{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": "true" }, "source": [ "

Table of Contents

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 初等関数" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "四則演算は”+ー*・”.分数は," ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.75\n" ] } ], "source": [ "\n", "from sympy import Rational\n", "\n", "print(3/4);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "であるが,Rational(有理数)というコマンドを使うと" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{3}{4}$" ], "text/plain": [ "3/4" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Rational(3/4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " と,分数のまま表示してくれる.\n", "\n", "sympyを使うと$x$を変数として,そのままの記号で使うことが可能となる.ちょっと変な記述だが," ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2 \n", "3⋅a - 4⋅a + 3\n" ] } ], "source": [ "from sympy import symbols, pprint, sqrt, log, sin, cos, pi, N\n", "\n", "x = symbols('a')\n", "eq1 = 3*x**2 -4*x + 3\n", "pprint(eq1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "とすると変数名としてのxとそこに割り当てられた記号としての$a$の関係がわかるだろう.\n", "\n", "その他の関数もそのまま直感的な名前が使える." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "√2\n" ] } ], "source": [ "pprint(sqrt(2))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log(a)\n" ] } ], "source": [ "pprint(log(x))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2 2 \n", "sin (a) + cos (a)\n" ] } ], "source": [ "pprint(sin(x)**2+cos(x)**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "値として取り出すのは,以下のふた通り." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3.14159265358979\n", "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068\n" ] } ], "source": [ "print( pi.evalf() )\n", "print( N(pi, 100) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ラジアンと角度(lost)\n", "\n", "mpmathをいれないと駄目? でも,mpmathの説明があまりまともにされてない.\n", "数値計算だよね.\n", "\n", "degreesとかradiansに関しては,sympyで用意されてないようだ." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "59.99999999999999" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from math import *\n", "degrees(pi/3)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0471975511965976" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "radians(60)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5000000000000001" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cos(pi/3)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{1}{2}$" ], "text/plain": [ "1/2" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy import cos, pi\n", "\n", "cos(pi/3)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "π\n" ] } ], "source": [ "pprint(pi)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "6004799503160661/18014398509481984\n" ] } ], "source": [ "print(Rational(1/3))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "SympyではRational, Real, Integerが数としてあるらしい.\n", "\n", "Pi/3などをrationalとしては扱えない.したがって,三角関数の変形ではミスることになるな.\n", "んーーーん.ちとしんどいかも." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%matplotlib inline\n", "\n", "from sympy import symbols\n", "from sympy.plotting import plot\n", "from sympy import sin, sinc\n", "\n", "x = symbols('x')\n", "plot(sinc(x), (x, -20, 20))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\infty i$" ], "text/plain": [ "oo*I" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy import acos, oo, pi\n", "acos(oo)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{\\pi}{2}$" ], "text/plain": [ "pi/2" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acos(0)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sympy import *\n", "x = symbols('x')\n", "p1 = plot(sinh(x), cosh(x), (x,-pi,pi),\n", " legend=True, show=False)\n", "p1[0].line_color = 'b'\n", "p1[1].line_color = 'r'\n", "p1.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# ユーザ定義関数\n", "## 簡単な定義\n", "単純にユーザが関数を定義するには下の通りすれば良い.その場合,入力はsubsを使う." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [], "source": [ "my_func = 2*x - 3" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2⋅x - 3\n", "2⋅a - 3\n" ] } ], "source": [ "from sympy import *\n", "a, x = symbols('a x')\n", "pprint(my_func.subs({x:x}))\n", "pprint(my_func.subs({x:a}))\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sympy.plotting import plot\n", "p1 = plot(my_func, (x,-2,2),\n", " legend=True, show=False)\n", "p1[0].line_color = 'r'\n", "p1.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## もう少し一般的な定義\n", "Python 標準のdefを使うことも可能." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sympy import *\n", "x = symbols('x')\n", "\n", "def func(x):\n", " return x**2\n", "\n", "p1 = plot(func(x), (x,-2,2),\n", " legend=True, show=False)\n", "p1[0].line_color = 'r'\n", "p1.show()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\frac{x^{3}}{3}$" ], "text/plain": [ "x**3/3" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integrate(func(x),x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## より厳密な定義\n", "\n", "より厳密に関数を定義するにはFunctionで定義する必要がある." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": true }, "outputs": [], "source": [ "f = Function('f')" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "d \n", "──(f(x))\n", "dx \n" ] } ], "source": [ "pprint(Derivative(f(x),x))" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[31mInit signature:\u001b[39m Function(*args)\n", "\u001b[31mDocstring:\u001b[39m \n", "Base class for applied mathematical functions.\n", "\n", "It also serves as a constructor for undefined function classes.\n", "\n", "See the :ref:`custom-functions` guide for details on how to subclass\n", "``Function`` and what methods can be defined.\n", "\n", "Examples\n", "========\n", "\n", "**Undefined Functions**\n", "\n", "To create an undefined function, pass a string of the function name to\n", "``Function``.\n", "\n", ">>> from sympy import Function, Symbol\n", ">>> x = Symbol('x')\n", ">>> f = Function('f')\n", ">>> g = Function('g')(x)\n", ">>> f\n", "f\n", ">>> f(x)\n", "f(x)\n", ">>> g\n", "g(x)\n", ">>> f(x).diff(x)\n", "Derivative(f(x), x)\n", ">>> g.diff(x)\n", "Derivative(g(x), x)\n", "\n", "Assumptions can be passed to ``Function`` the same as with a\n", ":class:`~.Symbol`. Alternatively, you can use a ``Symbol`` with\n", "assumptions for the function name and the function will inherit the name\n", "and assumptions associated with the ``Symbol``:\n", "\n", ">>> f_real = Function('f', real=True)\n", ">>> f_real(x).is_real\n", "True\n", ">>> f_real_inherit = Function(Symbol('f', real=True))\n", ">>> f_real_inherit(x).is_real\n", "True\n", "\n", "Note that assumptions on a function are unrelated to the assumptions on\n", "the variables it is called on. If you want to add a relationship, subclass\n", "``Function`` and define custom assumptions handler methods. See the\n", ":ref:`custom-functions-assumptions` section of the :ref:`custom-functions`\n", "guide for more details.\n", "\n", "**Custom Function Subclasses**\n", "\n", "The :ref:`custom-functions` guide has several\n", ":ref:`custom-functions-complete-examples` of how to subclass ``Function``\n", "to create a custom function.\n", "\u001b[31mFile:\u001b[39m ~/Desktop/Lectures/math_python/jupyter_num_calc/symbolic_math/ipynb_txt/venv/lib/python3.12/site-packages/sympy/core/function.py\n", "\u001b[31mType:\u001b[39m FunctionClass\n", "\u001b[31mSubclasses:\u001b[39m DefinedFunction, AppliedUndef, WildFunction, Coeff, IntegralTransform, _rf" ] } ], "source": [ "?Function" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "class my_func(Function):\n", " @classmethod\n", " def eval(cls, x):\n", " return 2*x**2-3*x+4\n", "\n", "plot(my_func(x))" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle 4 x - 3$" ], "text/plain": [ "4*x - 3" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "diff(my_func(x),x)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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