{"id":4986,"date":"2023-12-18T10:40:15","date_gmt":"2023-12-18T01:40:15","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=4986"},"modified":"2025-01-22T15:10:03","modified_gmt":"2025-01-22T06:10:03","slug":"maxima-%e3%81%a6%e3%82%99%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","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%8f%82%e8%80%83%ef%bc%9amaxima-%e7%b7%a8\/maxima-%e3%81%a6%e3%82%99%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\/","title":{"rendered":"Maxima \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\uff0cMaxima \u3092\u4f7f\u3063\u3066\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\/\">\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=\"quad_qags()-\u3067\u6570\u5024\u7a4d\u5206\u3059\u308b\"><code>quad_qags()<\/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\uff0c\u30a8\u30cd\u30eb\u30ae\u30fc\u4fdd\u5b58\u5247\u306e\u7a4d\u5206\u304b\u3089\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002<\/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>\u7a4d\u5206\u90e8\u5206\u306f\u6570\u5024\u7a4d\u5206 <code>quad_qags()<\/code> \u3092\u4f7f\u3046\u3002\uff08<code>romberg()<\/code> \u3067\u306f\u306a\u304f <code>quad_qags()<\/code> \u3092\u4f7f\u3046\uff01\uff09<\/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>\u3053\u306e\u7a4d\u5206\u304c\u4e00\u898b\u3084\u3063\u304b\u3044\u306a\u306e\u306f\uff0c\u7a4d\u5206\u7bc4\u56f2\u306e\u4e0a\u9650 $\\theta = \\theta_0$ \u3067\u88ab\u7a4d\u5206\u95a2\u6570\u306e\u5206\u6bcd\u304c\u30bc\u30ed\u306b\u306a\u308b\u3053\u3068\u3067\u3059\u3002$\\theta = \\theta_0$ \u3067\u88ab\u7a4d\u5206\u95a2\u6570\u304c\u767a\u6563\u3057\u3066\u3057\u307e\u3046\u306e\u3067\uff0c\u4f55\u304b\u30a8\u30e9\u30fc\u3067\u3082\u8d77\u3053\u308b\u306e\u304b\u3068\u601d\u3044\u304d\u3084\uff0c<code>quad_qags()<\/code> \u306f\u5927\u5909\u512a\u79c0\u3067\u4f55\u4e8b\u3082\u306a\u304b\u3063\u305f\u304b\u306e\u3088\u3046\u306b\u6570\u5024\u7a4d\u5206\u3057\u3066\u3057\u307e\u3044\u307e\u3059\uff01<\/p>\n<p>\u305f\u3081\u3057\u306b $\\theta_0 = 60^{\\circ}$ \u306e\u5834\u5408\u306e\u7a4d\u5206\u5024\u3092\u6570\u5024\u7a4d\u5206 <code>quad_qags()<\/code> \u3067\u6c42\u3081\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[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5ea6\u3092\u30e9\u30b8\u30a2\u30f3\u306b\u5909\u63db\u3059\u308b\u95a2\u6570\u3092\u6e96\u5099\u3057\u3066\u304a\u304f *\/<\/span>\r\n<span class=\"nf\">radians<\/span><span class=\"p\">(<\/span><span class=\"nv\">deg<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">deg<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span>180$\r\n\r\n<span class=\"nv\">th0<\/span><span class=\"o\">:<\/span> 60$\r\n<span class=\"nv\">theta0<\/span><span class=\"o\">:<\/span> <span class=\"nf\">radians<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">quad_qags<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">*<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">theta<\/span><span class=\"p\">)<\/span><span class=\"o\">-<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">theta0<\/span><span class=\"p\">)))<\/span>, \r\n          <span class=\"nv\">theta<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">theta0<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[1]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{4}$}\\left[ 1.073182007084969 , 1.400735083478821 \\times 10^{-10} , 315 , 0 \\right] \\]<\/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><code>quad_qags()<\/code> \u306f\uff14\u3064\u306e\u8981\u7d20\u306e\u30ea\u30b9\u30c8\u3092\u8fd4\u3057\u307e\u3059:<\/p>\n<p>\u7a4d\u5206\u306e\u8fd1\u4f3c\u5024<br \/>\n\u898b\u7a4d\u3082\u3089\u308c\u305f\u8fd1\u4f3c\u306e\u7d76\u5bfe\u8aa4\u5dee<br \/>\n\u88ab\u7a4d\u5206\u95a2\u6570\u306e\u8a55\u4fa1\u6570<br \/>\n\u30a8\u30e9\u30fc\u30b3\u30fc\u30c9<\/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=\"quad_qags()-\u3067-Tp1(th0)\"><code>quad_qags()<\/code> \u3067 <code>Tp1(th0)<\/code><\/h4>\n<p>\u7a4d\u5206\u3092\u4f7f\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u305f\u5468\u671f\u3092 <code>Tp1(th0)<\/code> \u3068\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[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">Tp1<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">block<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u5ea6\u3067\u5165\u529b\u3057\u305f th \u3092\u30e9\u30b8\u30a2\u30f3\u306b\u306a\u304a\u3059 *\/<\/span>\r\n  <span class=\"nv\">theta0<\/span><span class=\"o\">:<\/span> <span class=\"nf\">radians<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"cm\">\/* quad_gags() \u3067\u6570\u5024\u7a4d\u5206\u3057\uff0ctmp \u306b\u683c\u7d0d\u3059\u308b *\/<\/span>\r\n  <span class=\"nv\">ans<\/span><span class=\"o\">:<\/span> <span class=\"nf\">quad_qags<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">*<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">theta<\/span><span class=\"p\">)<\/span><span class=\"o\">-<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">theta0<\/span><span class=\"p\">)))<\/span>, <span class=\"nv\">theta<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">theta0<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u7a4d\u5206\u306e\u8fd1\u4f3c\u5024\u3092 ans[1] \u3068\u3057\u3066\u53d6\u308a\u51fa\u3059 *\/<\/span>\r\n  <span class=\"nf\">return<\/span><span class=\"p\">(<\/span><span class=\"nv\">ans<\/span><span class=\"p\">[<\/span>1<span class=\"p\">])<\/span>\r\n<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[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">Tp1<\/span><span class=\"p\">(<\/span><span class=\"mi\">60<\/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[3]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{6}$}1.073182007084969\\]<\/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=\"\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=\"quad_qags()-\u3067-Tp2(th0)\"><code>quad_qags()<\/code> \u3067 <code>Tp2(th0)<\/code><\/h4>\n<p>\u7f6e\u63db\u7a4d\u5206\u3092\u4f7f\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u305f\u5468\u671f\u3092 <code>Tp2(th0)<\/code> \u3068\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[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">Tp2<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">block<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u5ea6\u3067\u5165\u529b\u3057\u305f th \u3092\u30e9\u30b8\u30a2\u30f3\u306b\u306a\u304a\u3059 *\/<\/span>\r\n  <span class=\"nv\">theta0<\/span><span class=\"o\">:<\/span> <span class=\"nf\">radians<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">)<\/span>, \r\n  <span class=\"nv\">m<\/span><span class=\"o\">:<\/span> <span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">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  \r\n  <span class=\"cm\">\/* quad_gags() \u3067\u6570\u5024\u7a4d\u5206\u3057\uff0ctmp \u306b\u683c\u7d0d\u3059\u308b *\/<\/span>\r\n  <span class=\"nv\">ans<\/span><span class=\"o\">:<\/span> <span class=\"nf\">quad_qags<\/span><span class=\"p\">(<\/span>2<span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">*<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span>1<span class=\"o\">-<\/span><span class=\"nv\">m<\/span><span class=\"o\">*<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span>, <span class=\"nv\">t<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u7a4d\u5206\u306e\u8fd1\u4f3c\u5024\u3092 tmp[1] \u3068\u3057\u3066\u53d6\u308a\u51fa\u3057\uff0c\u4fc2\u6570\u3092\u304b\u3051\u3066\u5468\u671f\u3092\u304b\u3048\u3059 *\/<\/span>\r\n  <span class=\"nf\">return<\/span><span class=\"p\">(<\/span><span class=\"nv\">ans<\/span><span class=\"p\">[<\/span>1<span class=\"p\">])<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">Tp2<\/span><span class=\"p\">(<\/span><span class=\"mi\">60<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[5]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{8}$}1.073182007149364\\]<\/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<br \/>\n\u7b2c1\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206 $K(k)$ \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=\"elliptic_kc(m)-\u3067-Tp3(th0)\"><code>elliptic_kc(m)<\/code> \u3067 <code>Tp3(th0)<\/code><\/h4>\n<p>\u3042\u308a\u304c\u305f\u3044\u3053\u3068\u306b\uff0cMaxima \u3067\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u305f\u7b2c\u4e00\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206\u304c <code>elliptic_kc(m)<\/code> \u3068\u3057\u3066\u4f7f\u3048\u307e\u3059\u3002<\/p>\n<p>$$\\mbox{elliptic_kc(m)} = K(m) \\equiv \\int_0^{\\frac{\\pi}{2}}\\frac{1}{\\sqrt{1 &#8211; m \\sin^2 x}} dx$$<\/p>\n<p>\u7b2c1\u7a2e\u5b8c\u5168\u6955\u5186\u7a4d\u5206 <code>elliptic_kc(m)<\/code> \u3092\u4f7f\u3063\u3066\uff0c<code>Tp3(th0)<\/code> \u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3059\u308b\u3002\uff08$m = k^2$ \u306b\u6ce8\u610f\u3002\uff09<\/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-maxima\">\n<pre><span class=\"nf\">Tp3<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">block<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u5ea6\u3067\u5165\u529b\u3057\u305f th \u3092\u30e9\u30b8\u30a2\u30f3\u306b\u306a\u304a\u3059 *\/<\/span>\r\n  <span class=\"nv\">theta0<\/span><span class=\"o\">:<\/span> <span class=\"nf\">radians<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">)<\/span>, \r\n  <span class=\"nv\">m<\/span><span class=\"o\">:<\/span> <span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">theta0<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>,\r\n    \r\n  <span class=\"nf\">return<\/span><span class=\"p\">(<\/span>2<span class=\"o\">\/<\/span><span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">elliptic_kc<\/span><span class=\"p\">(<\/span><span class=\"nv\">m<\/span><span class=\"p\">))<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">ev<\/span><span class=\"p\">(<\/span><span class=\"nf\">Tp3<\/span><span class=\"p\">(<\/span><span class=\"mi\">60<\/span><span class=\"p\">))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[7]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{10}$}1.073182007149365\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"Tp3(th0)-\u306e\u30b0\u30e9\u30d5\"><code>Tp3(th0)<\/code> \u306e\u30b0\u30e9\u30d5<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[8]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5909\u6570 th0 \u306e\u521d\u671f\u5316 *\/<\/span>\r\n<span class=\"nf\">kill<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u5358\u632f\u308a\u5b50\u306e\u632f\u5e45\u3068\u5468\u671f\u306e\u95a2\u4fc2\"<\/span>,\r\n  <span class=\"cm\">\/* \u30b0\u30ea\u30c3\u30c9  *\/<\/span>\r\n  <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>, \r\n  <span class=\"cm\">\/* \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u632f\u5e45 \u03b8 (\u00b0)\"<\/span>, \r\n  <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u898f\u683c\u5316\u3055\u308c\u305f\u5468\u671f T\"<\/span>, \r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 90<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mf\">0.95<\/span>, 1<span class=\"o\">.<\/span>2<span class=\"p\">]<\/span>, \r\n  <span class=\"cm\">\/* \u7dda\u306e\u592a\u3055 *\/<\/span>\r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>,\r\n\r\n  <span class=\"cm\">\/* \u967d\u95a2\u6570 y = f(x) \u306e\u30b0\u30e9\u30d5 *\/<\/span>\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">Tp3<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">th0<\/span>, <span class=\"mi\">1<\/span>, <span class=\"mi\">90<\/span><span class=\"p\">)<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \"><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-7408\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mfuriTp3A.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u7df4\u7fd2\">\u7df4\u7fd2<\/h3>\n<p><code>Tp1(th0)<\/code>\uff0c<code>Tp2(th0)<\/code>\uff0c<code>Tp3(th0)<\/code> \u306e\u8aa4\u5dee\u3092\u8abf\u3079\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">th0<\/span><span class=\"o\">:<\/span> 1$\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>, <span class=\"s\">\"Tp1(~2d) = ~,15f~%\"<\/span>, <span class=\"nv\">th0<\/span>, <span class=\"nf\">Tp1<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">))<\/span>$\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>, <span class=\"s\">\"Tp2(~2d) = ~,15f~%\"<\/span>, <span class=\"nv\">th0<\/span>, <span class=\"nf\">Tp2<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">))<\/span>$\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>, <span class=\"s\">\"Tp3(~2d) = ~,15f~%\"<\/span>, <span class=\"nv\">th0<\/span>, <span class=\"nf\">Tp3<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">))<\/span>$\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>, <span class=\"s\">\" ~%\"<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"k\">for<\/span> <span class=\"nv\">th0<\/span><span class=\"o\">:<\/span><span class=\"mi\">10<\/span> <span class=\"k\">thru<\/span> <span class=\"mi\">90<\/span> <span class=\"k\">step<\/span> <span class=\"mi\">10<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>, <span class=\"s\">\"Tp1(~2d) = ~,15f~%\"<\/span>, <span class=\"nv\">th0<\/span>, <span class=\"nf\">Tp1<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">))<\/span>,\r\n  <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>, <span class=\"s\">\"Tp2(~2d) = ~,15f~%\"<\/span>, <span class=\"nv\">th0<\/span>, <span class=\"nf\">Tp2<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">))<\/span>,\r\n  <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>, <span class=\"s\">\"Tp3(~2d) = ~,15f~%\"<\/span>, <span class=\"nv\">th0<\/span>, <span class=\"nf\">Tp3<\/span><span class=\"p\">(<\/span><span class=\"nv\">th0<\/span><span class=\"p\">))<\/span>, \r\n  <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>, <span class=\"s\">\" ~%\"<\/span><span class=\"p\">)<\/span>\r\n<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) = 1.000019039102995\r\nTp2( 1) = 1.000019038921006\r\nTp3( 1) = 1.000019038921006\r\n \r\nTp1(10) = 1.001907188137489\r\nTp2(10) = 1.001907188143217\r\nTp3(10) = 1.001907188143216\r\n \r\nTp1(20) = 1.007669025790934\r\nTp2(20) = 1.007669025791545\r\nTp3(20) = 1.007669025791545\r\n \r\nTp1(30) = 1.017408797605583\r\nTp2(30) = 1.017408797595956\r\nTp3(30) = 1.017408797595956\r\n \r\nTp1(40) = 1.031340519129231\r\nTp2(40) = 1.031340519130037\r\nTp3(40) = 1.031340519130037\r\n \r\nTp1(50) = 1.049782960621873\r\nTp2(50) = 1.049782960623032\r\nTp3(50) = 1.049782960623032\r\n \r\nTp1(60) = 1.073182007084969\r\nTp2(60) = 1.073182007149364\r\nTp3(60) = 1.073182007149365\r\n \r\nTp1(70) = 1.102144909638067\r\nTp2(70) = 1.102144909639270\r\nTp3(70) = 1.102144909639270\r\n \r\nTp1(80) = 1.137492559922217\r\nTp2(80) = 1.137492559923922\r\nTp3(80) = 1.137492559923922\r\n \r\nTp1(90) = 1.180340599016036\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\uff0cMaxima \u3092\u4f7f\u3063\u3066\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%8f%82%e8%80%83%ef%bc%9amaxima-%e7%b7%a8\/maxima-%e3%81%a6%e3%82%99%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\/\">\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":7137,"menu_order":50,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-4986","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\/4986","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=4986"}],"version-history":[{"count":14,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4986\/revisions"}],"predecessor-version":[{"id":10062,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4986\/revisions\/10062"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/7137"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=4986"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}