{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# sympy_sample" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import sympy\n", "from sympy import (\n", " init_printing,\n", " # よく使いそうなものはImport\n", " Symbol, symbols,\n", " Abs,\n", " Rational,\n", " simplify, expand, factor,\n", " limit, Limit,\n", " diff, Derivative, dsolve,\n", " integrate, Integral,\n", " ln, log, expand_log,\n", " sqrt, root, exp,\n", " cos, sin, tan,\n", " acos, asin, atan,\n", " cosh, sinh, tanh,\n", " acosh, asinh, atanh,\n", " pi, oo, EulerGamma, Catalan, GoldenRatio,\n", " I, E, # ImaginaryUnit, Exp(1)\n", " sign,\n", " Sum, Product, Min, Max,\n", " Eq, solve, roots, Ne, # Equality, Unequality \n", " gamma, loggamma, polygamma, uppergamma,\n", " Function,\n", " satisfiable,\n", " Matrix\n", ")\n", "import sympy.abc\n", "from sympy.plotting.plot import Plot\n", "\n", "import matplotlib\n", "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'0.7.6.1'" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "init_printing()\n", "sympy.__version__" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Symbol" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMgAAAAUBAMAAAA6im/5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAU94c5QmdjFwAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left ( x, \\quad y, \\quad \\left ( a, \\quad b, \\quad c\\right )\\right )$$" ], "text/plain": [ "(x, y, (a, b, c))" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = Symbol('x')\n", "y = Symbol('y')\n", "x, y, symbols('a b c')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "sympy.core.symbol.Symbol" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(x)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "['adjoint',\n", " 'apart',\n", " 'args',\n", " 'args_cnc',\n", " 'as_base_exp',\n", " 'as_coeff_Add',\n", " 'as_coeff_Mul',\n", " 'as_coeff_add',\n", " 'as_coeff_exponent',\n", " 'as_coeff_mul',\n", " 'as_coefficient',\n", " 'as_coefficients_dict',\n", " 'as_content_primitive',\n", " 'as_dummy',\n", " 'as_expr',\n", " 'as_independent',\n", " 'as_leading_term',\n", " 'as_numer_denom',\n", " 'as_ordered_factors',\n", " 'as_ordered_terms',\n", " 'as_poly',\n", " 'as_powers_dict',\n", " 'as_real_imag',\n", " 'as_terms',\n", " 'assumptions0',\n", " 'atoms',\n", " 'cancel',\n", " 'canonical_variables',\n", " 'class_key',\n", " 'coeff',\n", " 'collect',\n", " 'combsimp',\n", " 'compare',\n", " 'compute_leading_term',\n", " 'conjugate',\n", " 'copy',\n", " 'could_extract_minus_sign',\n", " 'count',\n", " 'count_ops',\n", " 'default_assumptions',\n", " 'diff',\n", " 'doit',\n", " 'dummy_eq',\n", " 'equals',\n", " 'evalf',\n", " 'expand',\n", " 'extract_additively',\n", " 'extract_branch_factor',\n", " 'extract_multiplicatively',\n", " 'factor',\n", " 'find',\n", " 'free_symbols',\n", " 'fromiter',\n", " 'func',\n", " 'getO',\n", " 'getn',\n", " 'has',\n", " 'integrate',\n", " 'invert',\n", " 'is_Add',\n", " 'is_AlgebraicNumber',\n", " 'is_Atom',\n", " 'is_Boolean',\n", " 'is_Derivative',\n", " 'is_Dummy',\n", " 'is_Equality',\n", " 'is_Float',\n", " 'is_Function',\n", " 'is_Integer',\n", " 'is_Matrix',\n", " 'is_Mul',\n", " 'is_Not',\n", " 'is_Number',\n", " 'is_NumberSymbol',\n", " 'is_Order',\n", " 'is_Piecewise',\n", " 'is_Poly',\n", " 'is_Pow',\n", " 'is_Rational',\n", " 'is_Relational',\n", " 'is_Symbol',\n", " 'is_Vector',\n", " 'is_Wild',\n", " 'is_algebraic',\n", " 'is_algebraic_expr',\n", " 'is_antihermitian',\n", " 'is_bounded',\n", " 'is_commutative',\n", " 'is_comparable',\n", " 'is_complex',\n", " 'is_composite',\n", " 'is_constant',\n", " 'is_even',\n", " 'is_finite',\n", " 'is_hermitian',\n", " 'is_hypergeometric',\n", " 'is_imaginary',\n", " 'is_infinite',\n", " 'is_infinitesimal',\n", " 'is_integer',\n", " 'is_irrational',\n", " 'is_negative',\n", " 'is_noninteger',\n", " 'is_nonnegative',\n", " 'is_nonpositive',\n", " 'is_nonzero',\n", " 'is_number',\n", " 'is_odd',\n", " 'is_polar',\n", " 'is_polynomial',\n", " 'is_positive',\n", " 'is_prime',\n", " 'is_rational',\n", " 'is_rational_function',\n", " 'is_real',\n", " 'is_transcendental',\n", " 'is_unbounded',\n", " 'is_zero',\n", " 'iter_basic_args',\n", " 'leadterm',\n", " 'limit',\n", " 'lseries',\n", " 'match',\n", " 'matches',\n", " 'n',\n", " 'name',\n", " 'normal',\n", " 'nseries',\n", " 'nsimplify',\n", " 'powsimp',\n", " 'primitive',\n", " 'radsimp',\n", " 'ratsimp',\n", " 'rcall',\n", " 'refine',\n", " 'removeO',\n", " 'replace',\n", " 'rewrite',\n", " 'round',\n", " 'separate',\n", " 'series',\n", " 'simplify',\n", " 'sort_key',\n", " 'subs',\n", " 'taylor_term',\n", " 'together',\n", " 'transpose',\n", " 'trigsimp',\n", " 'xreplace']" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[a for a in dir(x) if not a.startswith('_')]" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWQAAAAUBAMAAABIYFpmAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\left [ a, \\quad b, \\quad c, \\quad x, \\quad y, \\quad z, \\quad X, \\quad Y, \\quad Z\\right ]$$" ], "text/plain": [ "[a, b, c, x, y, z, X, Y, Z]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "abc_symblos = [sympy.abc.a, sympy.abc.b, sympy.abc.c, sympy.abc.x, sympy.abc.y, sympy.abc.z, sympy.abc.X, sympy.abc.Y, sympy.abc.Z]\n", "abc_symblos" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[sympy.core.symbol.Symbol,\n", " sympy.core.symbol.Symbol,\n", " sympy.core.symbol.Symbol,\n", " sympy.core.symbol.Symbol,\n", " sympy.core.symbol.Symbol,\n", " sympy.core.symbol.Symbol,\n", " sympy.core.symbol.Symbol,\n", " sympy.core.symbol.Symbol,\n", " sympy.core.symbol.Symbol]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[type(s) for s in abc_symblos]" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz'" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "onechar_symbols = ''.join([a for a in dir(sympy.abc) if len(a) == 1])\n", "onechar_symbols" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import string\n", "onechar_symbols == string.ascii_uppercase + string.ascii_lowercase" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGUAAAAUBAMAAABmLO6YAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\left ( a, \\quad b, \\quad c\\right )$$" ], "text/plain": [ "(a, b, c)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.var('a:c')\n", "a, b, c" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOkAAAAUBAMAAACaFQcXAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIma7zZnddlTvRIkQ\nMqvFy5UvAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACNUlEQVRIDb2VMWzTQBSGvzixkzROawmVDXAX\nFpaCYEOqmcpGBUIMRbQTIIQgSwdgKQMIllbAhhgyISGE5CXKBHirspAggcTIRBgDYqigqLw7t0Q+\nXyUG5Dckvvfde7/f3bszlEKKtRklt69YTZgMRPFU0ap+BM5C0ap0wVP1Fms92F+solKrtFmRv9Li\nhWdW8T0B051biTXkH4C7wDGJfRFURlS7cS6NBnzI+Zl4xBnonEhMlILupT0AZQlwIq6C/xh3liOs\niSdjKfj4JePUg17IORrBZGQiDdxQ8hmmAawnUFvmKbhbeC2uMSWejKWA+xmnHiwlXJFGbH4zkQZu\n7IysAP9tAs2RUq3P0h/4v6mvGlM1wKb6BJnvtUs/jQg0kEJytaag2k9VZYX7MevIa3uhkUMDm6r/\ni5qqprZlROyC3sAOPinViWXVTf1VjtcO6GXOztUgsNTqb1KO7sphb2UD2AHVecO/C2Kl6kR05Py0\nnBsNqbXe8n9kZmuQ1tqPMmSew59jaWJ5ZSuQFbYBJ1Cqbsxz6eHh64O3ZZ+m2lwW59g0SFW962O3\nPL27837Y1repFdDcxAY2UKqVwfhG1D1cCzLJ04HuYVnPnL3kFVhAb1D6bgX3zi+d1dfh39t/RZ3X\nRi6zOB4qp6ynac3TD05agRc4ctdZIuBQgrr9ObqTrLF4ETbMzDKevjmUXWjlSX17e2QFze6bwApw\n5r6ivnTZr3qYz516nP8HymoXS6H8FGkz8AewLqkwVJgrOAAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( a_{0}, \\quad a_{1}, \\quad a_{2}, \\quad a_{3}, \\quad a_{4}\\right )$$" ], "text/plain": [ "(a₀, a₁, a₂, a₃, a₄)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a_list = sympy.var('a0:5')\n", "a_list" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABMAAAAMBAMAAABy/puxAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpmJdu8QRM1mu90y\nVKvMIHo8AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAcklEQVQIHWNgYFRWCWOAgFIBjg8MLCYGDAxs\nkQxMCxgmM9xjYGD6xsDtwLCdgT+BgXUBQ/4Btj8MrBcY8g0Y7jPwfGTgnsCQf4FhBa8MWBWHA+c+\nZqAoqwMD2xMbOXegWv4CqOFgEyBsJ5C5EMCsrMYAAPTDGWP7HMHDAAAAAElFTkSuQmCC\n", "text/latex": [ "$$a_{0}$$" ], "text/plain": [ "a₀" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a0" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAN8AAAAUBAMAAAD/+PVoAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n+AePwbYswN52dgAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( b_{0}, \\quad b_{1}, \\quad b_{2}, \\quad b_{3}, \\quad b_{4}\\right )$$" ], "text/plain": [ "(b₀, b₁, b₂, b₃, b₄)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b_list = symbols('b0:5')\n", "b_list" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "name 'b0' is not defined\n" ] } ], "source": [ "try:\n", " b0\n", "except NameError as e:\n", " print(e) " ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK8AAAAUBAMAAAAJsXDwAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nYQAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( c_{1}, \\quad c_{2}, \\quad c_{3}, \\quad c_{4}\\right )$$" ], "text/plain": [ "(c₁, c₂, c₃, c₄)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "symbols('c1:5')" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjYAAAAUBAMAAABsY2oSAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\natn7uO/zw//giNdMIahME57MRv+J/gPHYunWcSmpbgAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( d_{00}, \\quad d_{01}, \\quad d_{10}, \\quad d_{11}, \\quad d_{20}, \\quad d_{21}, \\quad d_{30}, \\quad d_{31}, \\quad d_{40}, \\quad d_{41}\\right )$$" ], "text/plain": [ "(d₀₀, d₀₁, d₁₀, d₁₁, d₂₀, d₂₁, d₃₀, d₃₁, d₄₀, d₄₁)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "symbols('d0:5:2')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## expression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 単項式" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAAJBAMAAAAWSsseAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAEHarIkSJZt3NVLsymT3i\nYlMAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABASURBVAgdY2AQUnZVU2BgTGBv4pjAwCbA9pDLgYGR\ngXMDAwjwKYCpcweAFJeAHgOTAEPcgn0M7gwMwkpC1wsYAB0ECeuXDPmiAAAAAElFTkSuQmCC\n", "text/latex": [ "$$x$$" ], "text/plain": [ "x" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "+x" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABoAAAAJBAMAAADeJiHIAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAEM3dMnarIkSJZlS7mYew\nZ0MAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABJSURBVAgdY2CAAsbQ9NapMA6DJMPiACM4byLDPIHt\nDELGIKDCIMCgA5cBMZ4i81ieIPE2sj5gCITxOV7zPGBfAOMxpgbGrmIAADZIDnWrpROlAAAAAElF\nTkSuQmCC\n", "text/latex": [ "$$- x$$" ], "text/plain": [ "-x" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "-x" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAD8AAAAUBAMAAADIGvgZAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIma7zZnddlTvRIkQ\nqzLsm4+cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyUlEQVQoFWNgYFRgwAkUQTLCOKUZGHgFgJKO\nQNx5AFMVxxwGBh4HBgamAAaeq/cxFZyN/QPUtJ2BgQ1kSj2mAgZ2kIKTDAxiQAq3ApYFDKV4FbAG\nMBjhVcDkwJCBVwFHAsMsvAr4PhBWgN8KrgTCjtwKdQPPFxADCYADinUDwzKgWOx8XwWGtANIsgwM\nrDe/XGJgYHkACWqQFAcozNEBMJyBkQUB3OiSID4wshgMoRLHoTQyBYpueIJRQJaBsplB1jIqAAkc\nAJjkAIi/M5gjUGHFAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left ( 1, \\quad 1\\right )$$" ], "text/plain": [ "(1, 1)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Abs(1), Abs(-1)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAAVBAMAAAC0+9ObAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAMhCJRHarImbdzVS7mbgs\npbQAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABcSURBVAgdYxBigAIhBhMY04QCpmpYSXAAUL8JA5MB\nx1TOBWAmswLzI+4CiCgD1wGgPRAr+ALgTDkBKJNbIY6BVQGswG/DOYYKiFq1UNUbDTBtQJVEMQPB\nCoFEIADzqxNO911KnQAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left\\lvert{x}\\right\\rvert$$" ], "text/plain": [ "│x│" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Abs(x)\n", "# RuntimeError: latex program is not installed" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 複素数" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEYAAAAQBAMAAABZ1xRdAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABA0lEQVQoFWNgwA0Yr5UdYGBg3oBVBddDsDDn\nAsYWoJoCFDWLIDzhyx/BjDoGhkwUeRAHqoaBCaJmMwPDegF0RWhqPjMwxC8AqxFSdlVTgKhGVcP4\nF6hGQegSAwNjAnsTxwRsali+MTCcT0iIY2BgE2D7yOWAVQ3QnPMpC24CzWHghARA5syZfTNnTgap\nhrgZbJciwyeQCL8CiAQBVPcwAN28fgEX2I/nD4AVYKrZzcBQL8BpIMDAJaDPwAQNBTRzgGF4k0F+\nQQIwBPYzuEMNQlYjP4GBYwHjG4Z4lgIGYSWh6wWoanjtfpozcBgwMCYpH2BgLoe5BELDzEEVReWJ\noHJhPABY3EO7gZ1I9wAAAABJRU5ErkJggg==\n", "text/latex": [ "$$x + 1.0 i$$" ], "text/plain": [ "x + 1.0⋅ⅈ" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x+1j" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFEAAAASBAMAAADRbS/HAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABS0lEQVQoFX2Qz0rDQBDGv21qTFOrS/oAXVvw\nJs3Nm/QiggcfwYTixVtOelMQHyBHc9s3qNCjB/MGAQUlVLAeBS9VFAQFJxsW0vTPHGa+2fntzO4A\ni409nsaAcbOYgP2qijXJrogMZklb5GfNh4kS58DJLJWdaBKVnBwCAz4XLZOfgCcLpNPZ2xIqL5Hs\nj0jh3INtCxxyMH/10grnkdVvIPH9I5j2GF3A5ObE7s0lqWdyLFMcNELcAgw1tTAziq7fosjN7uQ/\nUtM38QG+LsiTbYjMk5XeCfrRQNq0B4+v/WZAEmeerEzSxAteczlSVMZU5l1U8q2VSdp8ipb0MUSd\nXuXJO+yrltM9WyEsyd7hVQOM4AVAs+08UchM92zs/uzAcsH6nRjGGTH9l54itNOkzgsxLWiSrDed\n68wI2ZfWy6MV1MVyQldX2s8k/wHGhE54NVVosQAAAABJRU5ErkJggg==\n", "text/latex": [ "$$x + 1.0 i y$$" ], "text/plain": [ "x + 1.0⋅ⅈ⋅y" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x + 1j*y" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAAAQBAMAAABdIsRgAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAVO8Qq5l2zWaJ3SK7RPx7\nN2kAAAAJcEhZcwAADsQAAA7EAZUrDhsAAADgSURBVCgVY2DAANwz5wggBFkOMDAwKiP4YNZWBsYX\nYAZYhqWBwSTkMVQJYwKEkSfA8ArEQsiwoSu5dIH5OVgxXAbOgJkCtBtiEVwGzkAosZoAN8UsDMjE\nVLJzqQFcyYRLWJUwcOrClHALhMOVcJaXV6mXlzuA5RiUwMYAzWdmeAZXAmTA3LKbgeEcOOxATmAE\n+RfDLe8MkJSwOwANxFCiw8CwbgPIQpCMncAELEo6GBifMdgVQGTucTcwsDo99wBpQbiFNzTmAgOX\nA0SGpQMiCSFhzkUWQ2Mzgx2AJgjkAgCYpDzCnhDBhgAAAABJRU5ErkJggg==\n", "text/latex": [ "$$1 + 3.1 i$$" ], "text/plain": [ "1 + 3.1⋅ⅈ" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "1+3.1*I" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "sympy.core.numbers.ImaginaryUnit" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(I)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 多項式" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAADAAAAARBAMAAABp3DInAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAu0lEQVQYGWNgIAJwKeBQRKyEkLKrGsQMmA6h\nSwwsDxkYE9ibOCaADYdJJKxjYPrAwCbA9pHLAVmCZcFNBu4NDIwMnBtAwmwzZ854OXOmAQNQ5BED\nvwJQCEyA5GBGsX5kOH8AyAcTyBK8Exj0gMoE9BmYBEDicB3cBgybGRjiF+xncAeLwyV4N7B+Z2AQ\nVhK6XoAqwWim+wUiAiVhljMwAG1BBowOEJ4lg3wAsjic3c6wCc5GYQTpHmBgAABmTiJzFz7aNwAA\nAABJRU5ErkJggg==\n", "text/latex": [ "$$x + y$$" ], "text/plain": [ "x + y" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x + y" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAADAAAAANBAMAAAAdyPDHAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAApklEQVQYGWNgEFJ2VVNgQAZClxhYHjIwJrA3\ncUxAFmdIWMfA9IGBTYDtI5cDsgTLgpsM3BsYGBk4N4CEGWd0AEHnASCL4REDvwJQCEwAaThg/chw\n/gCQBybgokAG7wQGPQYGLgF9BiYBZHEGbgOGzQwM8Qv2M7ijiDPwbmD9zsAgrCR0vQBVgtFM9wuq\nCJwHtAUbsGSQD8AmztDOsAmrOEOQ7gEGBgBqECAhbGuYBwAAAABJRU5ErkJggg==\n", "text/latex": [ "$$x - y$$" ], "text/plain": [ "x - y" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x - y" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABcAAAANBAMAAACwSehuAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAjElEQVQIHWNgEFJ2VVNg1FVg8BNgYExgb+KY\nwMb1gEGfgYFNgO0jl4MX7wSG3QwMjAycGxgYBPgUGD4xAAG/ApCIF+D5A+KcPwAkbjIwPWBg4BLQ\nZ2ASYNjMwG0AlF+wn8GdgeE2Q3wBA4OwktB1EJV03wGoGgZuwhgMzBMYv8I5HAXcCnAOq9IdIBsA\nbTEaA7gEmncAAAAASUVORK5CYII=\n", "text/latex": [ "$$x y$$" ], "text/plain": [ "x⋅y" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x * y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 分数" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAALQAAAAOBAMAAAB0sisSAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAfI5NjwSNoO/AAAAAElFTkSuQmCC\n", "text/latex": [ "$$0.3333333333333333$$" ], "text/plain": [ "0.3333333333333333" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "1 / 3" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAAqBAMAAACXcryGAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAVO8Qq5l2zWYiibvdRH6G\nTkUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAB0SURBVBgZY2CAASEDIIvZ1Q9EMTDkUYMK0StpAJtG\nFvEOBB4QpXXWqo1AdZwBDHINDAxsDxn4DjAw8Ooy2BWAdYMEgV47BSI51wSDKAaGRRfAFJMyUGwC\nA/dDBga+x2CKaQMDz0sGBo4GBrkEoJKroXsZGAAuYx+6av2YygAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\frac{1}{3}$$" ], "text/plain": [ "1/3" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Rational(1, 3) " ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAApBAMAAADzOtVRAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAmElEQVQYGWNgEFJ2VVNgYExgb+KYwMAmwPaR\ny4GBkYFzAwMI8CuAqfMHgBSXgD4DkwBD/IL9DO4MDMJKQtcLwJJkEf/BgCytmJoYdRUY/AQY2Lge\nMOgzMHjxTmDYzcAgwKfA8AmoNl6A5w+QusnA9ABIbWbgNgBStxniQY4XTrrvAKRAsgwMzBMYvwIp\njgJuBSDFqnQHSAIAnCMf/cH6QSgAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\frac{x}{y}$$" ], "text/plain": [ "x\n", "─\n", "y" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x / y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 累乗" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAAUBAMAAAB/pwA+AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAfElEQVQIHWNggIDcvQJQFpsD8wQok8OB5wuM\nGcDyFcpkYOD6CGdyKMCZuXAW+wU4M4whBsrmmbVqI5TJ9///BwYGIWVXNQWwCGMCexMHxFI2AbaP\nXA4QUQbODWAGiOBXgDPPH4AyuQT0GZgEwJz4BfsZ3CHCwkpC1wvATAAvUhbC3/cGUAAAAABJRU5E\nrkJggg==\n", "text/latex": [ "$$x^{2}$$" ], "text/plain": [ " 2\n", "x " ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x ** 2" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABUAAAAQBAMAAAAL9CkWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAfElEQVQIHWNgAAPWZAYOAQiTgY1f4ByUyeAY\nwaANYzOYMRjB2a0Mb+DsHtYPcHaw9gQgW0jZVU2B0YG7gIGBMYG9iWMCc0IkUJhNgO0jlwNrWQKQ\nzcjAuQFIQQG/AozFwHD+AIzNJaDPwCQA4cUv2M/gDpUQVhK6DjQaBAB1cxLyJFHBUQAAAABJRU5E\nrkJggg==\n", "text/latex": [ "$$x^{y}$$" ], "text/plain": [ " y\n", "x " ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x ** y" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAACkAAAAUBAMAAADiqgm2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtklEQVQYGWNgwAA8EzCEGBh4LjegiTKD+Fzo\notyooqzJDBwCDAxoomz8AueA6tBEHSMYtDFFGcwYjBgsZ86bOVMB2bZWhjdY1PawfoCLPgCyICBY\nG+QjkG0sNz4rMDAIKbuqKTA6cBdARYEUAwNjAnsTxwTmhEgQB+wyEINNgO0jlwNrWQKIwwIiQICR\ngXMDhIVK8iug8iG88wcwRbkE9BmYBNDF4xfsZ3BHF2QQVhK6DnIqCgAAlVUeuLlUNuMAAAAASUVO\nRK5CYII=\n", "text/latex": [ "$$x^{y + 1}$$" ], "text/plain": [ " y + 1\n", "x " ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x ** (y + 1)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEYAAAAbBAMAAAAzEOSeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nu7BFAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left(x + y\\right)^{2}$$" ], "text/plain": [ " 2\n", "(x + y) " ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr_exp = (x + y) ** 2\n", "expr_exp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 展開と因数分解" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAASYAAAAcBAMAAAA+fA+WAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\left ( x^{2} + 2 x y + y^{2}, \\quad x^{2} + 2 x y + y^{2}\\right )$$" ], "text/plain": [ "⎛ 2 2 2 2⎞\n", "⎝x + 2⋅x⋅y + y , x + 2⋅x⋅y + y ⎠" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr_exp.expand(), expand(expr_exp)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMcAAAAmBAMAAACCM5LSAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nl6TJJPKIKHHbSWp+/nOS6j+mIsOzK+v2rAAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( \\left(x + y\\right)^{2}, \\quad \\left(x + y\\right)^{2}\\right )$$" ], "text/plain": [ "⎛ 2 2⎞\n", "⎝(x + y) , (x + y) ⎠" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expanded = expr_exp.expand()\n", "expanded.factor(), factor(expanded)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGkAAAAWBAMAAAAx2K8dAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$x^{2} + 2 x + 2$$" ], "text/plain": [ " 2 \n", "x + 2⋅x + 2" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(x ** 2 + 2 * x + 2).factor()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 簡略化" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFwAAAAqBAMAAADMuiG3AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n/wBK4GXzCqDQNAAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\frac{1}{x} \\left(x y + x\\right)$$" ], "text/plain": [ "x⋅y + x\n", "───────\n", " x " ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "complexity_expr = (x + x * y) / x\n", "complexity_expr" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIcAAAAUBAMAAABVOzPUAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nw4IzE1nxgkbdDI2exx+DAWin6uR33QAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( y + 1, \\quad y + 1\\right )$$" ], "text/plain": [ "(y + 1, y + 1)" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "complexity_expr.simplify(), simplify(complexity_expr)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 自然対数" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJ8AAAAUBAMAAABhQvLIAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRK5CYII=\n", "text/latex": [ "$$\\left ( \\log{\\left (x \\right )}, \\quad \\log{\\left (x \\right )}\\right )$$" ], "text/plain": [ "(log(x), log(x))" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ln(x), log(x)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAADsAAAAxBAMAAACWkMzmAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nOPGY/gJYabj2TbblbAAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\frac{\\log{\\left (x \\right )}}{\\log{\\left (y \\right )}}$$" ], "text/plain": [ "log(x)\n", "──────\n", "log(y)" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ln(x, y)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIsAAAAUBAMAAABPB9NaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nqAAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\log{\\left (x \\right )} + \\log{\\left (y \\right )}$$" ], "text/plain": [ "log(x) + log(y)" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ln(x) + ln(y)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAF0AAAAUBAMAAAAdCCxUAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nG2k5lpkW07V9L1rmhtC2rdDxPf4CdIhua6lw2lAAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\log{\\left (x + y \\right )}$$" ], "text/plain": [ "log(x + y)" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ln(x + y)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAF0AAAAUBAMAAAAdCCxUAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nG2k5lpkW07V9L1rmhtC2rdDxPf4CdIhua6lw2lAAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\log{\\left (x + y \\right )}$$" ], "text/plain": [ "log(x + y)" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expand_log(log(x + y), force=True)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEQAAAAcBAMAAAAq4AQbAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nqy524aWLb13cHn8AAj9hy2ElGC8AAAAASUVORK5CYII=\n", "text/latex": [ "$$\\log{\\left (x^{2} \\right )}$$" ], "text/plain": [ " ⎛ 2⎞\n", "log⎝x ⎠" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ln(x ** 2)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEUAAAAUBAMAAAApce1IAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$2 \\log{\\left (x \\right )}$$" ], "text/plain": [ "2⋅log(x)" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expand_log(log(x ** 2), force=True)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "asinh" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy.mpmath\n", "sympy.mpmath.log(2)\n", "import math\n", "sympy.asinh" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 代入" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABQAAAAUBAMAAAB/pwA+AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAfElEQVQIHWNggIDcvQJQFpsD8wQok8OB5wuM\nGcDyFcpkYOD6CGdyKMCZuXAW+wU4M4whBsrmmbVqI5TJ9///BwYGIWVXNQWwCGMCexMHxFI2AbaP\nXA4QUQbODWAGiOBXgDPPH4AyuQT0GZgEwJz4BfsZ3CHCwkpC1wvATAAvUhbC3/cGUAAAAABJRU5E\nrkJggg==\n", "text/latex": [ "$$x^{2}$$" ], "text/plain": [ " 2\n", "x " ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr_ex = x ** 2\n", "expr_ex" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAPBAMAAAAv0UM9AAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAMpndu3bvImbNiRBUq9OB\nhjcAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABESURBVAgdY2BgYBACYgYGExDBmgIiK6aAyAUgkqMA\nRG5lAJELQCSPAIjcxQAiz969++wqUIIBrIvhCYi55N0NEMXAAABbkhBrtxdTYQAAAABJRU5ErkJg\ngg==\n", "text/latex": [ "$$4$$" ], "text/plain": [ "4" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr_ex.subs(x, 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 無限と極限" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGQAAAAUBAMAAACJ7oWmAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\left ( \\infty, \\quad -\\infty\\right )$$" ], "text/plain": [ "(∞, -∞)" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "oo, -oo" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFQAAAAUBAMAAADhHQeeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\left ( \\infty, \\quad \\infty\\right )$$" ], "text/plain": [ "(∞, ∞)" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr_ex.limit(x, oo), limit(expr_ex, x, oo)" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEoAAAAUBAMAAADYerbFAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIma7zZnddlTvRIkQ\nMqvFy5UvAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABP0lEQVQoFX2Sv0vDUBDHP0mpCU3EgOBqBjcV\nqpuTdROhkKWToE7SsYu4dnK1a/sHOFfFUchQFXFod4dUnBzcir8H79oUW2LyhXd3fO/L3b13Dwyf\nbJie5Ofh5uI6S/gkyS3Y5lb1aeiAGWA2cEppEuGdGjMeuT72T4bKbbAAc30KH0lVqNTQ7HAE3YDC\nu1KTcF8+fbjcqwlZYR0W28x+Tyo0zvWsAZ06jxIvURVV8I9qFU6LZbmd3P6EVkpH6eS8aTsfIlXJ\n9HZiehVsqpETacdcETPxEirY+AJXap3p9PKq+ZKQU1gB67zpYXk6/ZXkqtz33MGUiDySilosC70r\n1eDh+BUOQ4n+4Fae67j7zbZQZd3QCPY4GCtDDdQYB7rtEZzYJ51sm7WYvkumY0Z+jv7CIfzYJ53W\nMXwxWZAd/QLTqkKvhIWc+gAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( 0, \\quad \\infty\\right )$$" ], "text/plain": [ "(0, ∞)" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "limit(expr_ex, x, 0), limit(expr_ex, x, -oo)" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMIAAAAyBAMAAAD8XRkbAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrkJggg==\n", "text/latex": [ "$$\\left ( \\lim_{x \\to 0^+} x^{2}, \\quad \\lim_{x \\to 0^-} x^{2}\\right )$$" ], "text/plain": [ "⎛ 2 2⎞\n", "⎜ lim x , lim x ⎟\n", "⎝x─→0⁺ x─→0⁻ ⎠" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Limit(expr_ex, x, 0), Limit(expr_ex, x, 0, '-')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 微分" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFcAAAAUBAMAAAAKKrydAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\left ( 2 x, \\quad 2 x\\right )$$" ], "text/plain": [ "(2⋅x, 2⋅x)" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr_ex.diff(), diff(expr_ex)" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC0AAAArBAMAAAAebRy0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMrvvmVREEIndzSJ2\nZqtw62vAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABGElEQVQ4EWNgAANGZQcIA53kD0AXgfDzC7CL\nd2IXZliCTZzb4+BXbOLJG5i+YxFnt2VgWYBFnOU7A2cDFnFmBYb6BCRxDid3MK++gSEeSZihm+EV\nRDyAQYt1A0JmNoM8mMd1gHceB0KYYRrD/gQQl/1N475jSOIMDPE4QmUOiio4h8MBzkRhXEHhwTls\nDWwCcA4SQyo0CM1e9jOvc3oY7P//R1IFYlYw3DwwC00MxG1n6C+IxiJewLAIJvofAT4Axf7AxFFp\nxo+ofCgvnOcDw3FMGbavTB+4L2CKs785fuQupjC6yAAmWkgAozgInGgxAxiSaDEDGJJokQIYahgs\n0aIHMDTRYgRwPTjRYgYwONFiCWBwosUMYADzqGBAhq3jCAAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\frac{d}{d x} x^{2}$$" ], "text/plain": [ "d ⎛ 2⎞\n", "──⎝x ⎠\n", "dx " ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Derivative(expr_ex)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 積分" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGkAAAA1BAMAAACw4NiFAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n3AAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( \\frac{x^{3}}{3}, \\quad \\frac{x^{3}}{3}\\right )$$" ], "text/plain": [ "⎛ 3 3⎞\n", "⎜x x ⎟\n", "⎜──, ──⎟\n", "⎝3 3 ⎠" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr_ex.integrate(), integrate(expr_ex)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFMAAABGBAMAAABCh7UbAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHaZZiKJVKtEu+8y\nzd3blrGjAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACfElEQVRIDe2VT2jTUBzHv4lt2sT+CRVGQXDZ\nCsVbK05BUQxMPM6gXjzZVcSbq4chDGHdwIOIWAUPelnPTmxRBuLFIHhQkVZP4mVloKBQ7RRWFbVm\nJi8vf2jyroLv8vt+f9/Pe7zml1DAWlxORTRfITaoZm8ta5PakyCEZAqk+0WIGvEBVQVWZYDlBgZ6\nr4NELeA0El3ElutdeRuxQTVy+gBGugtByL+a7Z1mvTm/8JAVHa2tsaIFVhD4yIxGvzCj/HdmVFpn\nRtNNZrRVdaHC/l0u7zQFxelwBldd3mka7i/gHVqaM3bqgex0+IBT7r00Tfym2lTz7r00jnyj2lRD\n34i4d1hC0dzx/IH3jJR3WJOE6BNB6qhnWGJJ1P9moicA5ptkk1lfXpgzf5bQcQfATN3deTwYmI2k\ndWcar5aI5sYv3SgTc7zcqiCz82ReIR1gUCF6BFNK1zLiChoyV4qspdokRnSgET2NGXnWMttVHIQg\nC+sxO0bMupmByHhLduGQjPfgkKzbHUD45TB0Go/AbT7vtOJIpa/UJH4SzW0g1jNMSycdo26lMznP\n9zBmRlwfUns2JhfAyzZMhyX2pV5UtYLXmKqWlioNnLBJLDWJ5hbHcoeJyeafLtay45kJlXSAQpXq\nEHVNDQFo/FmnOkTRCYSASPwII+yc37BlmIh7P5fhG1Kb42Nb6TYbZ1CtEjN6VGdGrzCTYH9Wov0y\nh5wudOL1EITEUvOFRnRIjZbvhhD/Y+cTyEwAx846O8M0d/n2SmRPQhmWO/o8sJwDbjpafjl3x1hy\nBEgafyQxf+7rGKj0CXjmC/yNmI59O15xRX/i7xzZrXPn3sj+gHb+AHvGg9vrbB+AAAAAAElFTkSu\nQmCC\n", "text/latex": [ "$$\\int_{-\\infty}^{\\infty} x^{2}\\, dx$$" ], "text/plain": [ "∞ \n", "⌠ \n", "⎮ 2 \n", "⎮ x dx\n", "⌡ \n", "-∞ " ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Integral(expr_ex, (x, -oo, oo))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 多変数" ] }, { "cell_type": "code", "execution_count": 58, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEIAAAAYBAMAAAC8bzZKAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABG0lEQVQoFWNggICkywJQFgqFEOYt4N2AIgXh\nIAnzJrB/wKYCWRirGQwMSMJyB7CYwcCAEGaahFUBsjCScchqkYR5fiFLwNlwYbkDLN8holwKcFmQ\nK2DCDBwO7A+xqEAIM/AkJTtgUQERFlJ2VVOAyIJImC1ClxhYIMYyJrA3cUzAVJGwjoEJEsxsAmwf\nuRwwVLAsuMnADYkqRgZOCAOkiG3mzBkvZ840YGBgZHjEwK8A1QhngPkwd7B+ZDh/AKoCzkBRwTuB\nQQ+igEtAn4FJAKoYSMHM4DZg2AwRjV+wn8EdoQCugncDKzSUhZWErhdgUcFopvsFSRiJCbMFmHgm\nIAkjMRkdIBxLBvkAJGEszHaGTVhEkYWCdA9AuABJTDpRft+dggAAAABJRU5ErkJggg==\n", "text/latex": [ "$$x^{3} + y^{3}$$" ], "text/plain": [ " 3 3\n", "x + y " ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr_ex2 = x ** 3 + y ** 3\n", "expr_ex2" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAM8AAAAcBAMAAAA0BfbtAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\left ( y^{3} + 8, \\quad x^{3} + 8, \\quad 16\\right )$$" ], "text/plain": [ "⎛ 3 3 ⎞\n", "⎝y + 8, x + 8, 16⎠" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr_ex2.subs(x, 2), expr_ex2.subs(y, 2), expr_ex2.subs([(x, 2), (y, 2)]) " ] }, { "cell_type": "code", "execution_count": 60, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJIAAAAcBAMAAAB47/sVAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( 3 x^{2}, \\quad 3 y^{2}, \\quad 0\\right )$$" ], "text/plain": [ "⎛ 2 2 ⎞\n", "⎝3⋅x , 3⋅y , 0⎠" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr_ex2.diff(x), expr_ex2.diff(y), expr_ex2.diff(x, y)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHEAAAAUBAMAAABIac8KAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrkJggg==\n", "text/latex": [ "$$\\left ( 6 y, \\quad 6, \\quad 6\\right )$$" ], "text/plain": [ "(6⋅y, 6, 6)" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr_ex2.diff(y, y), expr_ex2.diff(y, y, y), expr_ex2.diff(y, 3)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVwAAAA1BAMAAAD/tE45AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAElFTkSuQmCC\n", "text/latex": [ "$$\\left ( \\frac{x^{4}}{4} + x y^{3}, \\quad x^{3} y + \\frac{y^{4}}{4}, \\quad \\frac{x^{4} y}{4} + \\frac{x y^{4}}{4}\\right )$$" ], "text/plain": [ "⎛ 4 4 4 4⎞\n", "⎜x 3 3 y x ⋅y x⋅y ⎟\n", "⎜── + x⋅y , x ⋅y + ──, ──── + ────⎟\n", "⎝4 4 4 4 ⎠" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr_ex2.integrate(x), expr_ex2.integrate(y), expr_ex2.integrate(x, y) " ] }, { "cell_type": "code", "execution_count": 63, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQYAAAAyBAMAAABMh2gAAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nHWMP6/cfHS5GHRO1E1gAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left ( y^{3} + \\frac{1}{4}, \\quad \\infty \\operatorname{sign}{\\left (y^{3} \\right )} + \\infty\\right )$$" ], "text/plain": [ "⎛ 3 1 ⎛ 3⎞ ⎞\n", "⎜y + ─, ∞⋅sign⎝y ⎠ + ∞⎟\n", "⎝ 4 ⎠" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "integrate(expr_ex2, (x, 0, 1)), integrate(expr_ex2, (x, 0, oo))" ] }, { "cell_type": "code", "execution_count": 64, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAASIAAABMCAMAAAD+6UoaAAAAM1BMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADxgEwMAAAAEHRSTlMAmUR2zTIi3Ylm\nu+9UqxBOBCjCdwAAAAlwSFlzAAAOxAAADsQBlSsOGwAABplJREFUeAHlXNtihCgMFVHBC6z//7VL\ngg630NG2Q9ytDx3ETDgcSQiBaddVr3GoPvqrD0Qf93wURsX3f6o8GbK7Mh8029+lqDOa4Gjcp6z2\nL1Nk18SkPDOq4O1ZFFkpZkA6Sb1l7/ITt/Nqc7W6tKpHUWRN3y/r1M1i6kaZo//A/ZC7o2nHV5Q0\n9SiKkJVllQIg9rlPSHD/zk2/j6miZU3v4e5RFPk3OOx++LcwtSGdvkZiED2RokWhPxgJX1q+4h/W\n9HvyIqhB1G3EyPphs9//+gbDXvRWDbazaG3f13Xxm/51HMLTXkxn3STUblr4xYuAZy2Eo8lqNZhi\nsrmo457YvEeDVRQx0T1l/09puy+hY3s544eHf7e0hJGz7Q8yqAe9kYgXE9h6EMAHQAnWtVenLqF1\nG9d4nY+WkIZz7Gx7bRKVxq55HH69Mx+RbApJnx7IpDFS6Jl1s556lptqC2ncjwhbHVF94OYoyb2o\n4q5oDGn3DNiqK1JRXMDNzdF+Y0iDX8v2cYQUMzGdlhhX8pZbQxJ+7aqJ1QcSIeMAnJeas/XWkOSO\ns9VCrfIB01LzUSfg9p+tIfU+Mlrz3NHZ86qPOgXaf7aGZL2/3iuDZfSDjOBBS3F9sX1LmGgsrmoP\naYfgcTomthgKlmXNW0OaXVyd7G4JFxiyivaQVvDHfW3wLjVvLVxyab4aMt0SzhgpbttDGsBRz2cE\nmQOqGSDKXR5FIH1LOIcR37eHZGC615WwaAzL3BilL9s12x4oRULNLeHwtbLEAEmAQ8Y/JRw3uuoL\nWDncWLndEiaAhCoGSDiAlgoVpuatEfIt28mEx2WtpRYCHVSJAZIGNzRUUiGq5q0R/FjLDlBdK4Tv\nfDlSyABJgrsZ6PWHC5oqyTR0Lfnu7VaxPFK4r6mO6CCKHJCQIkVTtNViga5TLprKTwXUKCKFifMD\nBCNFFQekGWhQtM+pTXQO+KilNtmuepUiSnj4nivigLRBYL3SFOX2Z6U0Uy91xaBSitxBF5CbygMo\nk9DSu6Y3CosxVLqENxp+BdJBUXkmxOHbU5dqIaJ2SVqVngV4dSTFo/1md5ki7N3xF59BeKfwpTkU\nOCD1MIqyhg9EbuWWmBJshGjnZbekNsBPKJq2TgCVS76Qsyu8Dnz2TmFQfZZYIDmKrKOIsh0cYCc4\n9wmz25D3GJ/rAS614oePNp3wCkoLzQKnMjwPV1eIWok/LJD+8RRRhoYhU4az6HH0PBlFsDZ2FIxF\nImoFkmETw19fKYx0H0UWSCNQtJJJx6UMKMseR93IKEJbkvkOpsX4YjuTBF8qjHQfRRZI6IvoSX9N\nvXW32Q6drwQDIa6MogUsDv/EshaVLgN4tHcK4+/5Mgukg6LybJEzBvQaL5xwYmtxb3+ijBKkMopg\nVdaXwxNWv7MynXYPI4W2lo95te8KbSGdLSNFeQCED/M8mzVSwqneGkM5Rda4fGw6J4Jep0aPk5E9\nlCKFSlUG54nUfTaGdLSMcwRh4p0zqnomJIIditkoggfoj4LEl6VaLBF9qTUk3zQuQEiKTGkkEVqi\naJN4ybioKExchHheRdh6LtIakm8fl7GGGjCqmK9zxF/eK2eQCxVuVb5lL8g2hnQgxUhDUInZ2q5I\npYt5dS8lHN28fFVdXKShMaSjZWRHEhSNRF2ElqPIBAltbCNmXEnnkDioOdtkgrQAEyOROzOvNcKJ\nkP2TCdIA0a4LyYr+q7KqkGlcwQTJH3jI0h7QdcL2GjNSNMcD6Qjpy32F8XmuiAmSW+jDyypjsvln\nUVExAn6hggnSsZsvi7yHybMYv9DHH6pggqQ9N6+Ts69ePM/OOiZIC6ZvIHv9IgcLxU8e08ccd1yQ\n1JGtOD+h77ALaMgcNQcz2CYjpNd5ax0t693PG0fYyHnQxQhpO5f48cHrScvlzgK0AZWMkMJPP9bM\nGTXo93+jiUCMeF4c9AgKp5Dw6OMp1W3bX8gBNu0CFyR5TPnQ2TXEirPjZ7uZuP4wX2yQhkCLy+af\nG6SdglK6Q/RhBt6q54KUrAvtObm51AjMZ2vyfw7e9uGzAmyQ/AmEs3Nw6AMv/1+MID3/mIsLUhg3\nSIXfbXfFEbl61K89uSDJbKtUHsPIvzI8+vKUYcQFqTj5vPqZ3ht+8N4P4IkJ0nz6nhcF21HDNX28\ngJQFFkiWOPx0rO/h30w9LC5igQR77sWl/EyvhRbvz2kU3/5kBQOkPvPVvntjeQT4k/1+tm407hJi\ni3/iVrb6yBp35jdc/wIwOTt4+kqtZwAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( \\int_{0}^{1} x^{3} + y^{3}\\, dx, \\quad \\int_{0}^{\\infty} x^{3} + y^{3}\\, dx\\right )$$" ], "text/plain": [ "⎛1 ∞ ⎞\n", "⎜⌠ ⌠ ⎟\n", "⎜⎮ ⎛ 3 3⎞ ⎮ ⎛ 3 3⎞ ⎟\n", "⎜⎮ ⎝x + y ⎠ dx, ⎮ ⎝x + y ⎠ dx⎟\n", "⎜⌡ ⌡ ⎟\n", "⎝0 0 ⎠" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Integral(expr_ex2, (x, 0, 1)), Integral(expr_ex2, (x, 0, oo))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 累乗根" ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPEAAAAyBAMAAAB/mSAgAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n", "text/latex": [ "$$\\left ( \\sqrt{x}, \\quad \\sqrt[3]{x}, \\quad \\frac{1}{\\sqrt{x}}, \\quad \\frac{1}{\\sqrt[3]{x}}\\right )$$" ], "text/plain": [ "⎛ ___ 3 ___ 1 1 ⎞\n", "⎜╲╱ x , ╲╱ x , ─────, ─────⎟\n", "⎜ ___ 3 ___⎟\n", "⎝ ╲╱ x ╲╱ x ⎠" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sqrt(x), root(x, 3), root(x, -2), root(x, -3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 円周率" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAwAAAAJBAMAAAD0ltBnAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAdpmJMlQiZrurEN1E71u8\n6TcAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAA+SURBVAgdY2CQe/fu3SMGZpPAdLEEBlcGM0YHBiBo\n4FwAJFkmcIM4TAV8IN66BXwHgJQ0A68BkGpn4DRgAADO5AwIf9stDwAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\pi$$" ], "text/plain": [ "π" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pi" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "sympy.core.numbers.Pi" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(pi)" ] }, { "cell_type": "code", "execution_count": 68, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKAAAAAPBAMAAACRq9klAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIom7VJlmdt1E7xDN\nqzIhoty3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAACv0lEQVQ4Ea2U20tUURTGf3NzbM7MeAiMiKBh\nYioCU7CHyhcJ6iEIB2keupiHHhKE0B7Eh6SkXhPnJXoJTJTIEjwEUXRBKUgixAlSu4mD4LOXLPJ6\nWnvvGfEP6MA5Z813vu/ba6299sDO5FG2XXOFeNSdq8Wqr7DxZarz4D94BDSoBdEb8XNY7ams4cS7\n6pNJnic/gy9NnaNNzrjqdUduFQ15S/DK8fXyFv8K1kcuGdAIIp6XIARfDKfE87wN6xF7bMLLlHWK\niTUxowzDfYXo3ZQN32GCH/CEQJpqUKARRCuuw2nYazghIediD4ml2THA8Ig4wS1luOt9IcopaB0q\neQwz+R5RiEZuI4ipn/vhpeH4pSf5shH8CwovlKwNE9sNrV+yTH7cFcMTiqgNjUAb9tRwwHAEvM9w\nFeFNiazb8pBLGZbYRcPJpsswKBlm5VO3uz7bJoEGtSB2tS1PzLvibHGqiEiGK7Irhy5qP234gqJh\nDfuyUi/jjlS5ZK079IMGtSDg+kRbue4WOX5H1Rv9o7wOqyRMhoktQwh0Em0NVtZCac7yXC5IBQos\nCo4R/NY9UOQMCz7KyWV5EXmqnirDYH6bYWgRmm5W5iEDf6FFravAgqDRvkZ41S1wOgQvaZ/dxGcT\n0LbK8BlFw5jph2ywSzgNd8XQ0aAR/FTd7YX5WjESjp5fiK1RtrbN8Oz09OqUzlUaHFoTLmNwSlaV\niWzJatAIBqHx9YI4OIZjbSgy0RyRKkpVGaaH0GciOQSlIzTb8UXiacL2vPRQnYzSESPQSUuGAVtz\niP+WinuZtylxqGu1ZIL1LoOMnorkgDXbdLhvHHYnU1+JJax+A2oB5Ur+QBpoOATFMPzJ+iDqe5nj\n0AUNQ2OODL83aaLyCpkmf+a8DI7nyZakGvKgQS3w1U+4xCfkz0Fz8MlQkcpk5fmfr3+ITQ1tVgAc\nvAAAAABJRU5ErkJggg==\n", "text/latex": [ "$$3.14159265358979$$" ], "text/plain": [ "3.14159265358979" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pi.evalf()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 三角関数" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYMAAAAUBAMAAACdXkxuAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRU5ErkJggg==\n", "text/latex": [ "$$\\left ( \\cos{\\left (x \\right )}, \\quad \\sin{\\left (x \\right )}, \\quad \\tan{\\left (x \\right )}, \\quad -1, \\quad 0, \\quad 0\\right )$$" ], "text/plain": [ "(cos(x), sin(x), tan(x), -1, 0, 0)" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cos(x), sin(x), tan(x), cos(pi), sin(pi), tan(pi)" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJ4AAAAZBAMAAAAyHoooAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrkJggg==\n", "text/latex": [ "$$\\sin^{2}{\\left (x \\right )} + \\cos^{2}{\\left (x \\right )}$$" ], "text/plain": [ " 2 2 \n", "sin (x) + cos (x)" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cos(x) ** 2 + sin(x) ** 2" ] }, { "cell_type": "code", "execution_count": 71, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMkAAAA2BAMAAACfLKD6AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nYII=\n", "text/latex": [ "$$\\left ( \\frac{2 \\sin^{2}{\\left (x \\right )}}{\\sin{\\left (2 x \\right )}}, \\quad \\frac{\\sin{\\left (x \\right )}}{\\cos{\\left (x \\right )}}\\right )$$" ], "text/plain": [ "⎛ 2 ⎞\n", "⎜2⋅sin (x) sin(x)⎟\n", "⎜─────────, ──────⎟\n", "⎝ sin(2⋅x) cos(x)⎠" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# only tan\n", "tan(x).rewrite(sin), tan(x).rewrite(cos)" ] }, { "cell_type": "code", "execution_count": 72, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAARkAAAAUCAMAAACOJ7lPAAAAOVBMVEX///8AAAAAAAAAAAAAAAAA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\nInT6h9CmAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left ( \\operatorname{acos}{\\left (x \\right )}, \\quad \\operatorname{asin}{\\left (x \\right )}, \\quad \\operatorname{atan}{\\left (x \\right )}\\right )$$" ], "text/plain": [ "(acos(x), asin(x), atan(x))" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acos(x), asin(x), atan(x)" ] }, { "cell_type": "code", "execution_count": 73, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAARwAAAAUBAMAAACt/p8KAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\left ( \\cosh{\\left (x \\right )}, \\quad \\sinh{\\left (x \\right )}, \\quad \\tanh{\\left (x \\right )}\\right )$$" ], "text/plain": [ "(cosh(x), sinh(x), tanh(x))" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cosh(x), sinh(x), tanh(x)" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAATsAAAAUCAMAAADFj2qiAAAAOVBMVEX///8AAAAAAAAAAAAAAAAA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\ndKn0WyMAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left ( \\operatorname{acosh}{\\left (x \\right )}, \\quad \\operatorname{asinh}{\\left (x \\right )}, \\quad \\operatorname{atanh}{\\left (x \\right )}\\right )$$" ], "text/plain": [ "(acosh(x), asinh(x), atanh(x))" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "acosh(x), asinh(x), atanh(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 自然対数の底" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABMAAAAQBAMAAAAG6llRAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAEIl2mSJE3e9UMqtmzXCQ\nkgMAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABlSURBVAgdY2AAA2Uv6wUQFrPAXvYECJOL4Q6EASKf\nwplcD7ig7DimAiYoU9pMWRHIZFQ2CYCKpAewKkCYrJ0MIgsgTO4e44MQFgPfBiiDgYFPAc7kADIN\nIDzmCwwiMMNMbA5ABAE+RA6ieYoxNgAAAABJRU5ErkJggg==\n", "text/latex": [ "$$e^{x}$$" ], "text/plain": [ " x\n", "ℯ " ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "exp(x)" ] }, { "cell_type": "code", "execution_count": 76, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "sympy.core.function.FunctionClass" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(exp)" ] }, { "cell_type": "code", "execution_count": 77, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPwAAAAUBAMAAABbkk27AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\npaStFdnMvVCHm2L62PoXMI9D0GKMF7QAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left ( e, \\quad e, \\quad 2.71828182845905\\right )$$" ], "text/plain": [ "(ℯ, ℯ, 2.71828182845905)" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "E, exp(1), E.evalf()" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(sympy.core.numbers.Exp1, sympy.core.numbers.Exp1, exp)" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(E), type(exp(1)), type(exp(2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 符号関数" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAALAAAAAUBAMAAADfFKqVAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nt5xB0gv4cwjhBU1I9Nf0F9GblATQz8uSAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left ( -1, \\quad 1, \\quad \\operatorname{sign}{\\left (x \\right )}\\right )$$" ], "text/plain": [ "(-1, 1, sign(x))" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sign(-2), sign(2), sign(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## テイラー展開" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMQAAAAwBAMAAAC8i8hXAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nYII=\n", "text/latex": [ "$$1 - \\frac{x^{2}}{2} + \\frac{x^{4}}{24} + \\mathcal{O}\\left(x^{6}\\right)$$" ], "text/plain": [ " 2 4 \n", " x x ⎛ 6⎞\n", "1 - ── + ── + O⎝x ⎠\n", " 2 24 " ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cos(x).series(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ランダウの記号" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAADoAAAAcBAMAAADCYLEwAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\mathcal{O}\\left(x^{2}\\right)$$" ], "text/plain": [ " ⎛ 2⎞\n", "O⎝x ⎠" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.O(x ** 2)" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAOBAMAAAAPuiubAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAIpm7MhCriUTv3c12VLge\nopIAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABOSURBVAgdY2BUMnZgYAhjYH/BwJDKwDCTgWEWA0Oe\nA8O+ABAJBOsCgATHcxCTKwFEKoEIHgUQeYmBUYCBRYGBR4BBqrwoi4Fh37t3rxgAK5QOlzv7snYA\nAAAASUVORK5CYII=\n", "text/latex": [ "$$2$$" ], "text/plain": [ "2" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# ?? \n", "sympy.O(x ** 2).getn()" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAADoAAAAcBAMAAADCYLEwAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\mathcal{O}\\left(x^{2}\\right)$$" ], "text/plain": [ " ⎛ 2⎞\n", "O⎝x ⎠" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(x + sympy.O(x ** 2)).getO()" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAB0AAAAqBAMAAAC9wk0pAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEM3dMpm7du8iZolU\nq0RaI+fpAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAp0lEQVQoFWNgQAKuSGwQ0wyVz96Gyp+lhsrf\ngMrnmoDKF2dA5W9A5fM4oPKlGVD5Z+/e/XEd1cI2VC7DN1T+tv+3UAUGgidkDAIqDAz/QeADDZ0w\ne3cOsumcAQznFyAJsP9h4DdA4vP1McgrIPGBTBT1DAyM1ijSnJsDUfgMDDseoApwNCLxOScwsP1B\n4vN/ROVzJDAw/0SS51rAcL4Aic/wNDSPgQEAvEknuB6P3L4AAAAASUVORK5CYII=\n", "text/latex": [ "$$- \\frac{4}{3}$$" ], "text/plain": [ "-4/3" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(x**2 - 1).invert(2*x - 1)" ] }, { "cell_type": "code", "execution_count": 85, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAB0AAAAqBAMAAAC9wk0pAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEM3dMlTvq5l2ZiK7\niUTiBfEGAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAfUlEQVQoFWNgwA3CBJDlGCvqUfgMDPMHN789\nX30BsgcGhi1kDAIqDAz/QeADDR2xo+cIsumMBQz3HyAJsAswsCUg8dkMGNi/IPGZPqLygVLMH5Hk\ngcz3F1D55qhcjgZU/gxULmsDw25kEQ8GhtlIfG7bu+0GSHwmYHAZMAAAbgMkLgI1UYUAAAAASUVO\nRK5CYII=\n", "text/latex": [ "$$- \\frac{1}{2}$$" ], "text/plain": [ "-1/2" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(x - 1).invert(x + 1)" ] }, { "cell_type": "code", "execution_count": 86, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# sympy.plotting.plot(x**2 - 1, 2*x - 1, (x, -5, 5))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sum" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC0AAAA6BAMAAADW582KAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nTkSuQmCC\n", "text/latex": [ "$$\\sum_{x=1}^{y} x$$" ], "text/plain": [ " y \n", " ___ \n", " ╲ \n", " ╲ x\n", " ╱ \n", " ╱ \n", " ‾‾‾ \n", "x = 1 " ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Sum(x, (x, 1, y))" ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHgAAABABAMAAAAjY64hAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdlTdIu8yic1Eu2ar\nEJk85eg2AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAD4UlEQVRIDZ1XPYgTQRR+2fzsXnKbxEJEEC9w\n2AkXEQsLvUW0EMHESizkUlqZXGGn3KqFgsVdY2uuFEGMitgIF7ERFC5XaKUkIGihclHP8/dc3/y9\n2bvLbkanePPN+75vdiYzO7MB0OUMQGK6oduGaAvTnX0C8BB2G1luaJVV5ngcYD8UOjofjbJF4o7U\nOBwHdxXSJUrHAPcUkXsEGofMCiRblI4D1z3J2r4AaF6DpB6QpAdWeemByhyZVyBtZnY/yz5vyZrP\nuSB7krnI6pxgrFUyG//aAF0xQseX5l0AOw3XGcBe4656S5iPTz4G+91H2dOwKvWLKxaH6QbzV1na\n/T2YHJYd81CR+zFMNpjvNjCf7Q8mh2WdKioK/jDZYN5mK9xkj/+PMvIJTTNzzDkb6MKyw4v7EzWz\nHSacCGqsgtdHH0195Who2IeKL1w1GpSVOjdZUjC2XvQgxZ6OZVIvN71ugomKMy2w/giyHrRI9ZZQ\nHFhoQEL+PLlghZQJQnGg2Ya82OAAd8Tk4+RwsXO2JALKKj5k1e58EfRijYycCr7JgI1CFRw12pFA\nnSzRfVx57AHwwMx9SIuXGhszX/mKR1sB2ozkAWt0ol8WJ/AVjKrbjOAB6+RKyOxO4YSoLO04uq1I\nLQme3cVV5AET68y4RedI7TZye5I+NSW4zY5pHjDhrEKXhg354DSp7Y69ZnnUJJAtI+SBrVO3SgRM\n6nG74MxrQqM8WxweNporB7QKCsVQQ8BRH+wfPLA2e7IeNmz1hIjHei3UEDDtQ36NB9ZGs14qGFFX\nBzJWZwwSHeGhmMef2OeBpZx15nqJZNAs3YFj4H7XGUSpHjzweGBp/LX1k90TIeWrLUvvWwB71z/8\n+Hm8UHhAaRK/BGh7Ou2QWULL25xTGdwkSTLfVNlQbYfwRpjuQ1b9SrZeJ4t0S4Q2A5xwXr2IDzzi\n7xHCaUeWbpmOodA6jVQjDWGiPg+W3JKVkiLc5Z6CsfVEDzLiyHVPKuGhRXn+q0RUPdZS+8D5fpWX\nfXjrGJyErMPlGp72vOdlfVUFZncVzMoOuP9fAxvgRNxyxHSYYVdNpR2jiKESbIOkyzGKGGq0j6St\nTn0lzPgKxdbpeaRTcpcoZeaD2VCaRea4rGyylt/9G7KbmosdllqorScMzeJeLzTQPP12h+rDzJwT\nrzL7fk10nibnnrINit8KRnNW38r4TmTgGo3dzNyUA11gU9cLZmY+KB+WxEln+hngwy6aDdtSRx/+\nIarYZTrrrCrNIBqkW4q7D6+2T1+QrdSb30VFRNfPiRrtETQEubIWXtLQDB3xtO6lhmboMJf9BcIS\nFzgyOy2qAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left ( \\sum_{x=1}^{10} x, \\quad 55\\right )$$" ], "text/plain": [ "⎛ 10 ⎞\n", "⎜ ___ ⎟\n", "⎜ ╲ ⎟\n", "⎜ ╲ x ⎟\n", "⎜ ╱ , 55⎟\n", "⎜ ╱ ⎟\n", "⎜ ‾‾‾ ⎟\n", "⎝x = 1 ⎠" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Sum(x, (x, 1, 10)), Sum(x, (x, 1, 10)).doit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Product" ] }, { "cell_type": "code", "execution_count": 89, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC0AAAA6BAMAAADW582KAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMARImr3RAy7yJ2u81m\nVJmVTLLvAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABRElEQVQ4EWNgAAMhAwZXCAuVVPjKVoAqAuZx\nBDpwLsAizsCswDwBmziLAHsCVvEEeWzCDIyWq7GKRzCswSpuxLgBq7iMElZhWgqy/0eAb0gWcQj/\n/9UBAuf/701AEmdgWP8ZzL3/PwBFmEEfKv4FVXioikdObpwEThyo/mJV4PFkAcceqjhTANNX3gaQ\n11HFWRm4F4BE0cUZGPjBpmOK5yeAlaOZwxswn4ETHOKo5stfWM/QA9aAKh48M/LNASziELNBJKp6\n+omvhyQQfdT0w5H3///CBgbWpP//9zYgHMMATp8fGLhAqRQ5fSIpoTWTDRzdGLawPXbAEAML8BIj\nrvlscgJUO7J6zgBrFgHr3UBwgAFZnI1hD1Q1A4o4A8MP7OJsH9gYwOZMQFHfz+TABNPAWwBjMTAE\nT9RUhfI4nnyeAJMAAK2Nm9C8LNKFAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\prod_{x=1}^{y} x$$" ], "text/plain": [ " y \n", "┬───┬ \n", "│ │ x\n", "│ │ \n", "x = 1 " ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Product(x, (x, 1, y))" ] }, { "cell_type": "code", "execution_count": 90, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKwAAABABAMAAAB1mYESAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nseqqQbWThkv42lWDajMC8C+32pl/IJAUwgAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( \\prod_{x=1}^{10} x, \\quad 3628800\\right )$$" ], "text/plain": [ "⎛ 10 ⎞\n", "⎜┬───┬ ⎟\n", "⎜│ │ x, 3628800⎟\n", "⎜│ │ ⎟\n", "⎝x = 1 ⎠" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Product(x, (x, 1, 10)), Product(x, (x, 1, 10)).doit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Max/Min" ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAN4AAAAUBAMAAAAQOp5WAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nTkSuQmCC\n", "text/latex": [ "$$\\left ( \\max\\left(x, y\\right), \\quad \\min\\left(x, y\\right)\\right )$$" ], "text/plain": [ "(Max(x, y), Min(x, y))" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Max(x, y), Min(x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 方程式" ] }, { "cell_type": "code", "execution_count": 92, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGsAAAAWBAMAAAA1LX8gAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nYII=\n", "text/latex": [ "$$x^{2} + 2 x = 0$$" ], "text/plain": [ " 2 \n", "x + 2⋅x = 0" ] }, "execution_count": 92, "metadata": {}, "output_type": "execute_result" } ], "source": [ "equation = Eq(x ** 2 + 2 * x, 0)\n", "equation" ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEoAAAAUBAMAAADYerbFAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdt3NMolEECKZu6vv\nVGbHkCAIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA60lEQVQoFWMQMmEgBB6rMYTB1XDMXOUA58AY\nlXEhDEA1CFXVDKzfYJJw2pahqAFF1XYGhjNwWSiD7wADqwGKqkMMDPsd0JRxbWDg/Y6iyr4AUxX/\nBga2vyiqgMboF6CZVT+Bge0jmiq2r2iKGPoDGFi+oqli2oChagJMVbESCIACdya6IgYsNjJOwFAF\ndD0vmutvMnA0oKnjWsDAhxoSLBMYGNFVAUOVEzVUm0IjNzHUG6CapstQ44DiR/v//z8xMKmjqioV\n3IIa2xDpG6iqwDzkNAGRDiBGFbsAMar4sCgCul5IBZs4ipiQGgDWRjm3ApjHJAAAAABJRU5ErkJg\ngg==\n", "text/latex": [ "$$\\left [ -2, \\quad 0\\right ]$$" ], "text/plain": [ "[-2, 0]" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(equation)" ] }, { "cell_type": "code", "execution_count": 94, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEoAAAAUBAMAAADYerbFAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAdt3NMolEECKZu6vv\nVGbHkCAIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA60lEQVQoFWMQMmEgBB6rMYTB1XDMXOUA58AY\nlXEhDEA1CFXVDKzfYJJw2pahqAFF1XYGhjNwWSiD7wADqwGKqkMMDPsd0JRxbWDg/Y6iyr4AUxX/\nBga2vyiqgMboF6CZVT+Bge0jmiq2r2iKGPoDGFi+oqli2oChagJMVbESCIACdya6IgYsNjJOwFAF\ndD0vmutvMnA0oKnjWsDAhxoSLBMYGNFVAUOVEzVUm0IjNzHUG6CapstQ44DiR/v//z8xMKmjqioV\n3IIa2xDpG6iqwDzkNAGRDiBGFbsAMar4sCgCul5IBZs4ipiQGgDWRjm3ApjHJAAAAABJRU5ErkJg\ngg==\n", "text/latex": [ "$$\\left [ -2, \\quad 0\\right ]$$" ], "text/plain": [ "[-2, 0]" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# expr = 0 の方程式\n", "solve(x ** 2 + 2 * x)" ] }, { "cell_type": "code", "execution_count": 95, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIwAAAAVBAMAAABmhxuGAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAElFTkSuQmCC\n", "text/latex": [ "$$\\left \\{ -2 : 1, \\quad 0 : 1\\right \\}$$" ], "text/plain": [ "{-2: 1, 0: 1}" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "roots(x ** 2 + 2 * x)" ] }, { "cell_type": "code", "execution_count": 96, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJ8AAAAVBAMAAACqHiFtAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIma7zZnddlTvRIky\nEKtZsEGBAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAB30lEQVQ4EaWVPUgDMRTH/61naetdqYjOV9BZ\ndBMczsVJ5EDBQSg3SBEV0cGuTg5uzkXQydVbVKyDXdw7Kd06qKsOjpb6klwul/ZOTnzQ5H3l1yQv\nyQGpZcb+JdXcaMtoxkZ9RRq8n97RzMB49uO8oa94TmqFmRNAM3QLZdDm3tmBJGVOri2SsU6/Upma\nJR14SlOPBd4rAsCypFhdPF4Ct2RbDpB1owDr7SMFUGRJYKmNwhnA//AOyJWjQOA4BVBkSWDBQ+k7\nAHaAKfJHl/h3oNFTQOMSR/8B5rpimrleMMNRF/Npga9irGjZOkg6Du9w7QP8FGQdbJMrzZLz7JyF\nEgClvU+K4VKT99CgrglruUay1UosirlAMT2LBgZCCyV5PwDMzwAoQ4lA8JsQpukzZHWA0aWGgGmX\njLg9ZCBap4vxYA+LXvqisJsQijbDJ+AwqHLWwQ0lxRXF+gpHC0W7etEqZ3Yfqp48Nj6udGD1YtUW\nf1Br68QokGdRmJ9Do9/vS6DRGrp6jMJnnC8zVUkUqLxK43G6d/rjIOIcOKZyuZYKSI8D5vQ9ZIM5\n8IVjVJP8Hooc9h6y5yvxgbUpFhXDj1pDerFBrhG2TRn6BOxRr6Qe+wnAia1ShjRzk9WwAvwAMEGO\nk/u7jIUAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left ( \\left [ -1\\right ], \\quad \\left \\{ -1 : 2\\right \\}\\right )$$" ], "text/plain": [ "([-1], {-1: 2})" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "expr_ex3 = x ** 2 + 2 * x + 1\n", "solve(expr_ex3), roots(expr_ex3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##　不等式" ] }, { "cell_type": "code", "execution_count": 97, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "sympy.core.relational.StrictLessThan" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(1 > x)" ] }, { "cell_type": "code", "execution_count": 98, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAAUCAMAAAC9HKZGAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nGQcAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left ( x < 1, \\quad x \\leq 1, \\quad x > 1, \\quad x \\geq 1, \\quad 1 \\neq x\\right )$$" ], "text/plain": [ "(x < 1, x ≤ 1, x > 1, x ≥ 1, 1 ≠ x)" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" } ], "source": [ "1 > x, 1 >= x, 1 < x, 1 <= x, Ne(1, x)" ] }, { "cell_type": "code", "execution_count": 99, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQkAAAAQBAMAAAD36JewAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRK5CYII=\n", "text/latex": [ "$$\\Im{x} = 0 \\wedge -\\infty < \\Re{x} \\wedge \\Re{x} < 1$$" ], "text/plain": [ "im(x) = 0 ∧ -∞ < re(x) ∧ re(x) < 1" ] }, "execution_count": 99, "metadata": {}, "output_type": "execute_result" } ], "source": [ "## ??\n", "solve(1 > x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 連立方程式（Ex:鶴亀）" ] }, { "cell_type": "code", "execution_count": 100, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAH4AAAAVBAMAAAByPkciAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nAUXVCkPBnv//5oBv6rthn/Ry/QEAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left \\{ x : 2, \\quad y : 1\\right \\}$$" ], "text/plain": [ "{x: 2, y: 1}" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve([x + y - 3, 2 * x + 4 * y - 8], [x, y])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 名前付き" ] }, { "cell_type": "code", "execution_count": 101, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKsAAAAUBAMAAAAAWtCKAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\left ( \\gamma, \\quad Catalan, \\quad \\phi\\right )$$" ], "text/plain": [ "(EulerGamma, Catalan, GoldenRatio)" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "EulerGamma, Catalan, GoldenRatio" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ガンマ関数" ] }, { "cell_type": "code", "execution_count": 102, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAegAAAAUBAMAAAC0WbPpAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nVtYpvxUwB2X0OUOexoWH02NyNzP4H3SoMe5JPBRkAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left ( \\Gamma{\\left(x \\right)}, \\quad \\operatorname{loggamma}{\\left (x \\right )}, \\quad \\operatorname{polygamma}{\\left (x,y \\right )}, \\quad \\Gamma\\left(x, y\\right)\\right )$$" ], "text/plain": [ "(Γ(x), loggamma(x), polygamma(x, y), Γ(x, y))" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "gamma(x), loggamma(x), polygamma(x, y), uppergamma(x, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lambda" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGcAAAAUCAMAAACnKdOkAAAANlBMVEX///8AAAAAAAAAAAAAAAAA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\nsQAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left( x \\mapsto x + 1 \\right)$$" ], "text/plain": [ "x ↦ x + 1" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.Lambda(x, x+1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 関数定義？" ] }, { "cell_type": "code", "execution_count": 104, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHkAAAAUBAMAAABbvo/+AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\ngg==\n", "text/latex": [ "$$\\left ( f{\\left (x \\right )}, \\quad f{\\left (2 \\right )}\\right )$$" ], "text/plain": [ "(f(x), f(2))" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f_ = Function('f')\n", "f_(x), f_(2)" ] }, { "cell_type": "code", "execution_count": 105, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIcAAAAUBAMAAABVOzPUAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n7RzviTlNxJSgFRQ5+t7Df12P/wBsO4hJ7hamUgAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( \\operatorname{f_{2}}{\\left (x \\right )}, \\quad \\operatorname{f_{2}}{\\left (2 \\right )}\\right )$$" ], "text/plain": [ "(f₂(x), f₂(2))" ] }, "execution_count": 105, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f2_ = symbols('f2', cls=Function)\n", "f2_(x), f2_(2)" ] }, { "cell_type": "code", "execution_count": 106, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJ0AAAAUBAMAAABltyL1AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIma7zZnddlTvRIkQ\nqzLsm4+cAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACeElEQVQ4EZ1UPWgUURD+dve8u7ibY4kg2K2g\nlT9cBEFB9LQQsZCzCBYSXEGiZSxSWXiVbdRCSCyylZVgJETtXCRBLCQREbG73iKCQT0L8Zt5u3tv\nN4eFAzNvfr5vbt6+ew9wIuQykTtc3dAKyq4TlWON9tOKYo+Y4MplwGmLm8uH3LFXxSnDzoo/zt8X\nxVmNXv0CaqWR1iRflXHBKaNaCTqciup2pbLxNAEOileIP1u4Q0dwhjHMZd5LrtS6DjUvyetZxSzB\n/VJoAsEZxo7iO2aoe7XwgtaJxU0Lc1G8igjOMLJCIKuaWsIvlmBOEkcefQIa3HnwZRABK9Oy1ymp\nlEVxysjy75ceAv7xzwx3kU49ppWftF5E7Te2sdbDV8YHqFURnGGYymnc7QQX0FrmQXRUb0nB+UNT\n7wFHgfn2JRZC4J5UyqI4ZZi820fze62v/7xmDFAXpdL8RjOWALOc/gcNImCLS0UUR0ZwfoZyo99g\n/fVNGhdosQdV+/kxc1k/nJF+1BH9FKcMQijSz5NvQCfrp9N7m8zJfqXVyd8cIAKe0K+I4qz9ar+l\nBHgD7I5V9euOSR8vAg7zp54vhGiEI89DcdZ5uClwZ98D4HZxHqvshI2Exu/ywIFVbC3iEOOrCLa5\n2KI4ZWTZLlmtQeIuk2pUd/UsZV0GDqY+9hBcW2ANPOaZlKslirO/w/r0CWB98JgYOWaq3p4V5eh9\nS8UV48Q895COJYor3Te9Gmrk2lB5u5ub55Sz8z3wrV7sbnD/fg8wifqpWHleaRp5r96W+uW4yVI2\nC+StEuV76s6ZRk47q+kirMhOFLiR76kMowM5Q9KERf/P9/4vNlKF1n2Eev4AAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left ( f{\\left (\\infty \\right )}, \\quad f{\\left (-\\infty \\right )}\\right )$$" ], "text/plain": [ "(f(∞), f(-∞))" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f_(x).limit(x, oo), f_(x).limit(x, -oo)" ] }, { "cell_type": "code", "execution_count": 107, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEAAAAArBAMAAAA6dJN0AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrkJggg==\n", "text/latex": [ "$$\\frac{d}{d x} f{\\left (x \\right )}$$" ], "text/plain": [ "d \n", "──(f(x))\n", "dx " ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f_(x).diff(x)" ] }, { "cell_type": "code", "execution_count": 108, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAABMCAMAAAC208D2AAAAM1BMVEX///8AAAAAAAAAAAAAAAAA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\nxj8i/w9fDzYDSmsh1wAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( \\int f{\\left (x \\right )}\\, dx, \\quad \\int_{1}^{10} f{\\left (x \\right )}\\, dx\\right )$$" ], "text/plain": [ "⎛ 10 ⎞\n", "⎜⌠ ⌠ ⎟\n", "⎜⎮ f(x) dx, ⎮ f(x) dx⎟\n", "⎜⌡ ⌡ ⎟\n", "⎝ 1 ⎠" ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f_(x).integrate(x), f_(x).integrate((x, 1, 10))" ] }, { "cell_type": "code", "execution_count": 109, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAACUAAAAUBAMAAAD4luk4AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVJl2u4kiEO8yZt2r\nRM0tcn99AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+UlEQVQYGVWQsUrDQBiAv5prrqk2FhG7CMY3\nEIt0LX0CoUMHh2a2SxahD9AH8BGKgoMumRxFEFwVXB0y+ABJhYCFgn+O5KI/3N3Hd/z/f/dDGZfl\neVcJcIcl74RW+hXqxLobS2NLj5bmFblxRfjvgnv9fZwAdP/1QxK3BJtDd4VawhUPJ0/QTuAoImO7\nCxOm0QE0pMwCL6clRSK+kPBSvDVObBx8l66dowKTi/dTuE5MI2W3a3r0nJSB6aFz3kKaAZ1Mpe5S\n3nIOn2cXJkG/DE7vJde/LiqMZNV/m0lr9EbcvxlMI/UsToWyFaETOLw9Fqpnai9F/pn9L4ElNK+V\nnr0NAAAAAElFTkSuQmCC\n", "text/latex": [ "$$g{\\left (x \\right )}$$" ], "text/plain": [ "g(x)" ] }, "execution_count": 109, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g_ = Function('g')(x)\n", "g_" ] }, { "cell_type": "code", "execution_count": 110, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJkAAAAUBAMAAABsXIKPAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nOZNO8v+95H8ABAKIR+XWCucAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left ( g{\\left (\\infty \\right )}, \\quad g{\\left (-\\infty \\right )}\\right )$$" ], "text/plain": [ "(g(∞), g(-∞))" ] }, "execution_count": 110, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g_.limit(x, oo), g_.limit(x, -oo)" ] }, { "cell_type": "code", "execution_count": 111, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAD4AAAArBAMAAADS9CZfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nK5g5o7VIlR9KoIqZU60UC+8B4E7/AEAxeEFKJMXYAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\frac{d}{d x} g{\\left (x \\right )}$$" ], "text/plain": [ "d \n", "──(g(x))\n", "dx " ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g_.diff(x)" ] }, { "cell_type": "code", "execution_count": 112, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOkAAABMCAMAAAC/OGCMAAAAM1BMVEX///8AAAAAAAAAAAAAAAAA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\nQmCC\n", "text/latex": [ "$$\\left ( \\int g{\\left (x \\right )}\\, dx, \\quad \\int_{1}^{10} g{\\left (x \\right )}\\, dx\\right )$$" ], "text/plain": [ "⎛ 10 ⎞\n", "⎜⌠ ⌠ ⎟\n", "⎜⎮ g(x) dx, ⎮ g(x) dx⎟\n", "⎜⌡ ⌡ ⎟\n", "⎝ 1 ⎠" ] }, "execution_count": 112, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g_.integrate(x), g_.integrate((x, 1, 10))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 微分方程式" ] }, { "cell_type": "code", "execution_count": 113, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIMAAAArBAMAAACp/CbWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nTkSuQmCC\n", "text/latex": [ "$$f{\\left (x \\right )} + \\frac{d}{d x} f{\\left (x \\right )}$$" ], "text/plain": [ " d \n", "f(x) + ──(f(x))\n", " dx " ] }, "execution_count": 113, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f1 = Function('f')(x)\n", "f2 = Derivative(f1) + f1\n", "f2" ] }, { "cell_type": "code", "execution_count": 114, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHsAAAAVBAMAAACUF4xmAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrkJggg==\n", "text/latex": [ "$$f{\\left (x \\right )} = C_{1} e^{- x}$$" ], "text/plain": [ " -x\n", "f(x) = C₁⋅ℯ " ] }, "execution_count": 114, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dsolve(f2, f1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## vectorize " ] }, { "cell_type": "code", "execution_count": 115, "metadata": { "collapsed": true }, "outputs": [], "source": [ "## http://docs.sympy.org/dev/modules/core.html#vectorize" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## その他関数" ] }, { "cell_type": "code", "execution_count": 116, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABAAAAAOBAMAAADUAYG5AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAZUlEQVQIHWNggIBmKM3yH8pg/AFlMPyEMR4z\nMAgpu6opMMxlYExgb+KYwLCJgU2A7SOXA8N1BkYGzg1AhalAzK8AJHSA+PwBICHAwCWgz8AkAGTG\nL9jP4M7A+JJBWEnoegEDQzMA1dkSj//8SXoAAAAASUVORK5CYII=\n", "text/latex": [ "$$x!$$" ], "text/plain": [ "x!" ] }, "execution_count": 116, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.factorial(x)" ] }, { "cell_type": "code", "execution_count": 117, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAACMAAAAyBAMAAAAkfX9UAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n//Eh4Wit7Yn/A+XUZ2yZb5nIAAAAAElFTkSuQmCC\n", "text/latex": [ "$${\\binom{x}{y}}$$" ], "text/plain": [ "⎛x⎞\n", "⎜ ⎟\n", "⎝y⎠" ] }, "execution_count": 117, "metadata": {}, "output_type": "execute_result" } ], "source": [ "comb = sympy.binomial(x, y)\n", "comb" ] }, { "cell_type": "code", "execution_count": 118, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "binomial" ] }, "execution_count": 118, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(comb)" ] }, { "cell_type": "code", "execution_count": 119, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOBAMAAADkjZCYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAiXYyEM1Embsi72ZU\n3au6f2Q3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAVUlEQVQIHWNgYBBUNGBgcE1gD2BgaGfgaGBg\n+8kABBwLQCR/sFAZA4N/NAPXAQb/LwzsSxj4LzBwf2PgDWDg/s3AtwDEZgaKAxU/ZPA6wMDAWP6Y\nAQCADRI3fgJiQgAAAABJRU5ErkJggg==\n", "text/latex": [ "$$6$$" ], "text/plain": [ "6" ] }, "execution_count": 119, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.binomial(4, 2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 論理式" ] }, { "cell_type": "code", "execution_count": 120, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC4AAAARBAMAAABQu4N8AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6UlEQVQYGW2NPUvDUABFT9KmX0kxpJOTD4Vu\n1U6Cmx2kuJXuYjfX/oTi4trBtdA/oAR1cDObo+AiuukvsCB09b7Xpl3yIPfcc19IYH0ixyzXDUt2\nqpqN5yXqqtXiXLe8Vb3YKsnBWdvI7/Q82T15p/yNN6pe16ZSfSNK7T66x/+lElcWjVOpbygNxPL8\nkzDFo+7ewpuwq1nDDztGxYX4xZUSggVvmehCPGeihOaUQ2jER/ix9fDVWBB2eYTL+Qt958Gzu6aZ\nBkto7ScfY7czW8E77vyt2jp7uekPBeeEvUHBzA0PRTPDTgb/c7EnBTJYzUgAAAAASUVORK5CYII=\n", "text/latex": [ "$$x \\vee y$$" ], "text/plain": [ "x ∨ y" ] }, "execution_count": 120, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x | y" ] }, { "cell_type": "code", "execution_count": 121, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAC4AAAARBAMAAABQu4N8AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEHarIkSJZt3NVLsy\nme8Q6PJIAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVQYGWNgQAAHBBOFNReFB+fw7BCAs5EZ\nzEEKyFwhZVc1sIAkQwNYXOgSA8tDBsYE9iaOCSCBLCAEgYR1DEwfGNgE2D5yOYD4DQyeIIplwU0G\n7g0MjAycG0BcBnYFBuYDQJqR4REDvwKQASYYGDgEGHjAKlg/MpwHKQATDAxrgcwpQMzAO4FBj4GB\nS0CfgQnkcJAYSI6B24BhMwND/IL9DO5AHtgMoFlA9RtYvzMwCCsJXS8A8pgDgASTApBgNNP9AqSg\ngBVMHwCTQBuwAEsGeZBeDNDOsAlDDCQQpHuAgQEANYsmyRWbWQQAAAAASUVORK5CYII=\n", "text/latex": [ "$$x \\wedge y$$" ], "text/plain": [ "x ∧ y" ] }, "execution_count": 121, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x & y" ] }, { "cell_type": "code", "execution_count": 122, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAACQAAAATCAYAAAD4f6+NAAAABHNCSVQICAgIfAhkiAAAAgdJREFU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\nfAfsbGqGkgrf3gAAAABJRU5ErkJggg==\n", "text/latex": [ "$$x \\veebar y$$" ], "text/plain": [ "x ⊻ y" ] }, "execution_count": 122, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x ^ y" ] }, { "cell_type": "code", "execution_count": 123, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABgAAAAJBAMAAADa0/H1AAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAmd2JIqsyEHZEZs1Uuw+W\nkLUAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABNSURBVAgdY2CAAPaOkBkWUDZDMcOiBm0GISUgUGYw\nZ7ArOAKRcWUoYNgLU+QKZLxA4rA9Q3COczxgaIdw2Tjf8D5gWQCVY49ob1zFAABzAhDCauGgDQAA\nAABJRU5ErkJggg==\n", "text/latex": [ "$$\\neg x$$" ], "text/plain": [ "¬x" ] }, "execution_count": 123, "metadata": {}, "output_type": "execute_result" } ], "source": [ "~ x" ] }, { "cell_type": "code", "execution_count": 124, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAANMAAAAUBAMAAADlxBXmAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\left ( \\mathrm{True}, \\quad y, \\quad y, \\quad \\mathrm{False}\\right )$$" ], "text/plain": [ "(True, y, y, False)" ] }, "execution_count": 124, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(x | y).subs({x: True}), (x | y).subs({x: False}), (x & y).subs({x: True}), (x & y).subs({x: False})" ] }, { "cell_type": "code", "execution_count": 125, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "({y: True, x: True},\n", " {y: True, x: True},\n", " {y: False, x: True},\n", " {x: True},\n", " {x: False},\n", " {True: True})" ] }, "execution_count": 125, "metadata": {}, "output_type": "execute_result" } ], "source": [ "satisfiable(x | y), satisfiable(x & y), satisfiable(x ^ y), satisfiable(x), satisfiable(~ x), satisfiable(True)" ] }, { "cell_type": "code", "execution_count": 126, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMEAAAAUBAMAAADGn0QzAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRK5CYII=\n", "text/latex": [ "$$\\left ( \\neg (x \\vee y), \\quad \\neg (x \\wedge y)\\right )$$" ], "text/plain": [ "(¬(x ∨ y), ¬(x ∧ y))" ] }, "execution_count": 126, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy.logic.boolalg\n", "type(sympy.Nor)\n", "sympy.Nor(x, y), sympy.Nand(x, y)" ] }, { "cell_type": "code", "execution_count": 127, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAALsAAAAUBAMAAAAn9FFiAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nNJFaR3yPm36lPhBX4TWuv97luywsUQAAAABJRU5ErkJggg==\n", "text/latex": [ "$$ITE(x, True, False)$$" ], "text/plain": [ "ITE(x, True, False)" ] }, "execution_count": 127, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# if then else\n", "sympy.ITE(x, True, False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 行列" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 行列定義と転置" ] }, { "cell_type": "code", "execution_count": 128, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQgAAABLCAMAAAC7k+m7AAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\nAElFTkSuQmCC\n", "text/latex": [ "$$\\left ( \\left[\\begin{matrix}x & 1 & 2\\\\3 & y & 5\\\\6 & 7 & 8\\end{matrix}\\right], \\quad \\left[\\begin{matrix}x & 3 & 6\\\\1 & y & 7\\\\2 & 5 & 8\\end{matrix}\\right]\\right )$$" ], "text/plain": [ "⎛⎡x 1 2⎤, ⎡x 3 6⎤⎞\n", "⎜⎢ ⎥ ⎢ ⎥⎟\n", "⎜⎢3 y 5⎥ ⎢1 y 7⎥⎟\n", "⎜⎢ ⎥ ⎢ ⎥⎟\n", "⎝⎣6 7 8⎦ ⎣2 5 8⎦⎠" ] }, "execution_count": 128, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat = Matrix([\n", " [x, 1, 2], \n", " [3, y, 5], \n", " [6, 7, 8]])\n", "mat, mat.T\n", "# RuntimeError: latex program is not installed" ] }, { "cell_type": "code", "execution_count": 129, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAL4AAABLCAMAAAD59c0FAAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\nAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left ( \\left[\\begin{matrix}x\\\\y\\\\2\\end{matrix}\\right], \\quad \\left[\\begin{matrix}x & y & 2\\end{matrix}\\right]\\right )$$" ], "text/plain": [ "⎛⎡x⎤, [x y 2]⎞\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢y⎥ ⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣2⎦ ⎠" ] }, "execution_count": 129, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vec = Matrix([x, y, 2])\n", "vec, vec.T" ] }, { "cell_type": "code", "execution_count": 130, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPUAAAAyBAMAAAB2coBaAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n8gAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left ( \\left[\\begin{matrix}1 & 2 & 3\\\\4 & 5 & 6\\end{matrix}\\right], \\quad \\left[\\begin{matrix}0 & 1 & 2\\\\3 & 4 & 5\\end{matrix}\\right]\\right )$$" ], "text/plain": [ "⎛⎡1 2 3⎤, ⎡0 1 2⎤⎞\n", "⎜⎢ ⎥ ⎢ ⎥⎟\n", "⎝⎣4 5 6⎦ ⎣3 4 5⎦⎠" ] }, "execution_count": 130, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Matrix(2, 3, [1, 2, 3, 4, 5, 6]), Matrix(2, 3, range(6))" ] }, { "cell_type": "code", "execution_count": 131, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHgAAABLCAMAAACMVLPjAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nMA3/gMI5+Qfvsy8AMHY0QwAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left[\\begin{matrix}0 & 1 & 2 & 3\\\\1 & 2 & 3 & 4\\\\2 & 3 & 4 & 5\\end{matrix}\\right]$$" ], "text/plain": [ "⎡0 1 2 3⎤\n", "⎢ ⎥\n", "⎢1 2 3 4⎥\n", "⎢ ⎥\n", "⎣2 3 4 5⎦" ] }, "execution_count": 131, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Matrix(3, 4, lambda i, j: i + j)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 単位行列" ] }, { "cell_type": "code", "execution_count": 132, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFgAAABLCAMAAADDCbAzAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nxR99YOnjB5G2vSR/3mzMH1ja1v0A4UooEMbFTswAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left[\\begin{matrix}1 & 0 & 0\\\\0 & 1 & 0\\\\0 & 0 & 1\\end{matrix}\\right]$$" ], "text/plain": [ "⎡1 0 0⎤\n", "⎢ ⎥\n", "⎢0 1 0⎥\n", "⎢ ⎥\n", "⎣0 0 1⎦" ] }, "execution_count": 132, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.eye(3)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## すべての要素が1" ] }, { "cell_type": "code", "execution_count": 133, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAASIAAABLCAMAAADj7HqiAAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\naEXQnYsBAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left ( \\left[\\begin{matrix}1 & 1 & 1\\\\1 & 1 & 1\\\\1 & 1 & 1\\end{matrix}\\right], \\quad \\left[\\begin{matrix}1 & 1 & 1 & 1\\\\1 & 1 & 1 & 1\\\\1 & 1 & 1 & 1\\end{matrix}\\right]\\right )$$" ], "text/plain": [ "⎛⎡1 1 1⎤, ⎡1 1 1 1⎤⎞\n", "⎜⎢ ⎥ ⎢ ⎥⎟\n", "⎜⎢1 1 1⎥ ⎢1 1 1 1⎥⎟\n", "⎜⎢ ⎥ ⎢ ⎥⎟\n", "⎝⎣1 1 1⎦ ⎣1 1 1 1⎦⎠" ] }, "execution_count": 133, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.ones(3), sympy.ones(3, 4)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## ゼロ行列" ] }, { "cell_type": "code", "execution_count": 134, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAASIAAABLCAMAAADj7HqiAAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\nzEmO1/hEuWr/AeGEeX9+FuVIAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left ( \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right], \\quad \\left[\\begin{matrix}0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right]\\right )$$" ], "text/plain": [ "⎛⎡0 0 0⎤, ⎡0 0 0 0⎤⎞\n", "⎜⎢ ⎥ ⎢ ⎥⎟\n", "⎜⎢0 0 0⎥ ⎢0 0 0 0⎥⎟\n", "⎜⎢ ⎥ ⎢ ⎥⎟\n", "⎝⎣0 0 0⎦ ⎣0 0 0 0⎦⎠" ] }, "execution_count": 134, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sympy.zeros(3), sympy.zeros(3, 4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 要素の参照" ] }, { "cell_type": "code", "execution_count": 135, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGcAAAAUBAMAAABi2T6lAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrkJggg==\n", "text/latex": [ "$$\\left ( 1, \\quad y, \\quad 7\\right )$$" ], "text/plain": [ "(1, y, 7)" ] }, "execution_count": 135, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat[1], mat[4], mat[7]" ] }, { "cell_type": "code", "execution_count": 136, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGcAAAAUBAMAAABi2T6lAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nrkJggg==\n", "text/latex": [ "$$\\left ( 1, \\quad y, \\quad 7\\right )$$" ], "text/plain": [ "(1, y, 7)" ] }, "execution_count": 136, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat[0, 1], mat[1, 1], mat[2, 1]" ] }, { "cell_type": "code", "execution_count": 137, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFcAAAAyBAMAAADb31q2AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n4kpt7JSvQk2TRK7hXiYahRt6QjTyOHkGf3Z0CgNs6wQAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left[\\begin{matrix}x & 1 & 2\\\\3 & y & 5\\end{matrix}\\right]$$" ], "text/plain": [ "⎡x 1 2⎤\n", "⎢ ⎥\n", "⎣3 y 5⎦" ] }, "execution_count": 137, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat[0:2, 0:3]" ] }, { "cell_type": "code", "execution_count": 138, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOIAAABLCAMAAABa3avDAAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\nf3yeSg7rh9vtAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left ( \\left[\\begin{matrix}x & 1\\\\3 & y\\\\6 & 7\\end{matrix}\\right], \\quad \\left[\\begin{matrix}x & 1 & 2\\\\3 & y & 5\\end{matrix}\\right]\\right )$$" ], "text/plain": [ "⎛⎡x 1⎤, ⎡x 1 2⎤⎞\n", "⎜⎢ ⎥ ⎢ ⎥⎟\n", "⎜⎢3 y⎥ ⎣3 y 5⎦⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣6 7⎦ ⎠" ] }, "execution_count": 138, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat[:, 0:2], mat[0:2, :]" ] }, { "cell_type": "code", "execution_count": 139, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGkAAAAUBAMAAAB8EA4WAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nQIYoMQe/j0dIVOFFXpoAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left ( x, \\quad y, \\quad 2\\right )$$" ], "text/plain": [ "(x, y, 2)" ] }, "execution_count": 139, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vec[0], vec[1], vec[2]" ] }, { "cell_type": "code", "execution_count": 140, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAATAAAABLCAMAAADAtyt3AAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n", "text/latex": [ "$$\\left ( \\left[\\begin{matrix}100 & 1 & 2\\\\3 & y & 5\\\\6 & 7 & 100\\end{matrix}\\right], \\quad \\left[\\begin{matrix}x & 1 & 2\\\\3 & y & 5\\\\6 & 7 & 8\\end{matrix}\\right]\\right )$$" ], "text/plain": [ "⎛⎡100 1 2 ⎤, ⎡x 1 2⎤⎞\n", "⎜⎢ ⎥ ⎢ ⎥⎟\n", "⎜⎢ 3 y 5 ⎥ ⎢3 y 5⎥⎟\n", "⎜⎢ ⎥ ⎢ ⎥⎟\n", "⎝⎣ 6 7 100⎦ ⎣6 7 8⎦⎠" ] }, "execution_count": 140, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat2 = mat[:, :]\n", "mat2[0, 0] = mat2[2, 2] = 100\n", "mat2, mat" ] }, { "cell_type": "code", "execution_count": 141, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAS4AAABLCAMAAAD50JosAAAAP1BMVEX///8AAAAAAAAAAAAAAAAA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\n/+d3brJIOBMkAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left ( \\left[\\begin{matrix}10 & 1 & 2\\\\3 & y & 5\\\\6 & 7 & 10\\end{matrix}\\right], \\quad \\left[\\begin{matrix}10 & 1 & 2\\\\3 & y & 5\\\\6 & 7 & 10\\end{matrix}\\right]\\right )$$" ], "text/plain": [ "⎛⎡10 1 2 ⎤, ⎡10 1 2 ⎤⎞\n", "⎜⎢ ⎥ ⎢ ⎥⎟\n", "⎜⎢3 y 5 ⎥ ⎢3 y 5 ⎥⎟\n", "⎜⎢ ⎥ ⎢ ⎥⎟\n", "⎝⎣6 7 10⎦ ⎣6 7 10⎦⎠" ] }, "execution_count": 141, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat3 = mat2\n", "mat3[0, 0] = mat3[2, 2] = 10\n", "mat3, mat2" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## 代入" ] }, { "cell_type": "code", "execution_count": 142, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGMAAABLCAMAAABTGsn8AAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n5CrAD5uJEAAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left[\\begin{matrix}50 & 1 & 2\\\\3 & y & 5\\\\6 & 7 & 8\\end{matrix}\\right]$$" ], "text/plain": [ "⎡50 1 2⎤\n", "⎢ ⎥\n", "⎢3 y 5⎥\n", "⎢ ⎥\n", "⎣6 7 8⎦" ] }, "execution_count": 142, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat.subs(x, 50)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 演算" ] }, { "cell_type": "code", "execution_count": 143, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHoAAABLCAMAAACIoWPeAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n1uIP5Kw0dISWW2UAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left[\\begin{matrix}2 x & 2 & 4\\\\6 & 2 y & 10\\\\12 & 14 & 16\\end{matrix}\\right]$$" ], "text/plain": [ "⎡2⋅x 2 4 ⎤\n", "⎢ ⎥\n", "⎢ 6 2⋅y 10⎥\n", "⎢ ⎥\n", "⎣12 14 16⎦" ] }, "execution_count": 143, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat + mat" ] }, { "cell_type": "code", "execution_count": 144, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# mat + 2" ] }, { "cell_type": "code", "execution_count": 145, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFgAAABLCAMAAADDCbAzAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nrgYrgI5f00cAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right]$$" ], "text/plain": [ "⎡0 0 0⎤\n", "⎢ ⎥\n", "⎢0 0 0⎥\n", "⎢ ⎥\n", "⎣0 0 0⎦" ] }, "execution_count": 145, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat - mat" ] }, { "cell_type": "code", "execution_count": 146, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAU8AAABMCAMAAADa8MXaAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nXemxAAAAAElFTkSuQmCC\n", "text/latex": [ "$$\\left[\\begin{matrix}x^{2} + 15 & x + y + 14 & 2 x + 21\\\\3 x + 3 y + 30 & y^{2} + 38 & 5 y + 46\\\\6 x + 69 & 7 y + 62 & 111\\end{matrix}\\right]$$" ], "text/plain": [ "⎡ 2 ⎤\n", "⎢ x + 15 x + y + 14 2⋅x + 21⎥\n", "⎢ ⎥\n", "⎢ 2 ⎥\n", "⎢3⋅x + 3⋅y + 30 y + 38 5⋅y + 46⎥\n", "⎢ ⎥\n", "⎣ 6⋅x + 69 7⋅y + 62 111 ⎦" ] }, "execution_count": 146, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat * mat" ] }, { "cell_type": "code", "execution_count": 147, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAHoAAABLCAMAAACIoWPeAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\n6h56X831LzGgADG1T6n38YIl9y8xUrK/JUk2EfNpgQgAAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left[\\begin{matrix}3 x & 3 & 6\\\\9 & 3 y & 15\\\\18 & 21 & 24\\end{matrix}\\right]$$" ], "text/plain": [ "⎡3⋅x 3 6 ⎤\n", "⎢ ⎥\n", "⎢ 9 3⋅y 15⎥\n", "⎢ ⎥\n", "⎣18 21 24⎦" ] }, "execution_count": 147, "metadata": {}, "output_type": "execute_result" } ], "source": [ "3 * mat" ] }, { "cell_type": "code", "execution_count": 148, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQMAAABRCAMAAADhPjOxAAAAP1BMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADFBd4eAAAAFHRS\nTlMAMquZdlQQQOkwRCKJZt3Nu+9sTnx3CqcAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAe4SURBVHgB\n7VzbgqQoDEVQd1bxtsv/f+sGFAgEsGqrTD/M+NAl1xMOAULAFuL3frrt926/EJ2S6+/OgRDDHw7+\ncADD4I8eXBx0xj3yi1PDelZZr1FNZ9rj2PNts5wedEb18Ax1id9OWWyF0lTL9X49eh5b6lyKYffP\naJMuDro821fCS5WDzswXQmeexh6PS+VqbfoyB7NS+x4aVedgDX3zPQ6q2MvhurtGgRgOSHpLjqFR\n42jHnjae9yoHOq7IHNhba0qY1Wpk/wYHo1TS1FmVLumwvNqnxsFsljMD/H2dg/+PPb0w3l6XA4Tu\nGxwcrn+lh6xxsHuS3uLgA+zNz8BQR+X5Ggeb4+eOgw6pwRt6AMK3+G9hT+Z2zYscjLCgzVOv+wpb\nN3KcpVavKRU9wGqAOHgSe40TUKVlgYMRputl7cXa0J1WX7j6J+Mn/TIHc0i32XmwlzBPVyiIcmiY\n0zT04uBX70KJWw7WMAuXOVDBNkg4eBR7NHuhKTgq9gXEbje57zhQKlRd5sAkesmEvSfEBwnjS5DD\nRpnGXGDTbzjoIwXltXFIAZiwM1TbkPTBcuD3NNcVanMwWArmaygV9UCmPYLx8Pu3sVPto7UH7GGE\nbob0vm4GtfWgc1rQtzgwyDgAKC7sLaWekODlsMvoDhzM0YwjeZsczKvWOvrnSnowGDRYEAdPY+t0\nCJJ2eQ5G2fdjr5YGBUoeZpO1DNvpNfCTXokDmZkrXNidaaz3qC8IOR9GlDgIBtRVt+fgQyhSnGCb\n6kbelWWTQ4gxmw7ifEBa8VkE4WDzu5hyvYwcTLmxwoat8C6F8sAmh7VCvSF9icGG3Ztgv1IG0PpU\nSvwgjuijgGUnm0/ZOJjaFgKbHEIc+ahkwx7bkyKbHGCJ+321Vy8+bNO0kvjkmEln8GEfzf0znxxT\nvjTyrY1iy6cir4rul4+DhVhrfNgyX5J+iAOdmweMeqCaiyPqixk2PfutAzJhEAc22HF2ypenayOV\ngw+b8o8lj3LMdlM3NAcOLkjeD7tpClYQ5WAnfcGHrck4xOJHOXq3q2tbE7hk/r5p6Z0HkEQ52LKd\nM7bPnsbum82KHEz2fHJsEpY3Owmn5miJg6AkVzk+7Fc5cIJ9MBbuOFjjQCEcPI29kHX5EsH9xL6w\nwTEeCuNM7h08LNblOtfOXeWy9Kpx7rwSbw4f9kDsM9w8LMesV1X3JurzoNo5HXEN/n2HonOwx+hY\nOJocPIv9OgfQGl29tDAPQlmX1N48g9jrvrSDLDmY/2exp5f1wPboUVN16OXDjgXSm7ZUeMJBEtUD\nk3kT8bpwln8OGzioK7j469ffVwPOk4GdSBraN9l6sr4LiUI6v2W4hPHPr5h0vhnCHh/2v00OYpvO\nbA0O3FDo0yOC2NDDcaA83yU9yFwoiM+nseEGXEMPIgeHG+hrfae929XP/Yktj2/n0UE4taYctOaD\np7FfnQ/c0ULrbE4BSROZ2DwLztReDn9qTTlorY1PY7/KgZgU3Czzd6p809DvKHUf5jwUf73OSsu4\ntJY4qNuJT2O/zAFtFo1xcwKNpjGUg+3OTqSVpDEfYL9lH6SoSchO/GOwgZKkQoBysDf2TIUKkqhP\nsd+xlRPgLLDCtL7fXFCIRb7LwafYb+2ZYiPI29Sj7QBJzSMoB7LhP8hL5+FPsV/1H+S4n4UpB+pH\nfWktCz/aB5+1OS9NOeh/kAOqg1hePg4G4p7hw97JmvQzHHTEj8HHwVbfBQEZfHLQQz8+bHLUidWA\nkQM4b/SG9CUBGwdAf2PLxMnBmhtYbBzAtjHp+CyQyKF1r4NHMMsoulUqOIXRudXv88G9a+2/1ir5\n1oXM91ts2PSYzwvtfpEc4wYbprpRvpwXz4il46tzm2dZP2eCm33p1Tysg89i6xzZy3z+Ig52K2Ld\nXajO0Zy60GNlg/OQzM6TArHUPoAm+8SrFBt2wzFkRYlyTPmUdUnqf84xUB0r2lliY92nai9h+LrO\nXzbshmPIShLlSD6vSIWNoam6aYJbZzD3au8vK+iByEXhwiaXAmN73FuUw2wd+EgaPhSbv2F2S2OW\nQEFpLMDFNM/QKQQX9lCdwzI54KTRSnj4Se1Mzv7GNmYJNqiN2cIyXNKD/IJi4OBh7PyOcC47ksPZ\nEap2vmALjtmATiob5LSacERT4gBupiUluLAz2EQGGwhyiPN4uvn1T/hSmVQDC4FdMHrjKSxyoNLb\neUzYM9mwZuJHOU63+JKN2ST72pgOTo9y5zcnRQ7iJ1+uWibs83JD0pA0EOWQ7vSkpQdjY27xw8Tf\n7S9yACd5GJ0Je0tAsQDXe5Sju+aDQqaQNzP0cNbrZGFvfccCYwWvOzzYXdN3YJsQ5RD2nwWMrXUh\n/w4FUyAmtyYs3n4o60GqSTzY4fgvERcHkBxCKyWrWyYoNLcIEh1sqaJ5UebAfUEZ4FmwU9oDNn7B\ncuD4T98rHIxYMVmw+5stADSURQ5EKP48kAX7aMxhl1wsciAOxBH9DxzYS9ODdArGIQemAG6BBnua\nAXskFz8SYX6IAyGDocXAwXk7ptBuHMUgB4az76vflj2PfecTOUV7/P805QzANOz3FM9jr9gko5Jc\nMeAJtc9LeauVpAnuf0T13lhK01xoumzJx7HhPuELz3/ikWccencUgQAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left[\\begin{matrix}x & 1 & 2\\\\3 & y & 5\\\\6 & 7 & 8\\end{matrix}\\right] \\left(\\left[\\begin{matrix}x & 1 & 2\\\\3 & y & 5\\\\6 & 7 & 8\\end{matrix}\\right]\\right)^{-1}$$" ], "text/plain": [ " -1\n", "⎡x 1 2⎤⋅⎛⎡x 1 2⎤⎞ \n", "⎢ ⎥ ⎜⎢ ⎥⎟ \n", "⎢3 y 5⎥ ⎜⎢3 y 5⎥⎟ \n", "⎢ ⎥ ⎜⎢ ⎥⎟ \n", "⎣6 7 8⎦ ⎝⎣6 7 8⎦⎠ " ] }, "execution_count": 148, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat / mat" ] }, { "cell_type": "code", "execution_count": 149, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGMAAABNCAMAAACFQyrhAAAAZlBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\left[\\begin{matrix}\\frac{x}{3} & \\frac{1}{3} & \\frac{2}{3}\\\\1 & \\frac{y}{3} & \\frac{5}{3}\\\\2 & \\frac{7}{3} & \\frac{8}{3}\\end{matrix}\\right]$$" ], "text/plain": [ "⎡x ⎤\n", "⎢─ 1/3 2/3⎥\n", "⎢3 ⎥\n", "⎢ ⎥\n", "⎢ y ⎥\n", "⎢1 ─ 5/3⎥\n", "⎢ 3 ⎥\n", "⎢ ⎥\n", "⎣2 7/3 8/3⎦" ] }, "execution_count": 149, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat / 3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 内積" ] }, { "cell_type": "code", "execution_count": 150, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAAbBAMAAABl417BAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n", "text/latex": [ "$$\\left [ x^{2} + y + 4, \\quad 3 x + y^{2} + 10, \\quad 6 x + 7 y + 16\\right ]$$" ], "text/plain": [ "⎡ 2 2 ⎤\n", "⎣x + y + 4, 3⋅x + y + 10, 6⋅x + 7⋅y + 16⎦" ] }, "execution_count": 150, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat.dot(vec)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## 逆行列" ] }, { "cell_type": "code", "execution_count": 151, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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KQM6wqCqvPATrkZzWeMtlViSZqVyfo0t8d+kSa9vE9KtFq4ZZGRjA561kkYAM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\nQpH6gy4AAAAASUVORK5CYII=\n", "text/latex": [ "$$\\left[\\begin{matrix}- \\frac{\\left(x y - 3\\right) \\left(- \\frac{5 - \\frac{6}{x}}{x \\left(y - \\frac{3}{x}\\right)} + \\frac{2}{x}\\right) \\left(\\frac{21 - \\frac{18}{x}}{x \\left(y - \\frac{3}{x}\\right)} - \\frac{6}{x}\\right)}{8 x y - 35 x - 12 y + 48} + \\frac{1}{x} + \\frac{3}{x^{2} \\left(y - \\frac{3}{x}\\right)} & \\frac{\\left(7 - \\frac{6}{x}\\right) \\left(x y - 3\\right) \\left(- \\frac{5 - \\frac{6}{x}}{x \\left(y - \\frac{3}{x}\\right)} + \\frac{2}{x}\\right)}{\\left(y - \\frac{3}{x}\\right) \\left(8 x y - 35 x - 12 y + 48\\right)} - \\frac{1}{x \\left(y - \\frac{3}{x}\\right)} & - \\frac{\\left(x y - 3\\right) \\left(- \\frac{5 - \\frac{6}{x}}{x \\left(y - \\frac{3}{x}\\right)} + \\frac{2}{x}\\right)}{8 x y - 35 x - 12 y + 48}\\\\- \\frac{\\left(5 - \\frac{6}{x}\\right) \\left(x y - 3\\right) \\left(\\frac{21 - \\frac{18}{x}}{x \\left(y - \\frac{3}{x}\\right)} - \\frac{6}{x}\\right)}{\\left(y - \\frac{3}{x}\\right) \\left(8 x y - 35 x - 12 y + 48\\right)} - \\frac{3}{x \\left(y - \\frac{3}{x}\\right)} & \\frac{\\left(5 - \\frac{6}{x}\\right) \\left(7 - \\frac{6}{x}\\right) \\left(x y - 3\\right)}{\\left(y - \\frac{3}{x}\\right)^{2} \\left(8 x y - 35 x - 12 y + 48\\right)} + \\frac{1}{y - \\frac{3}{x}} & - \\frac{\\left(5 - \\frac{6}{x}\\right) \\left(x y - 3\\right)}{\\left(y - \\frac{3}{x}\\right) \\left(8 x y - 35 x - 12 y + 48\\right)}\\\\\\frac{\\left(x y - 3\\right) \\left(\\frac{21 - \\frac{18}{x}}{x \\left(y - \\frac{3}{x}\\right)} - \\frac{6}{x}\\right)}{8 x y - 35 x - 12 y + 48} & - \\frac{\\left(7 - \\frac{6}{x}\\right) \\left(x y - 3\\right)}{\\left(y - \\frac{3}{x}\\right) \\left(8 x y - 35 x - 12 y + 48\\right)} & \\frac{x y - 3}{8 x y - 35 x - 12 y + 48}\\end{matrix}\\right]$$" ], "text/plain": [ "⎡ ⎛ 6 ⎞ ⎛ ⎛ 6⎞ ⎞ \n", "⎢ ⎜ 5 - ─ ⎟ ⎜3⋅⎜7 - ─⎟ ⎟ \n", "⎢ ⎜ x 2⎟ ⎜ ⎝ x⎠ 6⎟ ⎛ 6⎞ \n", "⎢ (x⋅y - 3)⋅⎜- ───────── + ─⎟⋅⎜───────── - ─⎟ ⎜7 - ─⎟⋅(x⋅y \n", "⎢ ⎜ ⎛ 3⎞ x⎟ ⎜ ⎛ 3⎞ x⎟ ⎝ x⎠ \n", "⎢ ⎜ x⋅⎜y - ─⎟ ⎟ ⎜x⋅⎜y - ─⎟ ⎟ \n", "⎢ ⎝ ⎝ x⎠ ⎠ ⎝ ⎝ x⎠ ⎠ 1 3 \n", "⎢- ─────────────────────────────────────────── + ─ + ────────── ─────────────\n", "⎢ 8⋅x⋅y - 35⋅x - 12⋅y + 48 x 2 ⎛ 3⎞ ⎛ 3⎞ \n", "⎢ x ⋅⎜y - ─⎟ ⎜y - ─⎟⋅(8⋅x\n", "⎢ ⎝ x⎠ ⎝ x⎠ \n", "⎢ \n", "⎢ ⎛ ⎛ 6⎞ ⎞ \n", "⎢ ⎜3⋅⎜7 - ─⎟ ⎟ \n", "⎢ ⎛ 6⎞ ⎜ ⎝ x⎠ 6⎟ \n", "⎢ ⎜5 - ─⎟⋅(x⋅y - 3)⋅⎜───────── - ─⎟ \n", "⎢ ⎝ x⎠ ⎜ ⎛ 3⎞ x⎟ ⎛ 6\n", "⎢ ⎜x⋅⎜y - ─⎟ ⎟ ⎜5 - ─\n", "⎢ ⎝ ⎝ x⎠ ⎠ 3 ⎝ x\n", "⎢ - ────────────────────────────────── - ───────── ───────────\n", "⎢ ⎛ 3⎞ ⎛ 3⎞ 2 \n", "⎢ ⎜y - ─⎟⋅(8⋅x⋅y - 35⋅x - 12⋅y + 48) x⋅⎜y - ─⎟ ⎛ 3⎞ \n", "⎢ ⎝ x⎠ ⎝ x⎠ ⎜y - ─⎟ ⋅(8\n", "⎢ ⎝ x⎠ \n", "⎢ \n", "⎢ ⎛ ⎛ 6⎞ ⎞ \n", "⎢ ⎜3⋅⎜7 - ─⎟ ⎟ \n", "⎢ ⎜ ⎝ x⎠ 6⎟ \n", "⎢ (x⋅y - 3)⋅⎜───────── - ─⎟ \n", "⎢ ⎜ ⎛ 3⎞ x⎟ \n", "⎢ ⎜x⋅⎜y - ─⎟ ⎟ \n", "⎢ ⎝ ⎝ x⎠ ⎠ \n", "⎢ ───────────────────────── ───────\n", "⎢ 8⋅x⋅y - 35⋅x - 12⋅y + 48 ⎛ 3⎞\n", "⎢ ⎜y - ─⎟\n", "⎣ ⎝ x⎠\n", "\n", " ⎛ 6 ⎞ ⎛ 6 ⎞ ⎤\n", " ⎜ 5 - ─ ⎟ ⎜ 5 - ─ ⎟ ⎥\n", " ⎜ x 2⎟ ⎜ x 2⎟ ⎥\n", "- 3)⋅⎜- ───────── + ─⎟ -(x⋅y - 3)⋅⎜- ───────── + ─⎟ ⎥\n", " ⎜ ⎛ 3⎞ x⎟ ⎜ ⎛ 3⎞ x⎟ ⎥\n", " ⎜ x⋅⎜y - ─⎟ ⎟ ⎜ x⋅⎜y - ─⎟ ⎟ ⎥\n", " ⎝ ⎝ x⎠ ⎠ 1 ⎝ ⎝ x⎠ ⎠ ⎥\n", "────────────────────── - ───────── ───────────────────────────── ⎥\n", " ⎛ 3⎞ 8⋅x⋅y - 35⋅x - 12⋅y + 48 ⎥\n", "⋅y - 35⋅x - 12⋅y + 48) x⋅⎜y - ─⎟ ⎥\n", " ⎝ x⎠ ⎥\n", " ⎥\n", " ⎥\n", " ⎥\n", " ⎥\n", " ⎥\n", "⎞ ⎛ 6⎞ ⎛ 6⎞ ⎥\n", "⎟⋅⎜7 - ─⎟⋅(x⋅y - 3) -⎜5 - ─⎟⋅(x⋅y - 3) ⎥\n", "⎠ ⎝ x⎠ 1 ⎝ x⎠ ⎥\n", "──────────────────────── + ───── ──────────────────────────────────⎥\n", " 3 ⎛ 3⎞ ⎥\n", " y - ─ ⎜y - ─⎟⋅(8⋅x⋅y - 35⋅x - 12⋅y + 48)⎥\n", "⋅x⋅y - 35⋅x - 12⋅y + 48) x ⎝ x⎠ ⎥\n", " ⎥\n", " ⎥\n", " ⎥\n", " ⎥\n", " ⎥\n", " ⎥\n", " ⎛ 6⎞ ⎥\n", "-⎜7 - ─⎟⋅(x⋅y - 3) ⎥\n", " ⎝ x⎠ x⋅y - 3 ⎥\n", "─────────────────────────── ──────────────────────── ⎥\n", " 8⋅x⋅y - 35⋅x - 12⋅y + 48 ⎥\n", "⋅(8⋅x⋅y - 35⋅x - 12⋅y + 48) ⎥\n", " ⎦" ] }, "execution_count": 151, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat.inv()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 行列式" ] }, { "cell_type": "code", "execution_count": 152, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMEAAAASBAMAAAAQxqcuAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nnybrcdXf2WS1aWEkQ/fPVuKfwr9Z4rB6i9H4vwAAAABJRU5ErkJggg==\n", "text/latex": [ "$$8 x y - 35 x - 12 y + 48$$" ], "text/plain": [ "8⋅x⋅y - 35⋅x - 12⋅y + 48" ] }, "execution_count": 152, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat.det()" ] }, { "cell_type": "code", "execution_count": 153, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAABoAAABLCAMAAABZRmeuAAAAPFBMVEX///8AAAAAAAAAAAAAAAAA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\nmLYV+HIigR+CuxjaDkNGvAAAAABJRU5ErkJggg==\n", "text/latex": [ "$$\\left[\\begin{matrix}3\\\\7\\\\5\\end{matrix}\\right]$$" ], "text/plain": [ "⎡3⎤\n", "⎢ ⎥\n", "⎢7⎥\n", "⎢ ⎥\n", "⎣5⎦" ] }, "execution_count": 153, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mat_a = Matrix([\n", " [2, 3, 5], \n", " [3, 6, 2], \n", " [8, 3, 6]])\n", "mat_x = Matrix(3, 1, [3,7,5])\n", "mat_b = mat_a * mat_x\n", "mat_a.LUsolve(mat_b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## グラフ" ] }, { "cell_type": "code", "execution_count": 154, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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