public void testTimeObject() { // Current time // check("TimeObject()", // // "17:38:38"); check("TimeObject({10,45})", // "10:45:00"); check("TimeObject({11,11,11})", // "11:11:11"); check("TimeObject({03,02,01})", // "03:02:01"); } @Test public void testTimes() { check("0.0*Sin(#)", // "0"); check("8.88178*10^-16 * Binomial(50.0, #)", // "8.88178*10^-16*Binomial(50.0,#1)"); check("0.5^#1*(-0.5+1)^(50.0-#1)", // "8.88178*10^-16"); check("0.5^27.0*(-0.5+1)^(50.0-27.0)", // "8.88178*10^-16"); check("Times(Sqrt[2/Pi]*Sqrt[Pi])", // "Sqrt(2)"); check("Times(I, 1/2) // FullForm", // "Complex(0,Rational(1,2))"); check("Head(Times(I, 1/2))", // "Complex"); // check("(Sqrt(1/(2*Sqrt(10)))*Sqrt(-2+(2+Sqrt(10))*x^2)*Sqrt((2-(2-Sqrt(10))*x^2)/(2-(2+Sqrt(\n" // + "10))*x^2))*EllipticF(ArcSin(x/(Sqrt(2)*Sqrt(1/(4*Sqrt(10)))*Sqrt(-2+(2+Sqrt(10))*x^\n" // + "2))),1/10*(5+Sqrt(10))))/(Sqrt(2)*Sqrt(-2+4*x^2+3*x^4)*Sqrt(1/(2-(2+Sqrt(10))*x^\n" + // "2)))", // // "(Sqrt(1/(2*Sqrt(10)))*Sqrt(-2+(2+Sqrt(10))*x^2)*Sqrt((2+(-2+Sqrt(10))*x^2)/(2-(2+Sqrt(\n" + // "10))*x^2))*EllipticF(ArcSin(x/(Sqrt(2)*Sqrt(1/(4*Sqrt(10)))*Sqrt(-2+(2+Sqrt(10))*x^\n" + // "2))),1/10*(5+Sqrt(10))))/(Sqrt(2)*Sqrt(-2+4*x^2+3*x^4)*Sqrt(1/(2-(2+Sqrt(10))*x^\n" + // "2)))"); check("Sin(0.1851851851851852*Pi*x)", // "Sin(0.581776*x)"); check("-a*(2-x)", // "a*(-2+x)"); check("False*Log(x+y)", // "False*Log(x+y)"); check("Csch(x)^3 * Sinh(x)^(-2)", // "Csch(x)^5"); check("Csch(x)^3 * Sinh(x)^7", // "Sinh(x)^4"); check("2*4^(1+p)", // "2^(3+2*p)"); check("(2^(3/4)*x*7^(-15/4))", // "1/343*(2/7)^(3/4)*x"); check("125*2^(2+3*b)", // "125*2^(2+3*b)"); check("(1/2)*4^(1+p)", // "2^(1+2*p)"); // same as in MMA check("-(1/3)*(2+n)", // "1/3*(-2-n)"); check("-(2+n)", // "-2-n"); check("-3*(2+n)", // "-3*(2+n)"); check("2^(3+k)*4^(1+p)", // "2^(5+k+2*p)"); check("2*2^(1+p)", // "2^(2+p)"); check("(1/2)*4^(1+p)", // "2^(1+2*p)"); check("-(-b*c+a*d)*n", // "(b*c-a*d)*n"); check("5/7*Sqrt(7/6)", // "5/Sqrt(42)"); check("(Sqrt(3)*x)/Sqrt(2)", // "Sqrt(3/2)*x"); check("1/(sq(a)*sq(b))//FullForm", // "Times(Power(sq(a), -1), Power(sq(b), -1))"); check("(-Infinity)/Sin(-2)", // "Infinity"); check("(-Infinity)/(-2)", // "Infinity"); check("(-Infinity)/Log(2)", // "-Infinity"); check("(-Infinity)/2", // "-Infinity"); // github #35 check(" y^2*y^(-0.6666) ", // "y^1.3334"); check(" y*y^(-0.6666) ", // "y^0.3334"); check("x* y*y^(-0.6666) *z^(-1)", // "(x*y^0.3334)/z"); check("5/7*Sqrt(7/6)", // "5/Sqrt(42)"); check("Hold((-1)^(a) (b)) // FullForm", // "Hold(Times(Power(-1, a), b))"); check("Sqrt(1/2)*(1+x)", // "(1+x)/Sqrt(2)"); check("((5/21)^(2/3)*(7/6)^(2/7)) ", // "5^(2/3)/(2^(2/7)*3^(20/21)*7^(8/21))"); check("x*y/(y*z)", // "x/z"); check("x*y/(y^3*z)", // "x/(y^2*z)"); check("x*y/(y^(2/3)*z)", // "(x*y^(1/3))/z"); check("x*y/(y^(0.6666)*z) ", // "(x*y^0.3334)/z"); check("N(Pi, 30) * I", // "I*3.14159265358979323846264338327"); check("N(I*Pi, 30)", // "I*3.14159265358979323846264338327"); check("N(Pi * E, 30)", // "8.53973422267356706546355086954"); check("N(Pi, 30) * N(E, 30)", // "8.53973422267356706546355086954"); check("N(Pi, 30) * E // Precision", // "30"); check("N(Pi, 30) * E", // "8.53973422267356706546355086954"); check("Floor(Log(7,1024))", // "3"); check("10*2", // "20"); check("a*a", // "a^2"); check("x ^ 10 * x ^ -2", // "x^8"); check("{1, 2, 3} * 4", // "{4,8,12}"); check("Times @@ {1, 2, 3, 4}", // "24"); check("IntegerLength(Times@@Range(100))", // "158"); check("a /. n_. * x_ :> {n, x} ", // "{1,a}"); check("-a*b // FullForm", // "Times(-1, a, b)"); check("-(x - 2/3)", // "2/3-x"); check("-(h/2) // FullForm", // "Times(Rational(-1,2), h)"); check("x / x", // "1"); check("2*x^2 / x^2", // "2"); checkNumeric("3.*Pi", // "9.42477796076938"); check("Head(3 * I) ", // "Complex"); check("Head(Pi * I)", // "Times"); checkNumeric("-2.123456789 * x", // "-2.123456789*x"); checkNumeric("-2.123456789 * I", // "I*(-2.123456789)"); // issue #137 check("12*2^x*3^y", // "2^(2+x)*3^(1+y)"); check("8*2^x", // "2^(3+x)"); check("12*2^x", // "3*2^(2+x)"); check("-Infinity", // "-Infinity"); check("Times(I*Sqrt(2), I*Sqrt(3))", // "-Sqrt(6)"); check("Sin(x)^(-2)/Tan(x)", // "Cot(x)*Csc(x)^2"); check("Sin(x)/Tan(x)", // "Cos(x)"); check("Sin(x)^2/Tan(x)^3", // "Cos(x)^2*Cot(x)"); check("Sin(x)^3/Tan(x)^2", // "Cos(x)^2*Sin(x)"); check("Sin(x)^2/Tan(x)", // "Cos(x)*Sin(x)"); check("Sin(x)/Tan(x)^2", // "Cos(x)*Cot(x)"); check("Sin(x)^(-2)", // "Csc(x)^2"); check("Sin(x)/Tan(x)^(-2)", // "Sin(x)*Tan(x)^2"); check("Sin(x)/Cos(x)", // "Tan(x)"); check("Cos(x)*Tan(x)", // "Sin(x)"); check("Cos(x)/Sin(x)", // "Cot(x)"); check("Tan(x)/Sin(x)", // "Sec(x)"); check("Times()", // "1"); // OutputForm: I*Infinity is DirectedInfinity[I] check("I*Infinity", // "I*Infinity"); check("Gamma(a)*Gamma(1-a)", // "Pi*Csc(a*Pi)"); check("Gamma(a)^3*Gamma(1-a)^3", // "Pi^3*Csc(a*Pi)^3"); check("Gamma(a)^3*Gamma(1-a)^2", // "Pi^2*Csc(a*Pi)^2*Gamma(a)"); } @Test public void testTimesBy() { check("a = 10", // "10"); check("a *= 2", // "20"); check("a", // "20"); check("index={1,2,3,4,5,6,7,8,9}", // "{1,2,3,4,5,6,7,8,9}"); check("index[[3]]*=y", // "3*y"); check("index", // "{1,2,3*y,4,5,6,7,8,9}"); } @Test public void testTimeValue() { check("TimeValue(I*1/2,-I,0)", // "I*1/2"); check(" TimeValue(-0.8+I*1.2,-5,1009)", // "ComplexInfinity"); check("N(TimeValue((-8/10)+I*(12/10),-5,1009),20)", // "2.4078045838557934240*10^607+I*(-3.611706875783690136*10^607)"); check("TimeValue(Annuity(100, 12), .01, 0)", // "1125.508"); check("TimeValue(Annuity(100, 12), EffectiveInterest(.01, 0.25), 12)", // "1268.515"); check("TimeValue(AnnuityDue(100, 12), 0.1, 0)", // "749.5061"); check("TimeValue(Annuity(500,36,q), b, c)", // "(500*(-1+((1+b)^q)^(36/q)))/((-1+(1+b)^q)*((1+b)^q)^(36/q-c/q))"); check("TimeValue(AnnuityDue(500,36,q), b, c)", // "(500*(-1+((1+b)^q)^(36/q))*((1+b)^q)^(1-36/q+c/q))/(-1+(1+b)^q)"); check("TimeValue(Annuity(100, 12), 6/100, 0)", // "411863798761210257735000/491258904256726154641"); check("TimeValue(a,b,c)", // "a*(1+b)^c"); check("TimeValue(100, EffectiveInterest(.06, 1/12), 10)", // "181.9397"); check("TimeValue(Annuity(1000, 10), .06, 0)", // "7360.087"); check("TimeValue(Annuity(1000, 5), EffectiveInterest(.08, 1/4), 5)", // "5895.119"); check("TimeValue(AnnuityDue(100, 12), 6/100, 0)", // "8237275975224205154700/9269035929372191597"); check("TimeValue(AnnuityDue(1000, 10), .06, 0)", // "7801.692"); check("TimeValue(AnnuityDue(1000, 5), EffectiveInterest(.08, 1/4), 5)", // "6381.066"); } @Test public void testTogether() { check("Together((1/x-1/3)^3/(x-3)^2)", // "(3-x)/(27*x^3)"); check("Together((1/x-1/3)/(x-3))", // "-1/(3*x)"); check("Together(1/2+(1/3+I*1/2)*Sqrt(3))", // "1/6*(3+(2+I*3)*Sqrt(3))"); check("Together(1/2+I*1/2*Sqrt(3))", // "1/2*(1+I*Sqrt(3))"); check("Together(1/2*x+1/2*y+1/2*z)", // "1/2*(x+y+z)"); check("Together(1/2*x+1/6*y+1/4*z)", // "1/12*(6*x+2*y+3*z)"); check("Together( 8-8*Cos(2/7*Pi))", // "8*(1-Cos(2/7*Pi))"); check("Together(6/5*c*f+6/5*b*g+2/5*c*f*m+1/5*b*g*m+2/5*c*f*n+3/5*b*g*n)", // "1/5*(6*c*f+6*b*g+2*c*f*m+b*g*m+2*c*f*n+3*b*g*n)"); check("Together(Sqrt(2)+SparseArray({{0,1},{1,0}}))", // "SparseArray(Number of elements: 4 Dimensions: {2,2} Default value: 0)"); check("Together(1+(b*x)/a)", // "(a+b*x)/a"); // TODO ((1+x)*f(x))/x^2 check("f(x)/x+f(x)/x^2//Together", // "(f(x)+x*f(x))/x^2"); check("together(x^2/(x^2 - 1) + x/(x^2 - 1))", // "x/(-1+x)"); check("Together((2 + 2*x)/(2*Sqrt(2)))", // "(1+x)/Sqrt(2)"); // check("Together(-(5*c*f+5*b*g+2*c*f*m+b*g*m+2*c*f*n+3*b*g*n+30*c*g*x+10*c*g*m*x+15*c*g*n*x)^5/(3125*c^4*g^4*(6+2*m+3*n)^4))", // // // ""); check("Together((x+2*Sqrt(x)+1)/(1+Sqrt(x)))", // "1+Sqrt(x)"); check("Together(-a/(-(b-a*c)))", // "a/(b-a*c)"); check("Together(Simplify(Together(-a/(-(b-a*c)))))", // "a/(b-a*c)"); check("Together(1/2+I/3 + 3*a^(-1))", // "(18+(3+I*2)*a)/(6*a)"); check("Together(1/2 + 3/a )", // "(6+a)/(2*a)"); check("Together[(2 + 2*x)/(2*Sqrt[2])]", // "(1+x)/Sqrt(2)"); check("Together((1+a/(c+d)+b/(c+d))/(a+b))", // "(a+b+c+d)/((a+b)*(c+d))"); check("Together((a+b*x+c*x^2)^13/13)", // "(a+b*x+c*x^2)^13/13"); check("Together(1/(a + b) + 1/(c + d) - a)", // "(a+b+c-a^2*c-a*b*c+d-a^2*d-a*b*d)/((a+b)*(c+d))"); check("Together(1/a+1/b)", // "(a+b)/(a*b)"); check("Together(1/a+1/b+c)", // "(a+b+a*b*c)/(a*b)"); check("Together(1/c+d)", // "(1+c*d)/c"); check("Together(1/2+a)", // "1/2*(1+2*a)"); check("Together((1+a/(c+d)+b/(c+d))/(a+b))", // "(a+b+c+d)/((a+b)*(c+d))"); check("Together(1/a+1/b+c+d)", // "(a+b+a*b*c+a*b*d)/(a*b)"); check("Together(2*a+2*b)", // "2*(a+b)"); check("Together(-(a^2-c^2)/(a*b-b*c))", // "-(a+c)/b"); check("Together(1/Sqrt(1+1/x) )", // "Sqrt(x/(1+x))"); check("Together(1/Sqrt(1+1/x)+(1+1/x)^(3/2))", // "(Sqrt((1+x)/x)+x*Sqrt((1+x)/x)+x*Sqrt(x/(1+x)))/x"); check("Together(1/(2*Sqrt(3))+Sqrt(3)/2)", // "2/Sqrt(3)"); check("Together(1/2-Sqrt(5)/2+2/(1+Sqrt(5)))", // "0"); // check("Together(1/Sqrt(1+1/x) + (1+1/x)^(3/2) )", " "); check("Together(1+1/(1+1/x))", // "(1+2*x)/(1+x)"); check("Together(a/b+c/d)", // "(b*c+a*d)/(b*d)"); // TODO return {x (2 + y) / (1 + y) ^ 2} check("Together({x / (y+1) + x / (y+1)^2})", // "{(2*x+x*y)/(1+2*y+y^2)}"); check("Together(a / c + b / c)", // "(a+b)/c"); check("Together(f(a / c + b / c))", // "f(a/c+b/c)"); check("f(x)/x+f(x)/x^2//Together", // "(f(x)+x*f(x))/x^2"); check("Together(1 < 1/x + 1/(1 + x) < 2)", // "1<(1+2*x)/(x*(1+x))<2"); check("Together(1/(1+1/(1+1/a)))", // "(1+a)/(1+2*a)"); check("Together(1/(1+1/(1+1/(1+a))))", // "(2+a)/(3+2*a)"); check("ExpandAll(a*b)", // "a*b"); check("ExpandAll(a*b^(-1))", // "a/b"); check("(a*b)^(-1)", // "1/(a*b)"); check("Together(a/b + c/d)", // "(b*c+a*d)/(b*d)"); check("Together((-7*a^(-1)*b+1)*(-a^(-1)*b-1)^(-1))", // "(a-7*b)/(-a-b)"); check("Together(a*b^(-2)+c*d^(-3))", // "(b^2*c+a*d^3)/(b^2*d^3)"); check("Together(-a*b^(-2)-c*d^(-3))", // "(-b^2*c-a*d^3)/(b^2*d^3)"); check("Together((-8)*a^(-1)*(-a^(-1)*b-1)^(-1))", // "-8/(-a-b)"); check( "Together((2*(2*x^3-4*x+5)*x^3*(3*x^2+2)^(-1)-4*x*(2*x^3-4*x+5)*(3*x^2+2)^(-1)+5*(2*x^3-4*x+\n" + "5)*(3*x^2+2)^(-1)-4*x^4+8*x^2-10*x)*(3*x^2+2)^(-1)+x^2-2)", // "(17-60*x+12*x^2-10*x^3-6*x^4+x^6)/(2+3*x^2)^2"); check( "Together((4*x^6-8*x^4+10*x^3)*(3*x^2+2)^(-1)+(-8*x^4+16*x^2-20*x)*(3*x^2+2)^(-1)+(10*x^3\n" + "-20*x+25)*(3*x^2+2)^(-1)-4*x^4+8*x^2-10*x)", // "(25-60*x+32*x^2-10*x^3-8*x^6)/(2+3*x^2)"); check( "Together((2*(2*x^3-4*x+5)*x^3*(3*x^2+2)^(-1)-4*x*(2*x^3-4*x+5)*(3*x^2+2)^(-1)+5*(2*x^3-4*x+\n" + "5)*(3*x^2+2)^(-1)-4*x^4+8*x^2-10*x)*(x)^(-1)-2)", // "(25-64*x+32*x^2-16*x^3-8*x^6)/(x*(2+3*x^2))"); check("Together(a + c/g)", // "(c+a*g)/g"); check("Together(((7*b*a^(-1)-1)*(-b*a^(-1)-1)^(-1)+7)*a^(-1))", // "-8/(-a-b)"); check("ExpandAll((x^2-1)*x^2+x*(x^2-1))", // "-x-x^2+x^3+x^4"); check("together(x^2/(x^2 - 1) + x/(x^2 - 1))", // "x/(-1+x)"); check("Together((1/3*x-1/6)*(x^2-x+1)^(-1))", // "(-1+2*x)/(6*(1-x+x^2))"); check( "Together((-a^2*r^2*x-a*b*r*x-a*c*x-a^2*r^3-2*a*b*r^2-a*c*r-b^2*r-b*c)*((a*r^2+b*r)^2+2*c*(a*r^2+b*r)+c^2)^(-1))", // "(-b-a*r-a*x)/(c+b*r+a*r^2)"); check("Together((-8)*a^(-1)*(-a^(-1)*b-1)^(-1))", // "-8/(-a-b)"); check("Together(a/b + c/d)", // "(b*c+a*d)/(b*d)"); check("Together((-a^(-1)*b-1))", // "(-a-b)/a"); check("((-b-a)*a^(-1))^(-1)", // "a/(-a-b)"); check("Together(1/x + 1/(x + 1) + 1/(x + 2) + 1/(x + 3))", // "(6+22*x+18*x^2+4*x^3)/(x*(1+x)*(2+x)*(3+x))"); } @Test public void testTogetherIssue856() { // github issue #856 check("tg=Simplify(1/(Sqrt(7) - 2 *Sqrt(2)) + 1/(Sqrt(7) + 2 *Sqrt(2))) ", // "-2*Sqrt(7)"); check("tg=Together(1/(-2*Sqrt(2)+Sqrt(7))+1/(2*Sqrt(2)+Sqrt(7))) ", // "-2*Sqrt(7)"); check("tg=Together(1/(Sqrt(7) - 2 *Sqrt(2)) + 1/(Sqrt(7) + 2 *Sqrt(2))) ", // "-2*Sqrt(7)"); } @Test public void testToExpression() { check("ToExpression(\"\\\\begin{matrix}\n" // + "1 & 2 \\\\\\\\\n" // + " 7 & 8\n" // + "\\\\end{matrix}\"" // + ", TeXForm)", // "{{1,2},{7,8}}"); check("ToExpression(\"\\\\frac{x}{\\\\sqrt{5}}\", TeXForm)", // "x/Sqrt(5)"); check("ToExpression(\"1 + 2 - x \\\\times 4 \\\\div 5\", TeXForm)", // "3-4/5*x"); } @Test public void testToRadicals() { check("ToRadicals(Root((#^2 - 3*# - 1)&, 2))", // "3/2+Sqrt(13)/2"); check("ToRadicals(Root((-3*#-1)&, 1))", // "-1/3"); check("ToRadicals(Sin(Root((#^7-#^2-#+a)&, 1)))", // "Sin(Root(-#1-#1^2+#1^7+a&,1))"); check("ToRadicals(Root((#^7-#^2-#+a)&, 1)+Root((#^6-#^2-#+a)&, 1))", // "Root(-#1-#1^2+#1^6+a&,1)+Root(-#1-#1^2+#1^7+a&,1)"); check("ToRadicals(Root((#^3-#^2-#+a)&, 1))", // "1/3+4/3*2^(1/3)/(11+Sqrt(-256+(11-27*a)^2)-27*a)^(1/3)+(11+Sqrt(-256+(11-27*a)^2)-\n" + "27*a)^(1/3)/(3*2^(1/3))"); check("ToRadicals(Root((#^3-#^2-#+a)&, 2))", // "1/3+4/3*(2^(1/3)*(-1/2-I*1/2*Sqrt(3)))/(11+Sqrt(-256+(11-27*a)^2)-27*a)^(1/3)+((-\n" + "1/2+I*1/2*Sqrt(3))*(11+Sqrt(-256+(11-27*a)^2)-27*a)^(1/3))/(3*2^(1/3))"); check("ToRadicals(Root((#^3-#^2-#+a)&, 3))", // "1/3+4/3*(2^(1/3)*(-1/2+I*1/2*Sqrt(3)))/(11+Sqrt(-256+(11-27*a)^2)-27*a)^(1/3)+((-\n" + "1/2-I*1/2*Sqrt(3))*(11+Sqrt(-256+(11-27*a)^2)-27*a)^(1/3))/(3*2^(1/3))"); } @Test public void testToString() { check("ToString(Sqrt(1-1/x^2))", // "Sqrt(1 - 1/x^2)"); String expected = String.join("\n", // " -1+Sin(x)^2 == -Cos(x)^2 ", // " 1+Sin(x)^2 == 1 + Sin(x)^2 ", // " -1+Cos(x)^2 == -Sin(x)^2 ", // " 1+Cos(x)^2 == 1 + Cos(x)^2 ", // " -1+Tan(x)^2 == -1 + Tan(x)^2 ", // " 1+Tan(x)^2 == Sec(x)^2 ", // " -1+Cot(x)^2 == -1 + Cot(x)^2 ", // " 1+Cot(x)^2 == Csc(x)^2 ", // " -1+Sec(x)^2 == Tan(x)^2 ", // " 1+Sec(x)^2 == 1 + Sec(x)^2 ", // " -1+Csc(x)^2 == Cot(x)^2 ", // " 1+Csc(x)^2 == 1 + Csc(x)^2 ", // " -1+Sinh(x)^2 == -1 + Sinh(x)^2 ", // " 1+Sinh(x)^2 == Cosh(x)^2 ", // " -1+Cosh(x)^2 == Sinh(x)^2 ", // " 1+Cosh(x)^2 == 1 + Cosh(x)^2 ", // " -1+Tanh(x)^2 == -Sech(x)^2 ", // " 1+Tanh(x)^2 == 1 + Tanh(x)^2 ", // " -1+Coth(x)^2 == Csch(x)^2 ", // " 1+Coth(x)^2 == 1 + Coth(x)^2 ", // " -1+Sech(x)^2 == -Tanh(x)^2 ", // " 1+Sech(x)^2 == 1 + Sech(x)^2 ", // " -1+Csch(x)^2 == -1 + Csch(x)^2 ", // " 1+Csch(x)^2 == Coth(x)^2 "); check( "Outer((ToString(#2) <> \"+\" <> ToString(#1) <> \"(x)^2 == \" <> ToString( Simplify( #2 + (#1(x)^2))) )&," // + "{Sin,Cos,Tan,Cot,Sec,Csc,Sinh,Cosh,Tanh,Coth,Sech,Csch}," // + "{-1,+1}) //" // + "Flatten // TableForm ", // expected); expected = String.join("\n", // " -1-f(x)-Sin(x)^2+y+z == -1 + y + z - f(x) - Sin(x)^2 ", // " 1-f(x)-Sin(x)^2+y+z == y + z + Cos(x)^2 - f(x) ", // " -1-f(x)-Cos(x)^2+y+z == -1 + y + z - Cos(x)^2 - f(x) ", // " 1-f(x)-Cos(x)^2+y+z == y + z - f(x) + Sin(x)^2 ", // " -1-f(x)-Tan(x)^2+y+z == y + z - f(x) - Sec(x)^2 ", // " 1-f(x)-Tan(x)^2+y+z == 1 + y + z - f(x) - Tan(x)^2 ", // " -1-f(x)-Cot(x)^2+y+z == y + z - Csc(x)^2 - f(x) ", // " 1-f(x)-Cot(x)^2+y+z == 1 + y + z - Cot(x)^2 - f(x) ", // " -1-f(x)-Sec(x)^2+y+z == -1 + y + z - f(x) - Sec(x)^2 ", // " 1-f(x)-Sec(x)^2+y+z == y + z - f(x) - Tan(x)^2 ", // " -1-f(x)-Csc(x)^2+y+z == -1 + y + z - Csc(x)^2 - f(x) ", // " 1-f(x)-Csc(x)^2+y+z == y + z - Cot(x)^2 - f(x) ", // " -1-f(x)-Sinh(x)^2+y+z == y + z - Cosh(x)^2 - f(x) ", // " 1-f(x)-Sinh(x)^2+y+z == 1 + y + z - f(x) - Sinh(x)^2 ", // " -1-f(x)-Cosh(x)^2+y+z == -1 + y + z - Cosh(x)^2 - f(x) ", // " 1-f(x)-Cosh(x)^2+y+z == y + z - f(x) - Sinh(x)^2 ", // " -1-f(x)-Tanh(x)^2+y+z == -1 + y + z - f(x) - Tanh(x)^2 ", // " 1-f(x)-Tanh(x)^2+y+z == y + z - f(x) + Sech(x)^2 ", // " -1-f(x)-Coth(x)^2+y+z == -1 + y + z - Coth(x)^2 - f(x) ", // " 1-f(x)-Coth(x)^2+y+z == y + z - Csch(x)^2 - f(x) ", // " -1-f(x)-Sech(x)^2+y+z == -1 + y + z - f(x) - Sech(x)^2 ", // " 1-f(x)-Sech(x)^2+y+z == y + z - f(x) + Tanh(x)^2 ", // " -1-f(x)-Csch(x)^2+y+z == y + z - Coth(x)^2 - f(x) ", // " 1-f(x)-Csch(x)^2+y+z == 1 + y + z - Csch(x)^2 - f(x) "); check( "Outer((ToString(#2) <> \"-f(x)-\" <> ToString(#1) <> \"(x)^2+y+z == \" <> ToString( Simplify( #2 - f(x) - (#1(x)^2)+y+z)) )&," // + "{Sin,Cos,Tan,Cot,Sec,Csc,Sinh,Cosh,Tanh,Coth,Sech,Csch}," // + "{-1,+1}) //" // + "Flatten // TableForm ", // expected); expected = String.join("\n", // " Sinh(ArcSinh(x)) == x ", // " Sinh(ArcCosh(x)) == Sqrt(-1 + x)*Sqrt(1 + x) ", // " Sinh(ArcTanh(x)) == x/Sqrt(1 - x^2) ", // " Sinh(ArcCoth(x)) == 1/(Sqrt(-1 + x)*Sqrt(1 + x)) ", // " Sinh(ArcSech(x)) == Sqrt(-1 + 1/x)*Sqrt(1 + 1/x) ", // " Sinh(ArcCsch(x)) == 1/x ", // " Cosh(ArcSinh(x)) == Sqrt(1 + x^2) ", // " Cosh(ArcCosh(x)) == x ", // " Cosh(ArcTanh(x)) == 1/Sqrt(1 - x^2) ", // " Cosh(ArcCoth(x)) == 1/Sqrt(1 - 1/x^2) ", // " Cosh(ArcSech(x)) == 1/x ", // " Cosh(ArcCsch(x)) == Sqrt(1 + 1/x^2) ", // " Tanh(ArcSinh(x)) == x/Sqrt(1 + x^2) ", // " Tanh(ArcCosh(x)) == (Sqrt(-1 + x)*Sqrt(1 + x))/x ", // " Tanh(ArcTanh(x)) == x ", // " Tanh(ArcCoth(x)) == 1/x ", // " Tanh(ArcSech(x)) == Sqrt(-1 + 1/x)*Sqrt(1 + 1/x)*x ", // " Tanh(ArcCsch(x)) == 1/(Sqrt(1 + 1/x^2)*x) ", // " Coth(ArcSinh(x)) == Sqrt(1 + x^2)/x ", // " Coth(ArcCosh(x)) == x/(Sqrt(-1 + x)*Sqrt(1 + x)) ", // " Coth(ArcTanh(x)) == 1/x ", // " Coth(ArcCoth(x)) == x ", // " Coth(ArcSech(x)) == 1/(Sqrt(-1 + 1/x)*Sqrt(1 + 1/x)*x) ", // " Coth(ArcCsch(x)) == Sqrt(1 + 1/x^2)*x ", // " Sech(ArcSinh(x)) == 1/Sqrt(1 + x^2) ", // " Sech(ArcCosh(x)) == 1/x ", // " Sech(ArcTanh(x)) == Sqrt(1 - x^2) ", // " Sech(ArcCoth(x)) == (Sqrt(-1 + x)*Sqrt(1 + x))/x ", // " Sech(ArcSech(x)) == x ", // " Sech(ArcCsch(x)) == 1/Sqrt(1 + 1/x^2) ", // " Csch(ArcSinh(x)) == 1/x ", // " Csch(ArcCosh(x)) == 1/(Sqrt(-1 + x)*Sqrt(1 + x)) ", // " Csch(ArcTanh(x)) == (Sqrt(1 - x)*Sqrt(1 + x))/x ", // " Csch(ArcCoth(x)) == Sqrt(-1 + x)*Sqrt(1 + x) ", // " Csch(ArcSech(x)) == x/((1 + x)*Sqrt((1 - x)/(1 + x))) ", // " Csch(ArcCsch(x)) == x "); check( "Outer((ToString(#1) <> \"(\" <> ToString(#2) <> \"(x)) == \" <> ToString(InputForm(#1(#2(x)))))&," // + "{Sinh,Cosh,Tanh,Coth,Sech,Csch}," // + "{ArcSinh, ArcCosh, ArcTanh, ArcCoth, ArcSech, ArcCsch}) //" // + "Flatten // TableForm ", // expected); expected = String.join("\n", // " Sin(ArcSin(x)) == x ", // " Sin(ArcCos(x)) == Sqrt(1 - x^2) ", // " Sin(ArcTan(x)) == x/Sqrt(1 + x^2) ", // " Sin(ArcCot(x)) == 1/Sqrt(1 + x^2) ", // " Sin(ArcSec(x)) == Sqrt(1 - 1/x^2) ", // " Sin(ArcCsc(x)) == 1/x ", // " Cos(ArcSin(x)) == Sqrt(1 - x^2) ", // " Cos(ArcCos(x)) == x ", // " Cos(ArcTan(x)) == 1/Sqrt(1 + x^2) ", // " Cos(ArcCot(x)) == 1/Sqrt(1 + 1/x^2) ", // " Cos(ArcSec(x)) == 1/x ", // " Cos(ArcCsc(x)) == Sqrt(1 - 1/x^2) ", // " Tan(ArcSin(x)) == x/Sqrt(1 - x^2) ", // " Tan(ArcCos(x)) == Sqrt(1 - x^2)/x ", // " Tan(ArcTan(x)) == x ", // " Tan(ArcCot(x)) == 1/x ", // " Tan(ArcSec(x)) == Sqrt(1 - 1/x^2)*x ", // " Tan(ArcCsc(x)) == 1/(Sqrt(1 - 1/x^2)*x) ", // " Cot(ArcSin(x)) == Sqrt(1 - x^2)/x ", // " Cot(ArcCos(x)) == x/Sqrt(1 - x^2) ", // " Cot(ArcTan(x)) == 1/x ", // " Cot(ArcCot(x)) == x ", // " Cot(ArcSec(x)) == 1/(Sqrt(1 - 1/x^2)*x) ", // " Cot(ArcCsc(x)) == Sqrt(1 - 1/x^2)*x ", // " Sec(ArcSin(x)) == 1/Sqrt(1 - x^2) ", // " Sec(ArcCos(x)) == 1/x ", // " Sec(ArcTan(x)) == Sqrt(1 + x^2) ", // " Sec(ArcCot(x)) == Sqrt(1 + x^2)/x ", // " Sec(ArcSec(x)) == x ", // " Sec(ArcCsc(x)) == 1/Sqrt(1 - 1/x^2) ", // " Csc(ArcSin(x)) == 1/x ", // " Csc(ArcCos(x)) == 1/Sqrt(1 - x^2) ", // " Csc(ArcTan(x)) == Sqrt(1 + x^2)/x ", // " Csc(ArcCot(x)) == Sqrt(1 + x^2) ", // " Csc(ArcSec(x)) == 1/Sqrt(1 - 1/x^2) ", // " Csc(ArcCsc(x)) == x "); check( "Outer((ToString(#1) <> \"(\" <> ToString(#2) <> \"(x)) == \" <> ToString(InputForm(#1(#2(x)))))&," // + "{Sin,Cos,Tan,Cot,Sec,Csc}," // + "{ArcSin, ArcCos, ArcTan, ArcCot, ArcSec, ArcCsc}) //" // + "Flatten // TableForm ", // expected); check("ToString(InputForm(a+\"b\"))", // "\"b\" + a"); check("ToString(InputForm(d/2+f(x)))", // "d/2 + f(x)"); check("ToString(FullForm(d/2))", // "Times(Rational(1,2), d)"); } @Test public void testTotal() { check("Total({x^2, 3*x^3, 1})", // "1+x^2+3*x^3"); check("Total(f(1,2,1))", // "4"); check("Total(Derivative(1, 2, 1))", // "4"); check("Total( {{1, 2, 3}, {4, 5}, {6}})", // "Total({{1,2,3},{4,5},{6}})"); check("Total( {{1, 2, 3}, {4, 5}, {6}}, Infinity)", // "21"); check("Total( {{1, 2, 3}, {4, 5}, {6}}, {-1})", // "{6,9,6}"); check("Total({1, 2, 3})", // "6"); check("Total({{1, 2, 3}, {4, 5, 6}, {7, 8 ,9}})", // "{12,15,18}"); check("Total({{1, 2, 3}, {4, 5, 6}, {7, 8 ,9}}, 2)", // "45"); check("Total({{1, 2, 3}, {4, 5, 6}, {7, 8 ,9}}, {2})", // "{6,15,24}"); check("Total({x^2, 3*x^3, 1},{1})", // "1+x^2+3*x^3"); check("Total({x^2, 3*x^3, 1})", // "1+x^2+3*x^3"); check("Total({{1,2,3},{4,5,6},{7,8,9}})", // "{12,15,18}"); check("Total({{1,2,3},{4,5,6},{7,8,9}},{1})", // "{12,15,18}"); // total the rows check("Total({{1,2,3},{4,5,6},{7,8,9}},{2})", // "{6,15,24}"); check("Total({{1,2,3},{4,5,6},{7,8,9}},2)", // "45"); } @Test public void testTreeForm() { check("TreeForm(a+b)", // "JSFormData(var nodes = new vis.DataSet([\n" + // " {id: 1, label: 'Plus', level: 0}\n" + // ", {id: 2, label: 'a', level: 1}\n" + // ", {id: 3, label: 'b', level: 1}\n" + // "]);\n" + // "var edges = new vis.DataSet([\n" + // " {from: 1, to: 2 , arrows: { to: { enabled: true, type: 'arrow'}}}\n" + // ", {from: 1, to: 3 , arrows: { to: { enabled: true, type: 'arrow'}}}\n" + // "]);\n" + // ",treeform)"); } @Test public void testTrace() { check("Trace(u = 2; Do(u = u*u, {3}); u, Times)", // "{{{{u*u,2*2}},{{u*u,4*4}},{{u*u,16*16}}}}"); check("x=5;Trace(Mod((3 + x)^2, x - 1))", // "{{{{x,5},3+5,8},8^2,64},{{x,5},-1+5,4},Mod(64,4),0}"); check("Trace(u = 2; Do(u = u*u, {3}); u)", // "{{u=2,2},{{{{u,2},{u,2},2*2,4},4},{{{u,4},{u,4},4*4,16},16},{{{u,16},{u,16},16*\n" + "16,256},256},Null},{u,256},256}"); } @Test public void testTrigExpand() { // issue #930 check("TrigExpand(Sinh(a+b))", // "Cosh(b)*Sinh(a)+Cosh(a)*Sinh(b)"); check("TrigExpand(Sinh(a+b+c))", // "Cosh(b)*Cosh(c)*Sinh(a)+Cosh(a)*Cosh(c)*Sinh(b)+Cosh(a)*Cosh(b)*Sinh(c)+Sinh(a)*Sinh(b)*Sinh(c)"); check("TrigExpand(Sinh(a+b+c+d))", // "Cosh(b)*Cosh(c)*Cosh(d)*Sinh(a)+Cosh(a)*Cosh(c)*Cosh(d)*Sinh(b)+Cosh(a)*Cosh(b)*Cosh(d)*Sinh(c)+Cosh(d)*Sinh(a)*Sinh(b)*Sinh(c)+Cosh(a)*Cosh(b)*Cosh(c)*Sinh(d)+Cosh(c)*Sinh(a)*Sinh(b)*Sinh(d)+Cosh(b)*Sinh(a)*Sinh(c)*Sinh(d)+Cosh(a)*Sinh(b)*Sinh(c)*Sinh(d)"); // issue #930 check("TrigExpand(Cosh(a+b))", // "Cosh(a)*Cosh(b)+Sinh(a)*Sinh(b)"); check("TrigExpand(Cosh(a+b+c))", // "Cosh(a)*Cosh(b)*Cosh(c)+Cosh(c)*Sinh(a)*Sinh(b)+Cosh(b)*Sinh(a)*Sinh(c)+Cosh(a)*Sinh(b)*Sinh(c)"); check("TrigExpand(Cosh(a+b+c+d))", // "Cosh(a)*Cosh(b)*Cosh(c)*Cosh(d)+Cosh(c)*Cosh(d)*Sinh(a)*Sinh(b)+Cosh(b)*Cosh(d)*Sinh(a)*Sinh(c)+Cosh(a)*Cosh(d)*Sinh(b)*Sinh(c)+Cosh(b)*Cosh(c)*Sinh(a)*Sinh(d)+Cosh(a)*Cosh(c)*Sinh(b)*Sinh(d)+Cosh(a)*Cosh(b)*Sinh(c)*Sinh(d)+Sinh(a)*Sinh(b)*Sinh(c)*Sinh(d)"); // issue #930 check("TrigExpand(Sin(a+b))", // "Cos(b)*Sin(a)+Cos(a)*Sin(b)"); check("TrigExpand(Sin(a+b+c))", // "Cos(b)*Cos(c)*Sin(a)+Cos(a)*Cos(c)*Sin(b)+Cos(a)*Cos(b)*Sin(c)-Sin(a)*Sin(b)*Sin(c)"); check("TrigExpand(Sin(a+b+c+d))", // "Cos(b)*Cos(c)*Cos(d)*Sin(a)+Cos(a)*Cos(c)*Cos(d)*Sin(b)+Cos(a)*Cos(b)*Cos(d)*Sin(c)-Cos(d)*Sin(a)*Sin(b)*Sin(c)+Cos(a)*Cos(b)*Cos(c)*Sin(d)-Cos(c)*Sin(a)*Sin(b)*Sin(d)-Cos(b)*Sin(a)*Sin(c)*Sin(d)-Cos(a)*Sin(b)*Sin(c)*Sin(d)"); // issue #930 check("TrigExpand(Cos(a+b))", // "Cos(a)*Cos(b)-Sin(a)*Sin(b)"); check("TrigExpand(Cos(a+b+c))", // "Cos(a)*Cos(b)*Cos(c)-Cos(c)*Sin(a)*Sin(b)-Cos(b)*Sin(a)*Sin(c)-Cos(a)*Sin(b)*Sin(c)"); check("TrigExpand(Cos(a+b+c+d))", // "Cos(a)*Cos(b)*Cos(c)*Cos(d)-Cos(c)*Cos(d)*Sin(a)*Sin(b)-Cos(b)*Cos(d)*Sin(a)*Sin(c)-Cos(a)*Cos(d)*Sin(b)*Sin(c)-Cos(b)*Cos(c)*Sin(a)*Sin(d)-Cos(a)*Cos(c)*Sin(b)*Sin(d)-Cos(a)*Cos(b)*Sin(c)*Sin(d)+Sin(a)*Sin(b)*Sin(c)*Sin(d)"); check("TrigExpand( Csch(2*x) )", // "1/2*Csch(x)*Sech(x)"); check("TrigExpand( Csch(3*x) )", // "Csch(x)/(-1+4*Cosh(x)^2)"); check("TrigExpand( Csch(4*x) )", // "Csch(x)/(-4*Cosh(x)+8*Cosh(x)^3)"); check("TrigExpand(Cosh(x)*Csch(2*x)*Sinh(x))", // "1/2"); check("TrigExpand(Cos(x)*Csc(2*x)*Sin(x))", // "1/2"); check("TrigExpand(Cot(2*x))", // "Cot(x)/2-Tan(x)/2"); check("TrigExpand(Cosh(2*a))", // "Cosh(a)^2+Sinh(a)^2"); check("TrigExpand(Cosh(3*a))", // "Cosh(a)^3+3*Cosh(a)*Sinh(a)^2"); check("TrigExpand(Sinh(2*a))", // "2*Cosh(a)*Sinh(a)"); check("TrigExpand(Sinh(3*a))", // "3*Cosh(a)^2*Sinh(a)+Sinh(a)^3"); check("TrigExpand(Sinh(4*a))", // "4*Cosh(a)^3*Sinh(a)+4*Cosh(a)*Sinh(a)^3"); check("TrigExpand(Sinh(a+b))", // "Cosh(b)*Sinh(a)+Cosh(a)*Sinh(b)"); check("TrigExpand(Sinh(a+b+c))", // "Cosh(b)*Cosh(c)*Sinh(a)+Cosh(a)*Cosh(c)*Sinh(b)+Cosh(a)*Cosh(b)*Sinh(c)+Sinh(a)*Sinh(b)*Sinh(c)"); check("TrigExpand(Coth(a+b))", // "(Cosh(a)*Cosh(b))/(Cosh(b)*Sinh(a)+Cosh(a)*Sinh(b))+" // + "(Sinh(a)*Sinh(b))/(Cosh(b)*Sinh(a)+Cosh(a)*Sinh(b))"); check("TrigExpand(Tanh(a+b))", // "(Cosh(b)*Sinh(a))/(Cosh(a)*Cosh(b)+Sinh(a)*Sinh(b))+" // + "(Cosh(a)*Sinh(b))/(Cosh(a)*Cosh(b)+Sinh(a)*Sinh(b))"); check("TrigExpand(Tanh(a+b+c))", // "(Cosh(b)*Cosh(c)*Sinh(a))/(Cosh(a)*Cosh(b)*Cosh(c)+Cosh(c)*Sinh(a)*Sinh(b)+Cosh(b)*Sinh(a)*Sinh(c)+Cosh(a)*Sinh(b)*Sinh(c))+"// + "(Cosh(a)*Cosh(c)*Sinh(b))/(Cosh(a)*Cosh(b)*Cosh(c)+Cosh(c)*Sinh(a)*Sinh(b)+Cosh(b)*Sinh(a)*Sinh(c)+Cosh(a)*Sinh(b)*Sinh(c))+"// + "(Cosh(a)*Cosh(b)*Sinh(c))/(Cosh(a)*Cosh(b)*Cosh(c)+Cosh(c)*Sinh(a)*Sinh(b)+Cosh(b)*Sinh(a)*Sinh(c)+Cosh(a)*Sinh(b)*Sinh(c))+"// + "(Sinh(a)*Sinh(b)*Sinh(c))/(Cosh(a)*Cosh(b)*Cosh(c)+Cosh(c)*Sinh(a)*Sinh(b)+Cosh(b)*Sinh(a)*Sinh(c)+Cosh(a)*Sinh(b)*Sinh(c))"); check("TrigExpand(Csc(a+b+c))", // "1/(Cos(b)*Cos(c)*Sin(a)+Cos(a)*Cos(c)*Sin(b)+Cos(a)*Cos(b)*Sin(c)-Sin(a)*Sin(b)*Sin(c))"); check("TrigExpand(Sec(a+b+c))", // "1/(Cos(a)*Cos(b)*Cos(c)-Cos(c)*Sin(a)*Sin(b)-Cos(b)*Sin(a)*Sin(c)-Cos(a)*Sin(b)*Sin(c))"); check("TrigExpand(Cot(a+b+c))", // "(Cos(a)*Cos(b)*Cos(c))/(Cos(b)*Cos(c)*Sin(a)+Cos(a)*Cos(c)*Sin(b)+Cos(a)*Cos(b)*Sin(c)-Sin(a)*Sin(b)*Sin(c))+(-Cos(c)*Sin(a)*Sin(b))/(Cos(b)*Cos(c)*Sin(a)+Cos(a)*Cos(c)*Sin(b)+Cos(a)*Cos(b)*Sin(c)-Sin(a)*Sin(b)*Sin(c))+(-Cos(b)*Sin(a)*Sin(c))/(Cos(b)*Cos(c)*Sin(a)+Cos(a)*Cos(c)*Sin(b)+Cos(a)*Cos(b)*Sin(c)-Sin(a)*Sin(b)*Sin(c))+(-Cos(a)*Sin(b)*Sin(c))/(Cos(b)*Cos(c)*Sin(a)+Cos(a)*Cos(c)*Sin(b)+Cos(a)*Cos(b)*Sin(c)-Sin(a)*Sin(b)*Sin(c))"); check("TrigExpand(Tan(a+b+c))", // "(Cos(b)*Cos(c)*Sin(a))/(Cos(a)*Cos(b)*Cos(c)-Cos(c)*Sin(a)*Sin(b)-Cos(b)*Sin(a)*Sin(c)-Cos(a)*Sin(b)*Sin(c))+(Cos(a)*Cos(c)*Sin(b))/(Cos(a)*Cos(b)*Cos(c)-Cos(c)*Sin(a)*Sin(b)-Cos(b)*Sin(a)*Sin(c)-Cos(a)*Sin(b)*Sin(c))+(Cos(a)*Cos(b)*Sin(c))/(Cos(a)*Cos(b)*Cos(c)-Cos(c)*Sin(a)*Sin(b)-Cos(b)*Sin(a)*Sin(c)-Cos(a)*Sin(b)*Sin(c))+(-Sin(a)*Sin(b)*Sin(c))/(Cos(a)*Cos(b)*Cos(c)-Cos(c)*Sin(a)*Sin(b)-Cos(b)*Sin(a)*Sin(c)-Cos(a)*Sin(b)*Sin(c))"); check("TrigExpand(Csc(2*x))", // "1/2*Csc(x)*Sec(x)"); check("TrigExpand(Sec(2*x))", // "1/(Cos(x)^2-Sin(x)^2)"); check("TrigExpand(Cot(2*x))", // "Cot(x)/2-Tan(x)/2"); check("TrigExpand(Tan(2*x))", // "(2*Cos(x)*Sin(x))/(Cos(x)^2-Sin(x)^2)"); check("TrigExpand(Sin(2*x+3*y))", // "2*Cos(x)*Cos(y)^3*Sin(x)+3*Cos(x)^2*Cos(y)^2*Sin(y)-3*Cos(y)^2*Sin(x)^2*Sin(y)-6*Cos(x)*Cos(y)*Sin(x)*Sin(y)^\n" + "2-Cos(x)^2*Sin(y)^3+Sin(x)^2*Sin(y)^3"); check("trigexpand(Sin(2*x))", // "2*Cos(x)*Sin(x)"); check("trigexpand(Sin(x)*Tan(x))", // "Sin(x)*Tan(x)"); check("trigexpand(Sin(x + y))", // "Cos(y)*Sin(x)+Cos(x)*Sin(y)"); check("trigexpand(Cos(x + y))", // "Cos(x)*Cos(y)-Sin(x)*Sin(y)"); check("trigexpand(Sin(x + y + z))", // "Cos(y)*Cos(z)*Sin(x)+Cos(x)*Cos(z)*Sin(y)+Cos(x)*Cos(y)*Sin(z)-Sin(x)*Sin(y)*Sin(z)"); check("trigexpand(Cos(2*x))", // "Cos(x)^2-Sin(x)^2"); check("trigexpand(Sin(5*x))", // "5*Cos(x)^4*Sin(x)-10*Cos(x)^2*Sin(x)^3+Sin(x)^5"); } @Test public void testTrigReduce() { // check("TrigReduce(Tan(x)^2)", // // "(1-Cos(2*x))/(1+Cos(2*x))"); // check("TrigReduce(Tan(x)^3)", // // ""); check("TrigReduce(cos(x)^2)", // "1/2+Cos(2*x)/2"); check("TrigReduce(cos(x)^2*sin(x))", // "Sin(x)/4+Sin(3*x)/4"); check("TrigReduce(cos(x)^2+sin(x))", // "1/2+Cos(2*x)/2+Sin(x)"); check("TrigReduce(Sin(x)*Cos(y))", // "1/2*(Sin(x-y)+Sin(x+y))"); check("TrigReduce(-I*Cos(x)^2-2*Cos(x)*Sin(x)+I*Sin(x)^2)", // "-I*Cos(2*x)-Sin(2*x)"); check("TrigReduce(I*Cos(x)^4+I*2*Cos(x)^2*Sin(x)^2+I*Sin(x)^4)", // "I"); check("TrigReduce(Cos(a*x)*Sin(a*x)^2)", // "Cos(a*x)/4-Cos(3*a*x)/4"); check("TrigReduce(-a*Cos(x)^2+a*Sin(x)^2 )", // "-a*Cos(2*x)"); check("TrigReduce(Sin(x)*Tan(y))", // "1/2*(Cos(x-y)-Cos(x+y))*Sec(y)"); check("TrigReduce(Sin(x)*Tan(y))", // "1/2*(Cos(x-y)-Cos(x+y))*Sec(y)"); check("TrigReduce(Cos(x)*Tan(y))", // "1/2*Sec(y)*(-Sin(x-y)+Sin(x+y))"); check("TrigReduce(2*Cos(x)^2)", // "1+Cos(2*x)"); check("TrigReduce(2*Cos(x)*Sin(y))", // "-Sin(x-y)+Sin(x+y)"); check("TrigReduce(15*Sin(12*x)^2 + 12*Sin(15*x)^2)", // "27/2-15/2*Cos(24*x)-6*Cos(30*x)"); check("TrigReduce(2*Sinh(u)*Cosh(v))", // "Sinh(u-v)+Sinh(u+v)"); check("TrigReduce(3*Sinh(u)*Cosh(v)*k)", // "3/2*k*Sinh(u-v)+3/2*k*Sinh(u+v)"); // check("TrigReduce(2 Tan(x)*Tan(y))", // "(2*Cos(-y+x)-2*Cos(y+x))*(Cos(-y+x)+Cos(y+x))^(-1)"); } @Test public void testTrigToExp() { check("TrigToExp(Cos(Sin(x)))", // "1/(2*E^(I*((I*1/2)/E^(I*x)-I*1/2*E^(I*x))))+E^(I*((I*1/2)/E^(I*x)-I*1/2*E^(I*x)))/\n" // + "2"); String expected = String.join("\n", // " ArcSinh(x)==Log(x+Sqrt(1+x^2)) ", // " ArcCosh(x)==Log(x+Sqrt(-1+x)*Sqrt(1+x)) ", // " ArcTanh(x)==-Log(1-x)/2+Log(1+x)/2 ", // " ArcCoth(x)==-Log(1-1/x)/2+Log(1+1/x)/2 ", // " ArcSech(x)==Log(Sqrt(-1+1/x)*Sqrt(1+1/x)+1/x) ", // " ArcCsch(x)==Log(Sqrt(1+1/x^2)+1/x) "); check("Map(# == TrigToExp(#)&," // + "{ArcSinh(x), ArcCosh(x), ArcTanh(x)," // + "ArcCoth(x), ArcSech(x), ArcCsch(x)}) // TableForm", // expected); expected = String.join("\n", // " ArcSin(x)==-I*Log(I*x+Sqrt(1-x^2)) ", // " ArcCos(x)==Pi/2+I*Log(I*x+Sqrt(1-x^2)) ", // " ArcTan(x)==I*1/2*Log(1-I*x)-I*1/2*Log(1+I*x) ", // " ArcCot(x)==I*1/2*Log(1-I/x)-I*1/2*Log(1+I/x) ", // " ArcSec(x)==Pi/2+I*Log(Sqrt(1-1/x^2)+I/x) ", // " ArcCsc(x)==-I*Log(Sqrt(1-1/x^2)+I/x) "); check("Map(# == TrigToExp(#)&," // + "{ArcSin(x), ArcCos(x), ArcTan(x)," // + "ArcCot(x), ArcSec(x), ArcCsc(x)}) // TableForm", // expected); check("I*y+x", // "x+I*y"); check("TrigToExp(ArcTan(x, y))", // "-I*Log((x+I*y)/Sqrt(x^2+y^2))"); check("TrigToExp(Sin(x) < x < Tan(x))", // "(I*1/2)/E^(I*x)-I*1/2*E^(I*x) Unevaluated(##&[])", // "{{{1},{2},{1,2},{1,2,3}},{{2},{3}}}"); check("SetAttributes(symbolLength, HoldAll); " // + "symbolLength(s_Symbol) := StringLength(SymbolName(Unevaluated(s)))", // ""); check("testSymbol = 42", // "42"); check("symbolLength(testSymbol)", // "10"); check("Sqrt(Unevaluated(x))", // "Sqrt(x)"); check("Length(Unevaluated(5 + 6 + 7 + 8))", // "4"); check("Attributes(Unevaluated)", // "{HoldAllComplete,Protected}"); check("f(Unevaluated(x))", // "f(Unevaluated(x))"); check("Attributes(f) = {Flat};", // ""); check("f(Unevaluated(f(b, c)))", // "f(Unevaluated(b),Unevaluated(c))"); check("f(a, Unevaluated(f(b, c)))", // "f(a,Unevaluated(b),Unevaluated(c))"); check("g(a, Sequence(Unevaluated(b),Unevaluated(c)))", // "g(a,Unevaluated(b),Unevaluated(c))"); check("g(Unevaluated( Sequence(a,b,c)))", // "g(Unevaluated(Sequence(a,b,c)))"); check("Length(Unevaluated(5 + 6 + 7 + 8))", // "4"); check("f(x_) := x^2", // ""); check("ReplaceAll(Unevaluated(f(3)), 3 -> 1)", // "1"); check("F(x___Real):=List(x)^2; a=0.4;", // ""); check("F(Unevaluated(a), a, Unevaluated(a))", // "F(Unevaluated(a),0.4,Unevaluated(a))"); } @Test public void testIntersection() { check( "Intersection({1.1, 3.4, .5, 7.6, 7.1, 1.9}, {1.2, 3.3, 7.7, 1.3}, SameTest -> (Floor[#1] == Floor[#2] &))", // "{1.9,3.4,7.6}"); check("Intersection({2, -2, 1, 3, 1}, {2, 1, -2, -1}, SameTest -> (Abs(#1) == Abs(#2) &))", // "{1,2}"); check( "Intersection({{1, 2}, {3}, {4, 5, 6}, {9, 6}}, {{2, 1}, {8, 4, 3}}, SameTest->(Total(#1) == Total(#2) &))", // "{{1,2},{4,5,6}}"); check("Intersection(#1, #2, #1)", // "Slot()"); check("Intersection(#1, #1)", // "#1"); check("Intersection(#1,#1*#2)", // "#1⋂#1*#2"); check("Intersection({},{})", "{}"); check("Intersection({1},{2})", "{}"); check("Intersection({1,2,2,4},{2,3,4,5})", "{2,4}"); check("Intersection({2,3,4,5},{1,2,2,4})", "{2,4}"); } @Test public void testUnion() { // check("Union({},{})", "{}"); check("Union({1},{2})", "{1,2}"); check("Union({1,2,2,4},{2,3,4,5})", "{1,2,3,4,5}"); check("Union(#1,#1*#2)", // "Union(#1,#1*#2)"); check("Union(#1, #2)", // "Slot(1,2)"); // http://oeis.org/A001597 - Perfect powers: m^k where m > 0 and k >= 2. check("$min = 0; $max = 10^4; " // + "Union@ Flatten@ Table( n^expo, {expo, Prime@ Range@ PrimePi@ Log2@ $max}, {n, Floor(1 + $min^(1/expo)), $max^(1/expo)})", // "{1,4,8,9,16,25,27,32,36,49,64,81,100,121,125,128,144,169,196,216,225,243,256,289,\n" + "324,343,361,400,441,484,512,529,576,625,676,729,784,841,900,961,1000,1024,1089,\n" + "1156,1225,1296,1331,1369,1444,1521,1600,1681,1728,1764,1849,1936,2025,2048,2116,\n" + "2187,2197,2209,2304,2401,2500,2601,2704,2744,2809,2916,3025,3125,3136,3249,3364,\n" + "3375,3481,3600,3721,3844,3969,4096,4225,4356,4489,4624,4761,4900,4913,5041,5184,\n" + "5329,5476,5625,5776,5832,5929,6084,6241,6400,6561,6724,6859,6889,7056,7225,7396,\n" + "7569,7744,7776,7921,8000,8100,8192,8281,8464,8649,8836,9025,9216,9261,9409,9604,\n" + "9801,10000}"); check("Union({a,a,b,c})", // "{a,b,c}"); check("Union({9, 0, 0, 3, 2, 3, 6, 2, 9, 8, 4, 9, 0, 2, 6, 5, 7, 4, 9, 8})", // "{0,2,3,4,5,6,7,8,9}"); check("Union({a,a,b,c},{},{})", // "{a,b,c}"); check("Union({a,a,b,c},{},{z,z,z,x,x,x,y,y,y})", // "{a,b,c,x,y,z}"); check("Union({2, -2, 1, 3, 1}, SameTest->(Abs(#1)==Abs(#2) &))", // "{-2,1,3}"); check("Union({1.1, 3.4, .5, 7.6, 7.1, 1.9}, SameTest->(Floor(#1)==Floor(#2) &))", // "{0.5,1.1,3.4,7.1}"); check("Union({{1, 2}, {3}, {4, 5, 6}, {9, 6}}, SameTest->(Total(#1)==Total(#2)&))", // "{{3},{9,6}}"); } @Test public void testUnique() { EvalEngine.resetModuleCounter4JUnit(); check("Unique()", // "$1"); check("Unique(x)", // "x$2"); check("Unique(\"x\")", // "x3"); } @Test public void testUnitConvert() { check("UnitConvert(Quantity(\"StandardAccelerationOfGravity\"),\"m/s^2\")", // "196133/20000[m*s^-2]"); check("UnitConvert(Quantity(111, \"cm\"),\"m\" )", // "111/100[m]"); check("UnitConvert(Quantity(Pi, \"deg\"), \"rad\")", // "Pi^2/180[rad]"); check("UnitConvert(Quantity(Pi, \"rad\"), \"deg\")", // "180[deg]"); check("UnitConvert(Quantity(Pi, \"grad\"), \"rad\")", // "Pi^2/180[rad]"); check("UnitConvert(Quantity(Pi, \"rad\"), \"grad\")", // "180[grad]"); check("UnitConvert(Quantity(200, \"g\")*Quantity(981, \"cm*s^-2\") )", // "981/500[kg*m*s^-2]"); check("UnitConvert(Quantity(10^(-6), \"MOhm\") )", // "1[A^-2*kg*m^2*s^-3]"); check("UnitConvert(Quantity(10^(-6), \"MOhm\"),\"Ohm\" )", // "1[Ohm]"); check("UnitConvert(Quantity(1, \"nmi\"),\"km\" )", // "463/250[km]"); check("UnitConvert(Quantity(360, \"mV^-1*mA*s^2\"),\"Ohm^-1*s^2\" )", // "360[Ohm^-1*s^2]"); check("UnitConvert(Quantity(360, \"km*h^-1\"),\"m*s^-1\" )", // "100[m*s^-1]"); check("UnitConvert(Quantity(2, \"km^2\") )", // "2000000[m^2]"); check("UnitConvert(Quantity(2, \"km^2\"),\"cm^2\" )", // "20000000000[cm^2]"); check("UnitConvert(Quantity(3, \"Hz^-2*N*m^-1\") )", // "3[kg]"); check("UnitConvert(Quantity(3.8, \"lb\") )", // "1.72365[kg]"); check("UnitConvert(Quantity(8.2, \"nmi\"), \"km\")", // "15.1864[km]"); } @Test public void testUnitize() { // Unitize uses PossibleZeroQ // checkNumeric( // "N((E + Pi)^2 )", // // "34.33812894536713"); // checkNumeric( // "N((E + Pi)*(E + Pi) )", // // "34.33812894536713"); // checkNumeric( // "N(-E^2 - Pi^2 - 2*E*Pi)", // // "-34.33812894536714"); // check( // "N((E + Pi)^2 - E^2 - Pi^2 - 2*E*Pi)", // // "-7.10543*10^-15"); check("Unitize(I,2)", // "0"); check("Unitize(-I,1)", // "1"); check("Unitize(I)", // "1"); check("Unitize(-I)", // "1"); check("Unitize(Infinity)", // "1"); check("Unitize(-Infinity)", // "1"); check("Unitize((E + Pi)^2 - E^2 - Pi^2 - 2*E*Pi)", // "0"); check("Unitize(2^(2*I) - 2^(-2*I) - 2*I*Sin(Log(4)))", // "0"); check("Unitize(Sqrt(2) + Sqrt(3) - Sqrt(5 + 2*Sqrt(6)))", // "0"); check("Unitize({0, -1})", // "{0,1}"); check("Unitize(0)", // "0"); check("Unitize(0.0)", // "0"); check("Unitize(x)", // "Unitize(x)"); check("Unitize(3/4)", // "1"); check("Unitize(3*I)", // "1"); check("Unitize(Pi)", // "1"); check("Unitize(x)", // "Unitize(x)"); check("Unitize(x,dx)", // "Unitize(x,dx)"); } @Test public void testUnitStep() { check("UnitStep(-Infinity)", // "0"); check("UnitStep(Infinity)", // "1"); check("UnitStep(0)", // "1"); check("UnitStep(1)", // "1"); check("UnitStep(-1)", // "0"); check("UnitStep(Interval({0,42}))", // "Interval({1,1})"); check("UnitStep(Interval({-3,-1}))", // "Interval({0,0})"); check("UnitStep(Interval({-1,2}))", // "Interval({0,1})"); check("UnitStep(42)", // "1"); check("UnitStep(-1)", // "0"); check("UnitStep(-42)", // "0"); check("UnitStep({1.6, 1.6000000000000000000000000})", // "{1,1}"); check("UnitStep({-1, 0, 1})", // "{0,1,1}"); check("UnitStep(1, 2, 3)", // "1"); } @Test public void testUnset() { check("Indeterminate=.", // "$Failed"); check("0=.", // "$Failed"); check("a=.", // ""); check("$x=5;$x=.;$x", // "$x"); check("$f(x_):=x^2;$f(x_)=.;$f(3)", // "$f(3)"); } @Test public void testUpperCaseQ() { // print message: UpperCaseQ: String expected at position 1 in UpperCaseQ(abc). check("UpperCaseQ(abc)", // "UpperCaseQ(abc)"); check("UpperCaseQ(\"ABCDEFGHIJKLMNOPQRSTUVWXYZ\")", // "True"); check("UpperCaseQ(\"ABCDEFGHIJKLMNopqRSTUVWXYZ\")", // "False"); } @Test public void testUpValues() { check("u /: v(x_u) := {x}", // ""); check("UpValues(u)", // "{HoldPattern(v(x_u)):>{x}}"); } @Test public void testUpSet() { check("Part(f(x_), s1 : (_String | {_String ..}), s2 : (_String | {_String ..})) ^:= {x,s1,s2}", // ""); check("f(y)[[{\"a\",\"b\"},{\"X\",\"Y\"}]]", // "{y,{a,b},{X,Y}}"); check("ParameterRanges[Cartesian]^=Null;Null", // ""); check("ParameterRanges[Cartesian]^=Null;Null", // ""); check("$f($abc(0))^=100;$f($abc(0))", // "100"); } @Test public void testUpSetDelayed() { check("$f($h(0)) ^= h0;$f($h(x_)) ^:= 2*$f($h(x - 1));$f($h(10))", // "1024*h0"); check("a*b_ ^:= c", // ""); check("2*a", // "c"); check("2*a*d", // "c"); } @Test public void testValueQ() { check("ValueQ(x)", // "False"); check("x=1; ValueQ(x)", // "True"); check("ValueQ(True)", // "False"); } @Test public void testVariables() { check("Variables(FactorInteger(1232))", // "{}"); check("Variables({x+y,x,z})", // "{x,y,z}"); check("Variables(x + f(x)+Pi*E)", // "{x,f(x)}"); check("Variables(x^0.3 + f(x)+Pi*E)", // "{x^0.3,f(x)}"); check("Variables(Sin(x) + Cos(x))", // "{Cos(x),Sin(x)}"); check("Variables({a + b*x, c*y^2 + x/2})", // "{a,b,c,x,y}"); check("Variables((x + y)^2 + 3*z^2 - y*z + 7)", // "{x,y,z}"); check("Variables((a - b)/(x + y) - 2/z)", // "{a,b,x,y,z}"); check("Variables(Sqrt(x + y - z^2) + (-2*t)^(2/3))", // "{t,x,y,z}"); check("Variables(y + x*z)", "{x,y,z}"); check("Variables(a*x^2 + b*x + c)", // "{a,b,c,x}"); check("Variables({a + b*x, c*y^2 + x/2})", // "{a,b,c,x,y}"); check("Variables(x + Sin(y))", // "{x,Sin(y)}"); check("Variables(x + Sin(10))", // "{x}"); check("Variables(E^x)", // "{}"); check("Variables(a^x)", // "{a^x}"); } @Test public void testVariance() { check("Variance(BinomialDistribution(n, m))", // "(1-m)*m*n"); check("Variance(BernoulliDistribution(n))", // "(1-n)*n"); check("Variance(BetaDistribution(a,b))", // "(a*b)/((a+b)^2*(1+a+b))"); check("Variance(DiscreteUniformDistribution({l, r}))", // "1/12*(-1+(1-l+r)^2)"); check("Variance(ErlangDistribution(n, m))", // "n/m^2"); check("Variance(ExponentialDistribution(n))", // "1/n^2"); check("Variance(LogNormalDistribution(m,s))", // "(-1+E^s^2)*E^(2*m+s^2)"); check("Variance(NakagamiDistribution(n, m))", // "m+(-m*Pochhammer(n,1/2)^2)/n"); check("Variance(NormalDistribution(n, m))", // "m^2"); check("Variance(FrechetDistribution(n, m))", // "Piecewise({{m^2*(Gamma(1-2/n)-Gamma(1-1/n)^2),n>2}},Infinity)"); check("Variance(GammaDistribution(n, m))", // "m^2*n"); check("Variance(GeometricDistribution(n))", // "(1-n)/n^2"); check("Variance(GumbelDistribution(n, m))", // "1/6*m^2*Pi^2"); check("Variance(GompertzMakehamDistribution(m,n))", // "(E^n*(6*EulerGamma^2+Pi^2-6*E^n*ExpIntegralEi(-n)^2-12*n*HypergeometricPFQ({1,1,\n" + // "1},{2,2,2},-n)+12*EulerGamma*Log(n)+6*Log(n)^2))/(6*m^2)"); check("Variance(HypergeometricDistribution(n, ns, nt))", // "(n*ns*(1-ns/nt)*(-n+nt))/((-1+nt)*nt)"); check("Variance(PoissonDistribution(n))", // "n"); check("Variance(StudentTDistribution(4))", // "2"); check("Variance(StudentTDistribution(n))", // "Piecewise({{n/(-2+n),n>2}},Indeterminate)"); check("Variance(WeibullDistribution(n, m))", // "m^2*(-Gamma(1+1/n)^2+Gamma(1+2/n))"); check("Variance({1, 2, 3})", // "1"); check("Variance({7, -5, 101, 3})", // "7475/3"); check("Variance({1 + 2*I, 3 - 10*I})", // "74"); check("Variance({a, a})", // "0"); check("Variance({{1, 3, 5}, {4, 10, 100}})", // "{9/2,49/2,9025/2}"); check("Variance({Pi,E,3})//Together", // "1/3*(9-3*E+E^2-3*Pi-E*Pi+Pi^2)"); check("Variance({a,b,c,d})", // "1/12*(-(-3*a+b+c+d)*Conjugate(a)-(a-3*b+c+d)*Conjugate(b)-(a+b-3*c+d)*Conjugate(c)-(a+b+c-\n" + "3*d)*Conjugate(d))"); checkNumeric("Variance({1., 2., 3., 4.})", // "1.6666666666666667"); checkNumeric("Variance({{5.2, 7}, {5.3, 8}, {5.4, 9}})", // "{0.010000000000000018,1.0}"); checkNumeric("Variance({1.21, 3.4, 2, 4.66, 1.5, 5.61, 7.22})", // "5.16122380952381"); check("Variance({1.21, 3.4, 2+3*I, 4.66-0.1*I, 1.5, 5.61, 7.22})", // "6.46265"); // check("Variance(BernoulliDistribution(p))", "p*(1-p)"); // check("Variance(BinomialDistribution(n, p))", "n*p*(1-p)"); } @Test public void testVerbatim() { check("_ /. Verbatim(_)->t", // "t"); check("x /. Verbatim[_]->t", // "x"); } @Test public void testVertexList() { check("VertexList(Graph({1 -> 2, 2 -> 3, 1 -> 3, 4 -> 2}))", // "{1,2,3,4}"); check( "VertexList(Graph({1 \\[UndirectedEdge] 2, 2 \\[UndirectedEdge] 3, 3 \\[UndirectedEdge] 1}))", // "{1,2,3}"); check("VertexList(Graph({1 \\[DirectedEdge] 2, 2 \\[DirectedEdge] 3, 3 \\[DirectedEdge] 1}))", // "{1,2,3}"); } @Test public void testVertexEccentricity() { check("VertexEccentricity({1 -> 2, 2 -> 3, 3 -> 1, 3 -> 4, 4 -> 5, 5 -> 3}, 1)", // "4"); check( "VertexEccentricity(Graph({UndirectedEdge(1, 2), UndirectedEdge(1, 3), UndirectedEdge(1, 4), UndirectedEdge(2, 3), UndirectedEdge(3, 4)}, " + "{EdgeWeight->{1.6,1.4,0.62,1.9,2.1}}), 4)", // "2.22"); check( "VertexEccentricity({UndirectedEdge(1, 2), UndirectedEdge(1, 3), UndirectedEdge(1, 4), UndirectedEdge(2, 3), UndirectedEdge(3, 4)}, 4)", // "2"); } @Test public void testVertexQ() { check("VertexQ(Graph({1 -> 2, 2 -> 3, 1 -> 3, 4 -> 2}),3)", // "True"); check("VertexQ(Graph({1 -> 2, 2 -> 3, 1 -> 3, 4 -> 2}),5)", // "False"); } @Test public void testWeierstrassHalfPeriods() { // TODO improve see discussion: https://github.com/paulmasson/math/issues/7 check("WeierstrassHalfPeriods({1.0, 2.0 } )", // "{1.30836,-0.654182+I*1.22937}"); check("Table(WeierstrassHalfPeriods({1.0,x*I} ), {x,-2.0, 2.0, 1/4})", // "{{1.30139+I*0.299127,0.299127+I*1.30139},{1.32906+I*0.300747,0.300747+I*1.32906}," // + "{1.36146+I*0.301917,0.301917+I*1.36146},{1.40035+I*0.30217,0.30217+I*1.40035}," // + "{1.4486+I*0.300495,0.300495+I*1.4486},{1.5113+I*0.294424,0.294424+I*1.5113}," // + "{1.59835+I*0.276625,0.276625+I*1.59835},{1.72843+I*0.217942,0.217942+I*1.72843}," // + "{1.85407,I*1.85407},{1.72843+I*(-0.217942),-0.217942+I*1.72843},{1.59835+I*(-0.276625),-0.276625+I*1.59835}," // + "{1.5113+I*(-0.294424),-0.294424+I*1.5113},{1.4486+I*(-0.300495),-0.300495+I*1.4486}," // + "{1.40035+I*(-0.30217),-0.30217+I*1.40035},{1.36146+I*(-0.301917),-0.301917+I*1.36146}," // + "{1.32906+I*(-0.300747),-0.300747+I*1.32906},{1.30139+I*(-0.299127),-0.299127+I*1.30139}}"); // check("WeierstrassHalfPeriods({1.0, 2.0*I} )", // "{1.30139+I*(-0.299127),-0.299127+I*1.30139}"); } @Test public void testWeierstrassInvariants() { check("WeierstrassInvariants({1.0, 2.0*I} )", // "{8.12422,4.44305}"); check("Table(WeierstrassInvariants({1.0,x*I} ), {x,-2.0, 2.0, 1/4})", // "{{8.12422,4.44305},{8.15011,4.41322},{8.27476,4.26937},{8.87636,3.56885},{11.81705,-1.97659*10^-15},{27.07395,-22.08742},{129.9875,-284.3553},{2078.061,-18230.79},WeierstrassInvariants({1.0,0.0}),{2078.061,-18230.79},{129.9875,-284.3553},{27.07395,-22.08742},{11.81705,-1.97659*10^-15},{8.87636,3.56885},{8.27476,4.26937},{8.15011,4.41322},{8.12422,4.44305}}"); } @Test public void testWeierstrassP() { check("WeierstrassP(z, {0, 0}) ", // "1/z^2"); check("WeierstrassP(z, {3, 1}) ", // "1+3/2*Cot(Sqrt(3/2)*z)^2"); check("WeierstrassP(5., {1, 2}) ", // "18.35051+I*1.14908*10^-13"); check("WeierstrassP(12., {3, 2}) ", // "77.23116+I*4.34319*10^-13"); check("WeierstrassP(1/3, {1, 2}) // N // Chop", // "9.00644"); check("WeierstrassP(2.0, {1,2} )", // "2.65854+I*2.10942*10^-15"); check("Table(WeierstrassP(x,{1.0,3.0} ), {x,-2.0, 2.0, 1/4})", // "{4.55263+I*2.88658*10^-15,1.98649+I*8.88178*10^-16,1.20805+I*2.22045*10^-16,1.00064,1.16036+I*(-3.33067*10^-16),1.84015+I*(-5.55112*10^-16),4.01922+I*4.44089*10^-16,16.00354+I*2.22045*10^-16,ComplexInfinity,16.00354+I*2.22045*10^-16,4.01922+I*4.44089*10^-16,1.84015+I*(-5.55112*10^-16),1.16036+I*(-3.33067*10^-16),1.00064,1.20805+I*2.22045*10^-16,1.98649+I*8.88178*10^-16,4.55263+I*2.88658*10^-15}"); } @Test public void testWeierstrassPPrime() { check("WeierstrassPPrime(2.0, {1,2} )", // "8.39655+I*1.28374*10^-14"); check("WeierstrassPPrime(5., {1, 2}) ", // "157.1532+I*1.4773*10^-12"); check("WeierstrassPPrime(12., {3, 2}) ", // "1357.348+I*1.16055*10^-11"); check("WeierstrassPPrime(1/3, {1, 2}) // N // Chop", // "-53.95606"); check("Table(WeierstrassPPrime(x,{1.0,3.0} ), {x,-2.0, 2.0, 1/4})", // "{-19.23245+I*(-2.02665*10^-14),-5.13514+I*(-3.76819*10^-15),-1.68643+I*(-1.16607*10^-15),-0.0838866+I*(-5.45142*10^-16),1.44536+I*(-3.30329*10^-16),4.48151+I*2.98579*10^-16,15.89616+I*1.58114*10^-15,127.9683+I*1.1967*10^-15,ComplexInfinity,-127.9683+I*(-1.1967*10^-15),-15.89616+I*(-1.58114*10^-15),-4.48151+I*(-2.98579*10^-16),-1.44536+I*3.30329*10^-16,0.0838866+I*5.45142*10^-16,1.68643+I*1.16607*10^-15,5.13514+I*3.76819*10^-15,19.23245+I*2.02665*10^-14}"); // check("WeierstrassPPrime(z, {0, 0}) ", // "-2/z^3"); check("WeierstrassPPrime(z, {3, 1}) ", // "-3*Sqrt(3/2)*Cot(Sqrt(3/2)*z)*Csc(Sqrt(3/2)*z)^2"); } @Test public void testWhich() { check("n=5;Which(n == 3, x, n == 5, y)", // "y"); check("f(x_) := Which(x < 0, -x, x == 0, 0, x > 0, x);f(-3)", // "3"); check("Which(False, a)", // ""); check("Which(False, a, x, b, True, c)", // "Which(x,b,True,c)"); check("Which(a, b, c)", // "Which(a,b,c)"); check("$a = 2;which($a == 1, x, $a == 2, b)", // "b"); check("Which(1 < 0, a, x == 0, b, 0 < 1, c)", // "Which(x==0,b,0<1,c)"); check("$a = 2;which($a == 1, x, $a == 3, b)", // ""); check("$x=-2;Which($x < 0, -1, $x > 0, 1, True, Indeterminate)", // "-1"); check("$x=0;Which($x < 0, -1, $x > 0, 1, True, Indeterminate)", // "Indeterminate"); check("$x=3;Which($x < 0, -1, $x > 0, 1, True, Indeterminate)", // "1"); } @Test public void testWhile() { check("$n = 1; While($n \\[LessEqual] 4, $n++); $n", // "5"); check("While(False)", // ""); check("{a, b} = {27, 6}; While(b != 0, {a, b} = {b, Mod(a, b)});a", // "3"); check("i = 1; While(True, If(i^2 > 100, Return(i + 1), i++))", // "12"); check("$n = 1; While($n < 4, Print($n); $n++)", // ""); check("$n = 1; While(++$n < 4); $n", // "4"); check("$n = 1; While($n < 4, $n++); $n", // "4"); check("$n = 1; While(True, If($n > 10, Break()); $n++);$n", // "11"); } @Test public void testWhittakerM() { checkNumeric("N(WhittakerM(2, 1/2, 2*2*I))", // "0.3080150149255876+I*(-8.938966760794024)"); check("N(WhittakerM(2, 1/3, 1/7), 100)", // "0.1656497719066782903103648280719871043760680518713012567635165215951597907345740933330557755894455857"); check("WhittakerM(2, 1.33333333333333333333, 1)", // "0.576202738935656959011"); checkNumeric("N(WhittakerM(4/5, 2 - I, 2))", // "3.2795757038417443+I*(-3.256018217261299)"); checkNumeric("N(WhittakerM(I, 42, 0))", // "0.0"); check("D(WhittakerM(a,b,x), x)", // "(1/2-a/x)*WhittakerM(a,b,x)+((1/2+a+b)*WhittakerM(1+a,b,x))/x"); check("WhittakerM(k, -1/2, 0)", // "WhittakerM(k,-1/2,0)"); check("WhittakerM(k, -1/3, 0)", // "0"); check("WhittakerM(k, -2/3, 0)", // "ComplexInfinity"); check("WhittakerM(1, 1, 0)", // "0"); check("WhittakerM(0, 1, 0)", // "0"); check("WhittakerM(0, 0, 0)", // "0"); check("WhittakerM(2, 3, 1.7)", // "4.07202"); // TODO // check("WhittakerM(2, 0.5, 0.0)", // // "0"); check("Table( WhittakerM(3, 2.5, x), {x,-2.0,2,0.25})", // "{-21.74625,-12.85647,-7.14488,-3.64892,-1.64872,-0.613825,-0.160503,-0.0177054,0.0,0.013789,0.0973501,0.28995,0.606531,1.04543,1.59424,2.23412,2.94304}"); } @Test public void testWhittakerW() { checkNumeric("N(WhittakerW(2, 1/2, 2*2*I))", // "-0.6160300298511752+I*17.877933521588048"); check("D(WhittakerW(a,b,x), x)", // "(1/2-a/x)*WhittakerW(a,b,x)-WhittakerW(1+a,b,x)/x"); check("WhittakerW(0, 0, 0)", // "0"); check("N(WhittakerW(3/5, 1/3, 1/7), 100)", // "0.3970969447006262740475282170027027703019024268551490675205428794618470776851561601237869467558528364"); check("WhittakerW(2, 1.2222222222222222222, 1)", // "-0.2422894111164979908"); checkNumeric("N(WhittakerW(1/5, 2 - I, 2))", // "0.3147585139185293+I*(-1.2734460466128783)"); checkNumeric("WhittakerW(6, 4, 1.7)", // "1740.5462418091338"); // TODO checkNumeric("WhittakerW(2, 0.5, 0.0)", // "WhittakerW(2.0,0.5,0.0)"); checkNumeric("Table( WhittakerW(6, 4, x), {x,-2.0,2,0.25})", // "{2333.0618193174946+I*38.12532949300777,1090.9576562383036+I*73.57215676581899,464.5499885712876+I*152.94532831470107," // + "174.10978469218307+I*351.7626599831295,54.254490548428286+I*935.8127384437696,12.63276840854038+I*3129.88616177697," // + "1.7295419807639405+I*15861.825767596809,0.06481415341111611+I*220852.59445363315,WhittakerW(6.0,4.0,0.0),339121.7767806576," // + "37468.50169122885,11421.860441795448,5313.868067440274,3138.141359549763,2164.6812989167843,1662.3688694569853,1374.640737551975}"); } @Test public void testWith() { EvalEngine.resetModuleCounter4JUnit(); // print message: Set: Cannot unset object 2.0. check("With({x = 2.0}, x=3.0;Sqrt(x) + 1 )", // "2.41421"); check("With({x = 2.0}, Sqrt(x) + 1)", // "2.41421"); EvalEngine.resetModuleCounter4JUnit(); check("With({x = 2 + y}, Hold(With({y = 4}, x + y)))", // "Hold(With({y$1=4},2+y+y$1))"); EvalEngine.resetModuleCounter4JUnit(); check("xm=10;With({xm=xm}, Print(xm));xm", // "10"); check("u=test;With({w=Map(Function({#,x,v,flag}),u)}, w)", // "test"); check("With({x=2, y=16},x^y)", // "65536"); check("With({x = 7, y = a + 1}, x/y)", // "7/(1+a)"); check("With({x = a}, (1 + x^2) &)", // "1+a^2&"); check("Table(With({i = j}, Hold(i)), {j, 5})", // "{Hold(1),Hold(2),Hold(3),Hold(4),Hold(5)}"); check("With({e = Expand((1 + x)^5)}, Function(x, e))", // "Function(x$11,1+5*x+10*x^2+10*x^3+5*x^4+x^5)"); check("With({e = Expand((1 + x)^5)}, Function @@ {x, e})", // "Function(x,1+5*x+10*x^2+10*x^3+5*x^4+x^5)"); check("x=5;With({x = x}, Hold(x))", // "Hold(5)"); check("newton(f_, x0_) := With({fp = f'}, FixedPoint(# - f(#)/fp(#) &, x0))", // ""); check("newton(Cos,1.33)", // "1.5708"); check("newton(Cos(#)-#&,1.33)", // "0.739085"); check("With({f = Function(n, If(n == 0, 1, n*f(n - 1)))}, f(10))", // "10*f(9)"); // check("Timing(Do(With({x = 5}, x;), {10^5}))", ""); // check("Timing(Do(Module({x = 5}, x;), {10^5}))", ""); check("With({x=y,y=z,z=3}, Print({Hold(x),Hold(y),Hold(z)});{x,y,z})", // "{y,z,3}"); check("With({x=z},Module({x},x+y))", // "x$24+y"); check("f(x_) := With({q = False}, test /; q==0) /; x==1", // ""); check("f(1)", // "f(1)"); check("With({x = a}, x = 5); a", // "5"); check("With({t = 8}, With({t = 9}, t^2))", // "81"); check("Clear(a);With({t = a}, With({u = b}, t + u))", // "a+b"); check("With({tt = a}, (1 + tt^2) &)", // "1+a^2&"); check("With({x:=2,y:=3},{x,3*y})", // "{2,9}"); check("With({a=2},{b=a},{c=b},a+b+c)", // "6"); check("With({y = Sin(1.0)}, Sum(y^i, {i, 0, 10}))", // "5.36323"); check("With({t=Sin(10/2*Pi+#)}, t &)", // "-Sin(#1)&"); } @Test public void testYuleDissimilarity() { check("YuleDissimilarity({1, 0, 1, 1, 0}, {1, 1, 0, 1, 1})", // "2"); check("YuleDissimilarity({True, False, True}, {True, True, False})", // "2"); check("YuleDissimilarity({0, 0, 0, 0}, {0, 0, 0, 0})", // "0"); check("YuleDissimilarity({0, 1, 0, 1}, {1, 0, 1, 0})", // "2"); } @Test public void testZeta() { // https://en.wikipedia.org/wiki/Particular_values_of_the_Riemann_zeta_function check("Zeta'(0)", // "-Log(2*Pi)/2"); check("Zeta'(-1)", // "1/12-Log(Glaisher)"); checkNumeric("Zeta(3,-4.0)", // "Zeta(3.0,-4.0)"); checkNumeric("Zeta(2.2,3.1)", // "0.26067453797192913"); check("Zeta(6)", // "Pi^6/945"); check("Zeta(-1)", // "-1/12"); check("Zeta(-11)", // "691/32760"); check("Zeta(-42)", // "0"); check("Zeta(0)", // "-1/2"); check("Zeta(Infinity)", // "1"); check("N(Zeta(5/4),50)", // "4.5951118258429433806853780396946256522810297806045"); check("N(Zeta(3,2),50)", // "0.20205690315959428539973816151144999076498629234004"); check("D(Zeta(s, x), x)", // "-s*Zeta(1+s,x)"); check("Zeta(-3.0)", // "0.00833333"); check("Zeta(4.0)", // "1.08232"); check("Zeta(1.0+I)", // "0.582158+I*(-0.926849)"); check("Zeta(-3.0+I*1.0^(-100))", // "0.0143825+I*0.0103497"); check("Table(Zeta(2*x),{x,1,5,1})", // "{Pi^2/6,Pi^4/90,Pi^6/945,Pi^8/9450,Pi^10/93555}"); check("Table(Zeta(x),{x,0,-20,-1})", // "{-1/2,-1/12,0,1/120,0,-1/252,0,1/240,0,-1/132,0,691/32760,0,-1/12,0,3617/8160,0,-\n" + "43867/14364,0,174611/6600,0}"); check("Zeta(2)", // "Pi^2/6"); checkNumeric("Zeta(-2.5 + I)", // "0.02359361058637964+I*0.0014077996058383772"); check("Zeta(s, 0)", // "Zeta(s)"); check("Zeta(s, 1/2)", // "(-1+s^2)*Zeta(s)"); check("Zeta(s, -1)", // "1+Zeta(s)"); check("Zeta(s, 2)", // "-1+Zeta(s)"); check("Zeta(4, -12)", // "638942263173398977/590436101122560000+Pi^4/90"); check("Zeta(11, -12)", // "Zeta(11,-12)"); check("Zeta(-5, -12)", // "158938415/252"); } }