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

Table of Contents

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", " 等号 \n", "
\n", "
\n", " cc by Shigeto R. Nishitani, 2017-10-31 \n", "
\n", "\n", "* file: ~/python/doing_math_with_python/equals.ipynb" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# 等号(equals)の意味\n", "\n", "等号は，数学でいろいろな意味を持つことを中学校で学びます．\n", "それぞれの状況による意味の違いを人間は適当に判断していますが，\n", "プログラムであるpythonでは無理です．\n", "pythonでは，それぞれ違った記号や操作として用意され，\n", "人間がpythonに明示的に指示する必要がある．\n", "\n", "## 変数への代入= (equal)\n", "変数に値を代入する時には= (equal)を使います．例えば，" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "a=3\n", "b=2" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5\n" ] } ], "source": [ "print(a+b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "代数演算に変数名のまま使うには，Symbolあるいはsymbolsでpythonに教えてやる必要があります．" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy import *\n", "a,b,c,x = symbols('a,b,c,x')\n", "\n", "eq1 = a*x**2 + b*x + c" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2 \n", "a⋅x + b⋅x + c\n" ] } ], "source": [ "pprint(eq1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "値の代入はsubsで定義辞書を渡すことになります．" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "9⋅a + 3⋅b + c\n" ] } ], "source": [ "pprint(eq1.subs({x:3}))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2\n", "b⋅x + c + 2⋅x \n" ] } ], "source": [ "pprint(eq1.subs({a:2}))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "まちがって代入すると，それ以降のsubsが効かなくなるので，注意してください．" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2 \n", "a⋅x + b⋅x + c\n", " 2 \n", "a⋅x + b⋅x + c\n" ] } ], "source": [ "a=3\n", "pprint(eq1)\n", "pprint(eq1.subs({a:2}))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "その場合は，symbolsなどで元に戻す必要があります．" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "a = symbols('a')" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2\n", "b⋅x + c + 2⋅x \n" ] } ], "source": [ "pprint(eq1.subs({a:2}))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 方程式の解(solve)\n", "\n", "> 3x=2を満たすxを求めよ\n", "\n", "は片方の辺へ移項して，解きます．" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3⋅x - 2\n" ] } ], "source": [ "eq1 = 3*x - 2\n", "pprint(eq1)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[2/3]" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(eq1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2次方程式も同じようして解けます．" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2 \n", "a⋅x + b⋅x + c\n" ] } ], "source": [ "eq1 = a*x**2 + b*x + c\n", "pprint(eq1)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[{a: -(b*x + c)/x**2}]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(eq1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "おやおや，おかしいですね．とくべき未知数(x)を指定するのを忘れています．" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(-b + sqrt(-4*a*c + b**2))/(2*a), -(b + sqrt(-4*a*c + b**2))/(2*a)]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(eq1,x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "出力としてpythonの辞書形式で戻す場合には，dict=Trueが必要になります．" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[{x: (-b + sqrt(-4*a*c + b**2))/(2*a)}, {x: -(b + sqrt(-4*a*c + b**2))/(2*a)}]" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(eq1,x, dict=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "連立方程式も同じようにして解けます．" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{x: 3/2, y: -1/2}" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y = symbols('y')\n", "solve({x+y-1,x-y-2},{x,y})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "解析的に解けないときは，数値解を求める必要があります．これはpythonによる数値計算で詳述します．簡単なコマンドはなさそうです．" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "scrolled": true }, "outputs": [ { "ename": "NotImplementedError", "evalue": "multiple generators [exp(x), log(x)]\nNo algorithms are implemented to solve equation log(x) - exp(-x)", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNotImplementedError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0msolve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m/Users/bob/anaconda3/lib/python3.6/site-packages/sympy/solvers/solvers.py\u001b[0m in \u001b[0;36msolve\u001b[0;34m(f, *symbols, **flags)\u001b[0m\n\u001b[1;32m 1051\u001b[0m \u001b[0;31m###########################################################################\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1052\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mbare_f\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1053\u001b[0;31m \u001b[0msolution\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_solve\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0msymbols\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mflags\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1054\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1055\u001b[0m \u001b[0msolution\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_solve_system\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msymbols\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mflags\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m/Users/bob/anaconda3/lib/python3.6/site-packages/sympy/solvers/solvers.py\u001b[0m in \u001b[0;36m_solve\u001b[0;34m(f, *symbols, **flags)\u001b[0m\n\u001b[1;32m 1617\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1618\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mresult\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mFalse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1619\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mNotImplementedError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'\\n'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mjoin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mmsg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnot_impl_msg\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1620\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1621\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mflags\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'simplify'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mNotImplementedError\u001b[0m: multiple generators [exp(x), log(x)]\nNo algorithms are implemented to solve equation log(x) - exp(-x)" ] } ], "source": [ "solve(log(x)-exp(-x),x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "両辺ともに長い式の時には，右辺(rhs),左辺(lhs)なんかを使ってまとめたりします．" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2 2 \n", "sin (x) - 2⋅cos (x) + 3⋅cos(x) - cos(2⋅x)\n" ] }, { "data": { "text/plain": [ "[0, -I*log(-2/5 - sqrt(21)*I/5), -I*log(-2/5 + sqrt(21)*I/5)]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rhs = sin(x)**2 + 3*cos(x)\n", "lhs = 2*cos(x)**2 + cos(2*x)\n", "eq1 = rhs -lhs\n", "pprint(eq1)\n", "solve(eq1,x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 恒等式\n", "式の変形にも等号が使われます．例えば，\n", "$$\n", "(x-2)^2 = x^2 -4x +4\n", "$$\n", "なんかです．これは左辺と右辺がどんな$x$に対しても\n", "成り立っていること，恒等式であることを表現しています．\n", "\n", "このような式の変形においても，問題としては\n", "> $(x-2)^2$を展開(expand)せよ\n", "\n", "となります．ですので，" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy import *\n", "\n", "x = Symbol('x')\n", "eq1 = (x-2)**2" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2\n", "(x - 2) \n", " 2 \n", "x - 4⋅x + 4\n" ] } ], "source": [ "pprint(eq1)\n", "pprint(eq1.expand())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "となります．因数分解，微積分なども同様にそれぞれのコマンドが用意されています．これは別の章で詳しく解説します．" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 課題" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3点を通る2次方程式\n", "\n", "3点(1,2),(-3,4),(-1,1)を通る２次方程式を求めよ．" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy import *\n", "a,b,c,x = symbols('a,b,c,x')\n", "f = a*x**2 + b*x + c" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "eq1 = f.subs({x:1})-2" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": true }, "outputs": [], "source": [ "eq2 = f.subs({x:-3})-4\n", "eq3 = f.subs({x:-1})-1" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{a: 1/2, b: 1/2, c: 1}\n" ] } ], "source": [ "s1 = solve({eq1,eq2,eq3},{a,b,c})\n", "print(s1)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x**2/2 + x/2 + 1\n" ] } ], "source": [ "f1 = f.subs(s1)\n", "print(f1)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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PHpgeo3ck4eS+2VPMg1/uZcrAYP41dySusnyv3ZFytxF/mR5DXWMLa/cb8XJz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\ntV7TAsYBhzRNy9U0rQn4mLY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy.plotting import plot\n", "\n", "plot(f1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 関数と点の同時plot\n", "\n", "得られた関数と与えられた点を同時にplotするのに苦労した．\n", "func内で上で得られたf1を使いたかったが，だめ．\n", "symbolと値の取り扱いが混ざってしまうのかな．\n", "\n", "とりあえず，関数をベタ打ちすると以下のとおり表示OK.\n" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#from sympy.plotting import plot\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "def func(x):\n", " return x**2/2 + x/2 + 1\n", "\n", "xx = np.linspace(-3,2, 100)\n", "plt.plot(xx, func(xx))\n", "px=[1,-3,-1]\n", "py=[2,4,1]\n", "plt.plot(px,py,'o', color='r')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.3" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "base_numbering": 1, "nav_menu": { "height": "12px", "width": "252px" }, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": {}, "toc_section_display": "block", "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 2 }