{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f9b18ef0",
   "metadata": {},
   "source": [
    "# Symbols!\n",
    "\n",
    "Announcements:\n",
    "- Lessons 7,8 due today\n",
    "- HW 3 due Monday\n",
    "- Midterm 1 starts tomorrow!\n",
    "\n",
    "Today's Music:\n",
    "- Door Into Summer, Jacob's Trouble; cover of the Monkey's song"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2be67dc7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a6f66442",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "58dea1e1",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cfbfd37a",
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "cannot assign to expression here. Maybe you meant '==' instead of '='? (3597255088.py, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  Input \u001b[0;32mIn [4]\u001b[0;36m\u001b[0m\n\u001b[0;31m    x + 2 = 10\u001b[0m\n\u001b[0m    ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m cannot assign to expression here. Maybe you meant '==' instead of '='?\n"
     ]
    }
   ],
   "source": [
    "x + 2 = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3c176744",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x + 2 == 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fa0b1a11",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = sympy.symbols('x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "64a12b27",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x$"
      ],
      "text/plain": [
       "x"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "dd692b8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "[a,b,c] = sympy.symbols('a b c')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "798f49d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a$"
      ],
      "text/plain": [
       "a"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e6478441",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a + b$"
      ],
      "text/plain": [
       "a + b"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + b "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "acb03ef5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a + 30$"
      ],
      "text/plain": [
       "a + 30"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a + 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "23031f56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a^{4}$"
      ],
      "text/plain": [
       "a**4"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a ** 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "fd1d615f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 * x == x + x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a7ca9ddd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x + a == a + x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "be8fa85a",
   "metadata": {},
   "outputs": [
    {
     "ename": "SyntaxError",
     "evalue": "invalid syntax (1432706681.py, line 1)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  Input \u001b[0;32mIn [15]\u001b[0;36m\u001b[0m\n\u001b[0;31m    2 x == 10\u001b[0m\n\u001b[0m      ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
     ]
    }
   ],
   "source": [
    "2 x == 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3a4fdd7e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 * x == 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "a833caf5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.solve(2 * x == 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "21dffd81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.solve(sympy.Eq(2 * x,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "def37232",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-sqrt(5), sqrt(5)]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.solve(sympy.Eq(x ** 2,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "923d6954",
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'sin' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Input \u001b[0;32mIn [20]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m sin(x)\n",
      "\u001b[0;31mNameError\u001b[0m: name 'sin' is not defined"
     ]
    }
   ],
   "source": [
    "sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a835dba7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sin{\\left(x \\right)}$"
      ],
      "text/plain": [
       "sin(x)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "b1212041",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.5707963267949 - 0.622362503714779*I, 1.5707963267949 + 0.622362503714779*I]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.solve(sympy.Eq(sympy.sin(x),1.2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "08c6c475",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = sympy.S('y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "8b2ba31d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{x: pi - asin(1/tan(y))}, {x: asin(1/tan(y))}]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.solve(sympy.Eq(sympy.sin(y)*sympy.sin(x),sympy.cos(y)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "96c3ed12",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "    An equal relation between two objects.\n",
      "\n",
      "    Explanation\n",
      "    ===========\n",
      "\n",
      "    Represents that two objects are equal.  If they can be easily shown\n",
      "    to be definitively equal (or unequal), this will reduce to True (or\n",
      "    False).  Otherwise, the relation is maintained as an unevaluated\n",
      "    Equality object.  Use the ``simplify`` function on this object for\n",
      "    more nontrivial evaluation of the equality relation.\n",
      "\n",
      "    As usual, the keyword argument ``evaluate=False`` can be used to\n",
      "    prevent any evaluation.\n",
      "\n",
      "    Examples\n",
      "    ========\n",
      "\n",
      "    >>> from sympy import Eq, simplify, exp, cos\n",
      "    >>> from sympy.abc import x, y\n",
      "    >>> Eq(y, x + x**2)\n",
      "    Eq(y, x**2 + x)\n",
      "    >>> Eq(2, 5)\n",
      "    False\n",
      "    >>> Eq(2, 5, evaluate=False)\n",
      "    Eq(2, 5)\n",
      "    >>> _.doit()\n",
      "    False\n",
      "    >>> Eq(exp(x), exp(x).rewrite(cos))\n",
      "    Eq(exp(x), sinh(x) + cosh(x))\n",
      "    >>> simplify(_)\n",
      "    True\n",
      "\n",
      "    See Also\n",
      "    ========\n",
      "\n",
      "    sympy.logic.boolalg.Equivalent : for representing equality between two\n",
      "        boolean expressions\n",
      "\n",
      "    Notes\n",
      "    =====\n",
      "\n",
      "    Python treats 1 and True (and 0 and False) as being equal; SymPy\n",
      "    does not. And integer will always compare as unequal to a Boolean:\n",
      "\n",
      "    >>> Eq(True, 1), True == 1\n",
      "    (False, True)\n",
      "\n",
      "    This class is not the same as the == operator.  The == operator tests\n",
      "    for exact structural equality between two expressions; this class\n",
      "    compares expressions mathematically.\n",
      "\n",
      "    If either object defines an ``_eval_Eq`` method, it can be used in place of\n",
      "    the default algorithm.  If ``lhs._eval_Eq(rhs)`` or ``rhs._eval_Eq(lhs)``\n",
      "    returns anything other than None, that return value will be substituted for\n",
      "    the Equality.  If None is returned by ``_eval_Eq``, an Equality object will\n",
      "    be created as usual.\n",
      "\n",
      "    Since this object is already an expression, it does not respond to\n",
      "    the method ``as_expr`` if one tries to create `x - y` from ``Eq(x, y)``.\n",
      "    This can be done with the ``rewrite(Add)`` method.\n",
      "\n",
      "    .. deprecated:: 1.5\n",
      "\n",
      "       ``Eq(expr)`` with a single argument is a shorthand for ``Eq(expr, 0)``,\n",
      "       but this behavior is deprecated and will be removed in a future version\n",
      "       of SymPy.\n",
      "\n",
      "    \n"
     ]
    }
   ],
   "source": [
    "print(sympy.Eq.__doc__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "4a34987f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.core.symbol.Symbol"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "eb7764b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.core.symbol.Symbol"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "7719c2d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "e1 = sympy.S('x + y / 3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "d684b6d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.core.add.Add"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(e1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "1a253ecf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x + \\frac{y}{3}$"
      ],
      "text/plain": [
       "x + y/3"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "048f27b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{x: 10 - y/3}]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.solve(sympy.Eq(e1,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "79d48717",
   "metadata": {},
   "outputs": [],
   "source": [
    "f1 = sympy.S('x / 20')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "9bb6e243",
   "metadata": {},
   "outputs": [],
   "source": [
    "f2 = sympy.S('1 / 10')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "12e7f142",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{x}{20} + \\frac{1}{10}$"
      ],
      "text/plain": [
       "x/20 + 1/10"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f1 + f2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "7c2a1350",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{x + 2}{20}$"
      ],
      "text/plain": [
       "(x + 2)/20"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.together(f1 + f2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "2832c599",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{x}{20} + \\frac{1}{10}$"
      ],
      "text/plain": [
       "x/20 + 1/10"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.simplify(f1 + f2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "1b59a751",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 x$"
      ],
      "text/plain": [
       "2*x"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x + x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "5da25821",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a \\left(x + 1\\right) + x^{2}$"
      ],
      "text/plain": [
       "a*(x + 1) + x**2"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.factor(x ** 2 + a * x + a,a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "9cc788ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a x + a + x^{2}$"
      ],
      "text/plain": [
       "a*x + a + x**2"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.factor(x ** 2 + a * x + a,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "9e30f8a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle a x + a + x^{2}$"
      ],
      "text/plain": [
       "a*x + a + x**2"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.factor(x ** 2 + a * x + a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "f8bd6337",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7f22336e0490>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.plot(sympy.sin(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "65165d61",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7f2222999e40>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.plot(sympy.sin(x) + sympy.cos(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "3adbbd25",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "b681e95e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sin{\\left(x \\right)}$"
      ],
      "text/plain": [
       "sin(x)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sp.sin(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "c824da57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{x: 55/14, y: 5/7}"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.solve( [ sympy.Eq(2 * x + 3 * y, 10), sympy.Eq(4 * x - 8 * y , 10)])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae9d51c9",
   "metadata": {},
   "source": [
    "# In-class problem\n",
    "Write a function `howManyZeros`.\n",
    "\n",
    "`howManyZeros('x ** 2 + 10 * x + 5')  -->  2`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "aca91587",
   "metadata": {},
   "outputs": [],
   "source": [
    "def howManyZeros(eqn):\n",
    "    return len(sp.solve(sp.S(eqn)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "35e78411",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-4/3]"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.solve(sympy.S('x * 3 + 4'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "ff13d0a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-5 - 2*sqrt(5), -5 + 2*sqrt(5)]"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sympy.solve(sympy.S('x ** 2 + 10 * x + 5'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "31bd4ca0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "howManyZeros('x ** 2 + 10 * x + 5')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "47565b0f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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