{ "cells": [ { "cell_type": "markdown", "metadata": { "toc": "true" }, "source": [ "# Table of Contents\n", "

1  連立方程式
2  展開(expand) 因数分解(factor)
3  3点を通る２次方程式
" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5\n" ] } ], "source": [ "from sympy import Symbol, pprint\n", "a = 3\n", "b = 2\n", "pprint(a+b)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "3⋅x + 2\n" ] } ], "source": [ "x = Symbol('x')\n", "eq1 = a*x+b\n", "pprint(eq1)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[-2/3]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy import solve\n", "solve(eq1, x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 連立方程式\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{x: -6, y: 2}" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sympy import Matrix, solve_linear_system\n", "from sympy.abc import x, y\n", "\n", "system = Matrix(( (1, 4, 2), (-2, 1, 14)))\n", "solve_linear_system(system, x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 展開(expand) 因数分解(factor)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2 2\n", "x + 2⋅x⋅y + y \n" ] } ], "source": [ "from sympy import *\n", "pprint(expand((x+y)**2))" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " ⎛ 2 ⎞\n", "(x - 1)⋅⎝x + 1⎠\n" ] } ], "source": [ "pprint(factor(x**3 - x**2 + x - 1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3点を通る２次方程式\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": 33, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy import *\n", "f, x, a, b, c = symbols('f x a b c')\n", "f = a*x**2 + b*x + c" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a*x**2 + b*x + c\n" ] } ], "source": [ "print(f)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true }, "outputs": [], "source": [ "class my_func(Function):\n", " @classmethod\n", " def eval(cls, x):\n", " return a*x**2 + b*x + c" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2 \n", "a⋅x + b⋅x + c\n" ] } ], "source": [ "pprint(my_func(x))" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": true }, "outputs": [], "source": [ "eq1 = my_func(1)\n", "eq2 = my_func(-3)\n", "eq3 = my_func(-1)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a + b + c\n", "9⋅a - 3⋅b + c\n", "a - b + c\n" ] } ], "source": [ "pprint(eq1)\n", "pprint(eq2)\n", "pprint(eq3)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy.abc import a, b, c\n", "\n", "system = Matrix(( (1, 1, 1, 2), (9, -3, 1, 4),\n", "(1, -1, 1, 1)))\n", "s1 = solve_linear_system(system, a, b, c)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{a: 1/2, b: 1/2, c: 1}\n" ] } ], "source": [ "pprint(s1)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1/2\n", "1/2\n", "1\n" ] } ], "source": [ "pprint(s1[a])\n", "pprint(s1[b])\n", "pprint(s1[c])" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sympy import sin\n", "eq = sin(x+1) - x**2" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "ename": "NotImplementedError", "evalue": "multiple generators [x, sin(x + 1)]\nNo algorithms are implemented to solve equation -x**2 + sin(x + 1)", "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[0meq\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 [x, sin(x + 1)]\nNo algorithms are implemented to solve equation -x**2 + sin(x + 1)" ] } ], "source": [ "solve(eq, x)" ] }, { "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": "3.6.1" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": 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