{"id":7400,"date":"2025-01-10T11:00:02","date_gmt":"2025-01-10T02:00:02","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=7400"},"modified":"2025-01-23T10:14:28","modified_gmt":"2025-01-23T01:14:28","slug":"sympy-%e3%81%a7%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e6%ba%96\/sympy-%e3%81%a7%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81\/","title":{"rendered":"SymPy \u3066\u3099\u5358\u632f\u308a\u5b50\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247\u304b\u3089\u5468\u671f\u3092\u6c42\u3081\u308b"},"content":{"rendered":"<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u304b\u3089\u5f97\u3089\u308c\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247\u304b\u3089\uff0cPython \u306e SymPy\u3092\u4f7f\u3063\u3066\uff08\u304b\u3064 SciPy \u3068 NumPy \u306f\u4f7f\u308f\u305a\u306b\uff09\u6570\u5024\u7a4d\u5206\u306b\u3088\u3063\u3066\u5468\u671f\u3092\u6c42\u3081\u308b\u3002\u5c0e\u51fa\u306b\u3064\u3044\u3066\u306f\u4ee5\u4e0b\u3092\u53c2\u7167\uff1a<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e6%ba%96\/\" target=\"_blank\" rel=\"noopener\">\u5358\u632f\u308a\u5b50\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247\u304b\u3089\u5468\u671f\u3092\u6c42\u3081\u308b\u6e96\u5099<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<p><!--more--><\/p>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u30e9\u30a4\u30d6\u30e9\u30ea\u306e-import\">\u30e9\u30a4\u30d6\u30e9\u30ea\u306e import<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"kn\">from<\/span> <span class=\"nn\">sympy.abc<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">sympy<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n\r\n<span class=\"c1\"># SymPy Plotting Backends (SPB) \u3067\u30b0\u30e9\u30d5\u3092\u63cf\u304f<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">spb<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n\r\n<span class=\"c1\"># ax \u7528<\/span>\r\n<span class=\"kn\">import<\/span> <span class=\"nn\">matplotlib.pyplot<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">plt<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30e9\u30d5\u3092 SVG \u3067 Notebook \u306b\u30a4\u30f3\u30e9\u30a4\u30f3\u8868\u793a<\/span>\r\n<span class=\"o\">%<\/span><span class=\"k\">config<\/span> InlineBackend.figure_formats = ['svg']\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"SymPy-\u306e-N()-\u3067\u6570\u5024\u7a4d\u5206\u3059\u308b\">SymPy \u306e <code>N()<\/code> \u3067\u6570\u5024\u7a4d\u5206\u3059\u308b<\/h3>\n<p>\u632f\u5e45 $\\theta_0$ \u306e\u5358\u632f\u308a\u5b50\u306e\u5468\u671f $T_p$ \u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\nT_p(\\theta_0) &amp;=&amp;<br \/>\n\\frac{2}{\\pi} \\int_{0}^{\\theta_0} \\frac{1}{\\sqrt{2(\\cos\\theta-\\cos\\theta_0)}}d\\theta \\\\<br \/>\n&amp;=&amp;<br \/>\n\\frac{\\sqrt{2}}{\\pi} \\int_{0}^{\\theta_0} \\frac{1}{\\sqrt{\\cos\\theta-\\cos\\theta_0}}d\\theta<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3053\u308c\u3092 <code>Tp(th0)<\/code> \u3068\u5b9a\u7fa9\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u305f\u3081\u3057\u306b\uff0c$\\theta_0 = 80^{\\circ}$ \u3068\u3057\u3066\u8a08\u7b97\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u30e9\u30b8\u30a2\u30f3\u306b\u5909\u63db<\/span>\r\n<span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">rad<\/span><span class=\"p\">(<\/span><span class=\"mi\">80<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># Tp \u306e\u8a08\u7b97<\/span>\r\n<span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"n\">pi<\/span><span class=\"o\">*<\/span><span class=\"n\">integrate<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">\/<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">)<\/span><span class=\"o\">-<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">theta0<\/span><span class=\"p\">)),<\/span> <span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta0<\/span><span class=\"p\">))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[2]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle \\frac{\\sqrt{2} \\int\\limits_{0}^{\\frac{4 \\pi}{9}} \\frac{1}{\\sqrt{\\cos{\\left(\\theta \\right)} &#8211; \\cos{\\left(\\frac{4 \\pi}{9} \\right)}}}\\, d\\theta}{\\pi}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u89e3\u6790\u7684\u306b\u7a4d\u5206\u3067\u304d\u306a\u3044\u5834\u5408\uff0cSymPy \u306f\u5f0f\u3092\u305d\u306e\u307e\u307e\u8fd4\u3057\u307e\u3059\u3002<\/p>\n<p>\u3053\u308c\u3092\u6570\u5024\u7684\u306b\u6c42\u3081\u308b\u306b\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b <code>N()<\/code> \u3067\u56f2\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Jupyter Notebook \u3067\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u30bb\u30eb\u306e1\u884c\u76ee\u306b <code>%%time<\/code> \u3092\u5165\u308c\u308b\u3068\uff0c\u8a08\u7b97\u306b\u304b\u304b\u3063\u305f\u6642\u9593\u3092\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">rad<\/span><span class=\"p\">(<\/span><span class=\"mi\">80<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">N<\/span><span class=\"p\">(<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"n\">pi<\/span> <span class=\"o\">*<\/span> \r\n  <span class=\"n\">integrate<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">\/<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">)<\/span><span class=\"o\">-<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">theta0<\/span><span class=\"p\">)),<\/span> <span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta0<\/span><span class=\"p\">)))<\/span>\r\n<span class=\"c1\"># \u3051\u3063\u3053\u3046\u6642\u9593\u304c\u304b\u304b\u308b<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 4.42 s, sys: 9.76 ms, total: 4.43 s\r\nWall time: 4.43 s\r\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[3]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle 1.13749255992392$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"SymPy-\u306e-N()-\u3067-Tp1(th0)\">SymPy \u306e <code>N()<\/code> \u3067 <code>Tp1(th0)<\/code><\/h4>\n<p>\u521d\u3081\u304b\u3089 <code>N()<\/code> \u3067\u6570\u5024\u7a4d\u5206\u3057\u305f\u3092\u8fd4\u3059\u95a2\u6570\u3092 <code>Tp1(th0)<\/code> \u3068\u3057\u3066\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"k\">def<\/span> <span class=\"nf\">Tp1<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"sd\">\"\"\"\u5ea6\u3067\u4e0e\u3048\u3089\u308c\u305f\u632f\u5e45 th0 \u304b\u3089<\/span>\r\n<span class=\"sd\">       \u898f\u683c\u5316\u3055\u308c\u305f\u5358\u632f\u308a\u5b50\u306e\u898f\u683c\u5316\u3055\u308c\u305f\u5468\u671f\u3092\u6c42\u3081\u308b\"\"\"<\/span>\r\n    <span class=\"c1\"># \u5ea6\u3067\u4e0e\u3048\u3089\u308c\u305f th0 \u304b\u3089\u30e9\u30b8\u30a2\u30f3\u3078\u5909\u63db<\/span>\r\n    <span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">rad<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">ans<\/span> <span class=\"o\">=<\/span> <span class=\"n\">N<\/span><span class=\"p\">(<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"n\">pi<\/span> <span class=\"o\">*<\/span> \r\n            <span class=\"n\">integrate<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">\/<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">)<\/span><span class=\"o\">-<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">theta0<\/span><span class=\"p\">)),<\/span> <span class=\"p\">(<\/span><span class=\"n\">theta<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">theta0<\/span><span class=\"p\">)))<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">ans<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">Tp1<\/span><span class=\"p\">(<\/span><span class=\"mi\">80<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 4.27 s, sys: 28.3 ms, total: 4.3 s\r\nWall time: 4.3 s\r\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[5]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle 1.13749255992392$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>SymPy \u306f\u89e3\u6790\u7684\u306a\u5fae\u5206\u3084\u7a4d\u5206\u304c\u3067\u304d\u308b\u306e\u3067\u4fbf\u5229\u3067\u3059\u304c\uff0c\u6570\u5024\u7a4d\u5206\u306e\u5834\u5408\u3060\u3068\u5999\u306b\u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>SymPy \u306e\u7a4d\u5206\u305d\u306e\u3082\u306e\u304c\u9045\u304f\u3066\u3064\u304b\u3044\u3082\u306e\u306b\u306a\u3089\u306a\u3044\u3068\u3044\u3046\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\uff0c\u5ff5\u306e\u305f\u3081\u3002\u7a4d\u5206\u7bc4\u56f2\uff08\u7aef\u70b9\uff09\u3067\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u767a\u6563\u3059\u308b\u3088\u3046\u306a\u30b1\u30fc\u30b9\u3092 <code>N()<\/code> \u3067\u6570\u5024\u8a08\u7b97\u3059\u308b\u5834\u5408\uff0c\u3044\u308d\u3044\u308d\u8003\u3048\u3066\u9670\u3067\u3042\u306e\u624b\u3053\u306e\u624b\u3092\u8a66\u3057\u3066\u3044\u308b\u305f\u3081\u304b\u3068\u63a8\u5bdf\u3057\u307e\u3059\u3002\u306e\u3061\u306b\u793a\u3059\u3088\u3046\u306b\uff0c\u3053\u306e\u7a4d\u5206\u306f\u9069\u5f53\u306a\u5909\u6570\u5909\u63db\u306b\u3088\u3063\u3066\uff0c\u7a4d\u5206\u7bc4\u56f2\u5185\u3067\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u767a\u6563\u3057\u306a\u3044\u5f62\u306b\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u5834\u5408\u306b\u306f\uff0c<code>N()<\/code> \u3082\u305d\u3093\u306a\u306b\u6642\u9593\u304c\u304b\u304b\u3089\u305a\u306b\u7b54\u3048\u3092\u51fa\u3057\u3066\u304f\u308c\u307e\u3059\u3088\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u7f6e\u63db\u7a4d\u5206\u3067\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u767a\u6563\u3057\u306a\u3044\u3088\u3046\u306b\u3059\u308b\">\u7f6e\u63db\u7a4d\u5206\u3067\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u767a\u6563\u3057\u306a\u3044\u3088\u3046\u306b\u3059\u308b<\/h3>\n<p><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e6%ba%96\/#1\">\u3053\u306e\u3078\u3093<\/a>\u306b\u307e\u3068\u3081\u3066\u3044\u308b\u3088\u3046\u306b\uff0c\u5909\u6570\u5909\u63db\u306b\u3088\u3063\u3066<br \/>\n\\begin{eqnarray}<br \/>\n\\int_0^{\\theta_0} \\frac{1}{\\sqrt{2(\\cos\\theta-\\cos\\theta_0)}} d\\theta<br \/>\n&amp;=&amp;<br \/>\n\\int_0^{\\pi\/2} \\frac{dt}{\\sqrt{1 &#8211; k^2 \\sin^2 t}}, \\\\ \\quad k &amp;\\equiv&amp; \\sin\\frac{\\theta_0}{2}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3068\u66f8\u3051\u308b\u3002\u3053\u306e\u5f62\u306b\u3059\u308b\u3068\uff0c\u7a4d\u5206\u7bc4\u56f2\u5185\u3067\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u767a\u6563\u3059\u308b\u3053\u3068\u3082\u306a\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"SymPy-\u306e-N()-\u3067-Tp2(th0)\">SymPy \u306e <code>N()<\/code> \u3067 <code>Tp2(th0)<\/code><\/h4>\n<p>\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u767a\u6563\u3057\u306a\u3044\u3088\u3046\u306b\u5909\u6570\u5909\u63db\u3092\u884c\u3063\u305f\u3042\u3068\u306b\uff0c\u6570\u5024\u7a4d\u5206\u3059\u308b\u95a2\u6570\u3092 <code>Tp2(th0)<\/code> \u3068\u3057\u3066\u5b9a\u7fa9\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"k\">def<\/span> <span class=\"nf\">Tp2<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">N<\/span><span class=\"p\">(<\/span><span class=\"n\">rad<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">))<\/span>\r\n    <span class=\"n\">m<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">theta0<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span>\r\n    <span class=\"n\">ans<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span><span class=\"o\">\/<\/span><span class=\"n\">N<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"n\">N<\/span><span class=\"p\">(<\/span><span class=\"n\">integrate<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">\/<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">m<\/span><span class=\"o\">*<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">)))<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">ans<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">Tp2<\/span><span class=\"p\">(<\/span><span class=\"mi\">80<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 932 ms, sys: 4.02 ms, total: 936 ms\r\nWall time: 935 ms\r\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[7]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle 1.13749255992392$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u7b2c1\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206\u3092\u4f7f\u3046\">\u7b2c1\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206\u3092\u4f7f\u3046<\/h3>\n<p><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e6%ba%96\/#1\">\u3053\u306e\u3078\u3093<\/a>\u306b\u307e\u3068\u3081\u3066\u3044\u308b\u3088\u3046\u306b\uff0c<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u7b2c1\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206<\/strong><\/span> $K(k)$ \u3092\u4f7f\u3046\u3068\uff0c\u632f\u5e45 $\\theta_0$ \u306e\u5358\u632f\u308a\u5b50\u306e\u5468\u671f $T_p$ \u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\nT_p(\\theta_0) &amp;=&amp;<br \/>\n\\frac{2}{\\pi} \\int_{0}^{\\theta_0} \\frac{1}{\\sqrt{2(\\cos\\theta-\\cos\\theta_0)}}d\\theta \\\\<br \/>\n&amp;=&amp; \\frac{2}{\\pi} K(k) \\\\<br \/>\n&amp;=&amp; \\frac{2}{\\pi}\\int_0^{\\pi\/2} \\frac{dt}{\\sqrt{1-k^2 \\sin^2 t}}, \\quad k \\equiv \\sin\\frac{\\theta_0}{2}<br \/>\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"SymPy-\u306e-elliptic_k()-\u3067-Tp3(th0)\">SymPy \u306e <code>elliptic_k()<\/code> \u3067 <code>Tp3(th0)<\/code><\/h4>\n<p>\u3042\u308a\u304c\u305f\u3044\u3053\u3068\u306b\uff0cSymPy \u3067\u306f<span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u7b2c1\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206<\/strong><\/span> <code>elliptic_k()<\/code> \u304c\u4f7f\u3048\u308b\u3002<\/p>\n<p><code>elliptic_k(m)<\/code> $\\displaystyle \\equiv \\int_0^{\\pi\/2} \\frac{dt}{\\sqrt{1-m \\sin^2 t}}$\u3002 $m \\equiv k^2$ \u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3002<\/p>\n<p><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>\u7b2c1\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206<\/strong><\/span> <code>elliptic_k()<\/code> \u3092\u4f7f\u3063\u3066\u5468\u671f\u3092\u8fd4\u3059\u95a2\u6570\u3092 <code>Tp3(th0)<\/code> \u3068\u3057\u3066\u5b9a\u7fa9\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[8]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"k\">def<\/span> <span class=\"nf\">Tp3<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">theta0<\/span> <span class=\"o\">=<\/span> <span class=\"n\">N<\/span><span class=\"p\">(<\/span><span class=\"n\">rad<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">))<\/span>\r\n    <span class=\"n\">m<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">theta0<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span>\r\n    <span class=\"n\">ans<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span><span class=\"o\">\/<\/span><span class=\"n\">N<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"n\">elliptic_k<\/span><span class=\"p\">(<\/span><span class=\"n\">m<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">ans<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">Tp3<\/span><span class=\"p\">(<\/span><span class=\"mi\">80<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 425 \u00b5s, sys: 48 \u00b5s, total: 473 \u00b5s\r\nWall time: 479 \u00b5s\r\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[9]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle 1.13749255992392$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"Tp3(th0)-\u306e\u30b0\u30e9\u30d5\"><code>Tp3(th0)<\/code> \u306e\u30b0\u30e9\u30d5<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[10]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u632f\u5e45<\/span>\r\n<span class=\"n\">th0s<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"o\">+<\/span> <span class=\"p\">[<\/span><span class=\"mi\">10<\/span><span class=\"o\">*<\/span><span class=\"n\">i<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span><span class=\"mi\">10<\/span><span class=\"p\">)]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[11]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u5468\u671f<\/span>\r\n<span class=\"n\">Tp3s<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n\r\n<span class=\"c1\"># \u5404\u632f\u5e45\u3054\u3068\u306e\u5468\u671f<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">th0<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">th0s<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"n\">Tp3s<\/span> <span class=\"o\">+=<\/span> <span class=\"p\">[<\/span><span class=\"n\">Tp3<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)]<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'\u03b8_0 = <\/span><span class=\"si\">%2d<\/span><span class=\"s1\">\u00b0 \u306e\u3068\u304d\uff0c'<\/span> <span class=\"o\">%<\/span> <span class=\"n\">th0<\/span><span class=\"p\">,<\/span> <span class=\"n\">end<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">''<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'\u5468\u671f T = <\/span><span class=\"si\">%.15f<\/span><span class=\"s1\">'<\/span> <span class=\"o\">%<\/span> <span class=\"n\">Tp3s<\/span><span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">])<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>\u03b8_0 =  1\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.000019038921006\r\n\u03b8_0 = 10\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.001907188143217\r\n\u03b8_0 = 20\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.007669025791545\r\n\u03b8_0 = 30\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.017408797595956\r\n\u03b8_0 = 40\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.031340519130037\r\n\u03b8_0 = 50\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.049782960623032\r\n\u03b8_0 = 60\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.073182007149365\r\n\u03b8_0 = 70\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.102144909639270\r\n\u03b8_0 = 80\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.137492559923922\r\n\u03b8_0 = 90\u00b0 \u306e\u3068\u304d\uff0c\u5468\u671f T = 1.180340599016096\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[12]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># SymPy Plotting Backends \u3067\u30b0\u30e9\u30d5<\/span>\r\n<span class=\"c1\"># \u7d30\u304b\u306a\u8a2d\u5b9a\u306f\u30d0\u30c3\u30af\u30a8\u30f3\u30c9\u306e matplotlib ax \u3067<\/span>\r\n\r\n<span class=\"c1\"># \u304a\u307e\u3058\u306a\u3044\u3002\u3053\u308c\u3067 ax \u304c\u4f7f\u3048\u308b\u3002<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"c1\"># x \u306e\u76ee\u76db\u3092 10 \u523b\u307f\u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">([<\/span><span class=\"mi\">10<\/span><span class=\"o\">*<\/span><span class=\"n\">i<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">10<\/span><span class=\"p\">)])<\/span>\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\u70b9\u7dda\u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">ls<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n         <span class=\"n\">list_2d<\/span><span class=\"p\">(<\/span><span class=\"n\">th0s<\/span><span class=\"p\">,<\/span> <span class=\"n\">Tp3s<\/span><span class=\"p\">,<\/span> <span class=\"n\">scatter<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">,<\/span> \r\n                 <span class=\"n\">rendering_kw<\/span><span class=\"o\">=<\/span><span class=\"p\">{<\/span><span class=\"s2\">\"ms\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">}),<\/span> \r\n         <span class=\"n\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s2\">\"\u632f\u5e45 \u03b8 (\u00b0)\"<\/span><span class=\"p\">,<\/span> \r\n         <span class=\"n\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s2\">\"\u898f\u683c\u5316\u3055\u308c\u305f\u5468\u671f T\"<\/span><span class=\"p\">,<\/span> \r\n         <span class=\"n\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s2\">\"\u5358\u632f\u308a\u5b50\u306e\u632f\u5e45\u3068\u5468\u671f\"<\/span><span class=\"p\">,<\/span> \r\n         <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">91<\/span><span class=\"p\">),<\/span> \r\n         <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mf\">0.98<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.2<\/span><span class=\"p\">),<\/span> \r\n         <span class=\"n\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">,<\/span> <span class=\"c1\"># \u4e00\u65e6 False \u306b\u3057\u3066...<\/span>\r\n         <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ax<\/span>       <span class=\"c1\"># ax \u306e\u8a2d\u5b9a\u3092\u53cd\u6620<\/span>\r\n<span class=\"p\">)<\/span><span class=\"p\">;<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-10002\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/SMPfuri-01.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u307e\u3068\u3081\">\u307e\u3068\u3081<\/h3>\n<p>SymPy \u306e <code>N(integrate())<\/code> \u3067\u6570\u5024\u7a4d\u5206\u3057\u305f\u5834\u5408\u3068\u7b2c\u4e00\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206 <code>elliptic_k(m)<\/code> \u3092\u4f7f\u3063\u305f\u5834\u5408\u306e\u5468\u671f\u3092\u6c42\u3081\u305f\u3002<code>N()<\/code> \u3092\u4f7f\u3063\u305f\u5834\u5408\uff0c\u304b\u306a\u308a\u6642\u9593\u304c\u304b\u304b\u308b\u3053\u3068\u304c\u308f\u304b\u3063\u305f\u3002<\/p>\n<p>\u3057\u304b\u3057\uff0c\u8a08\u7b97\u6642\u9593\u306b\u306f\u5927\u5dee\u304c\u3042\u308b\u3082\u306e\u306e\uff0c\u6570\u5024\u8a08\u7b97\u306e\u7d50\u679c\u306f\u540c\u3058\u5024\u3092\u8fd4\u3059\u3053\u3068\u3082\u4ee5\u4e0b\u306e\u3053\u3068\u304b\u3089\u308f\u304b\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[13]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">th0s<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"o\">+<\/span> <span class=\"p\">[<\/span><span class=\"mi\">10<\/span><span class=\"o\">*<\/span><span class=\"n\">i<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span><span class=\"mi\">10<\/span><span class=\"p\">)]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[14]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">Tp1s<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">th0<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">th0s<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"n\">Tp1s<\/span> <span class=\"o\">+=<\/span> <span class=\"p\">[<\/span><span class=\"n\">Tp1<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 40.3 s, sys: 64.8 ms, total: 40.4 s\r\nWall time: 40.4 s\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[15]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">Tp2s<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">th0<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">th0s<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"n\">Tp2s<\/span> <span class=\"o\">+=<\/span> <span class=\"p\">[<\/span><span class=\"n\">Tp2<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 18.9 s, sys: 140 ms, total: 19 s\r\nWall time: 19 s\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[16]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">Tp3s<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"n\">th0<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">th0s<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"n\">Tp3s<\/span> <span class=\"o\">+=<\/span> <span class=\"p\">[<\/span><span class=\"n\">Tp3<\/span><span class=\"p\">(<\/span><span class=\"n\">th0<\/span><span class=\"p\">)]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 2.62 ms, sys: 0 ns, total: 2.62 ms\r\nWall time: 2.63 ms\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[17]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">th0s<\/span><span class=\"p\">)):<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'Tp1(<\/span><span class=\"si\">%2d<\/span><span class=\"s1\">)=<\/span><span class=\"si\">%.15f<\/span><span class=\"s1\">'<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">th0s<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">],<\/span> <span class=\"n\">Tp1s<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]))<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'Tp2(<\/span><span class=\"si\">%2d<\/span><span class=\"s1\">)=<\/span><span class=\"si\">%.15f<\/span><span class=\"s1\">'<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">th0s<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">],<\/span> <span class=\"n\">Tp2s<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]))<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">'Tp3(<\/span><span class=\"si\">%2d<\/span><span class=\"s1\">)=<\/span><span class=\"si\">%.15f<\/span><span class=\"s1\">'<\/span> <span class=\"o\">%<\/span> <span class=\"p\">(<\/span><span class=\"n\">th0s<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">],<\/span> <span class=\"n\">Tp3s<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]))<\/span>\r\n    <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s1\">''<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>Tp1( 1)=1.000019038921006\r\nTp2( 1)=1.000019038921006\r\nTp3( 1)=1.000019038921006\r\n\r\nTp1(10)=1.001907188143217\r\nTp2(10)=1.001907188143217\r\nTp3(10)=1.001907188143217\r\n\r\nTp1(20)=1.007669025791545\r\nTp2(20)=1.007669025791545\r\nTp3(20)=1.007669025791545\r\n\r\nTp1(30)=1.017408797595956\r\nTp2(30)=1.017408797595956\r\nTp3(30)=1.017408797595956\r\n\r\nTp1(40)=1.031340519130037\r\nTp2(40)=1.031340519130037\r\nTp3(40)=1.031340519130037\r\n\r\nTp1(50)=1.049782960623032\r\nTp2(50)=1.049782960623032\r\nTp3(50)=1.049782960623032\r\n\r\nTp1(60)=1.073182007149364\r\nTp2(60)=1.073182007149365\r\nTp3(60)=1.073182007149365\r\n\r\nTp1(70)=1.102144909639270\r\nTp2(70)=1.102144909639270\r\nTp3(70)=1.102144909639270\r\n\r\nTp1(80)=1.137492559923922\r\nTp2(80)=1.137492559923922\r\nTp3(80)=1.137492559923922\r\n\r\nTp1(90)=1.180340599016096\r\nTp2(90)=1.180340599016096\r\nTp3(90)=1.180340599016096\r\n\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u304b\u3089\u5f97\u3089\u308c\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247\u304b\u3089\uff0cPython \u306e SymPy\u3092\u4f7f\u3063\u3066\uff08\u304b\u3064 SciPy \u3068 NumPy \u306f\u4f7f\u308f\u305a\u306b\uff09\u6570\u5024\u7a4d\u5206\u306b\u3088\u3063\u3066\u5468\u671f\u3092\u6c42\u3081\u308b\u3002\u5c0e\u51fa\u306b\u3064\u3044\u3066\u306f\u4ee5\u4e0b\u3092\u53c2\u7167\uff1a<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e6%ba%96\/sympy-%e3%81%a7%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n<ul>\n<li>\u5358\u632f\u308a\u5b50\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247\u304b\u3089\u5468\u671f\u3092\u6c42\u3081\u308b\u6e96\u5099<\/li>\n<\/ul>\n","protected":false},"author":33,"featured_media":0,"parent":4976,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-7400","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/7400","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=7400"}],"version-history":[{"count":10,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/7400\/revisions"}],"predecessor-version":[{"id":10067,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/7400\/revisions\/10067"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4976"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=7400"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}