{"id":7839,"date":"2024-02-29T16:29:40","date_gmt":"2024-02-29T07:29:40","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=7839"},"modified":"2024-02-29T18:17:24","modified_gmt":"2024-02-29T09:17:24","slug":"maxima-%e3%81%a7%e6%a5%95%e5%86%86%e3%82%84%e5%9b%9e%e8%bb%a2%e6%a5%95%e5%86%86%e4%bd%93%e3%82%92%e6%8f%8f%e3%81%8f","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/7839\/","title":{"rendered":"Maxima \u3067\u6955\u5186\u3084\u56de\u8ee2\u6955\u5186\u4f53\u3092\u63cf\u304f"},"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>\u7406\u5de5\u7cfb\u306e\u6570\u5b66 B \u306e\u6388\u696d\u3067\uff0c\u6955\u5186\u306e\u5468\u9577\u3084\u9762\u7a4d\uff0c\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\u7a4d\u3084\u4f53\u7a4d\u3092\u6c42\u3081\u3066\u3044\u308b\u306e\u3067\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/%e7%a9%8d%e5%88%86%ef%bc%9a%e3%81%84%e3%81%8f%e3%81%a4%e3%81%8b%e3%81%ae%e5%bf%9c%e7%94%a8\/%e5%8f%82%e8%80%83%ef%bc%9amaxima-%e3%81%a7%e6%a5%95%e5%86%86%e3%81%ae%e9%9d%a2%e7%a9%8d%e3%83%bb%e5%91%a8%ef%bc%8c%e5%9b%9e%e8%bb%a2%e6%a5%95%e5%86%86%e4%bd%93%e3%81%ae%e8%a1%a8%e9%9d%a2%e7%a9%8d\/\">\u53c2\u8003\uff1aMaxima \u3067\u6955\u5186\u306e\u9762\u7a4d\u30fb\u5468\uff0c\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\u7a4d\u30fb\u4f53\u7a4d<\/a><\/li>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/%e7%a9%8d%e5%88%86%ef%bc%9a%e3%81%84%e3%81%8f%e3%81%a4%e3%81%8b%e3%81%ae%e5%bf%9c%e7%94%a8\/%e5%8f%82%e8%80%83%ef%bc%9asympy-%e3%81%a7%e6%a5%95%e5%86%86%e3%81%ae%e9%9d%a2%e7%a9%8d%e3%83%bb%e5%91%a8%ef%bc%8c%e5%9b%9e%e8%bb%a2%e6%a5%95%e5%86%86%e4%bd%93%e3%81%ae%e8%a1%a8%e9%9d%a2%e7%a9%8d\/\">\u53c2\u8003\uff1aSymPy \u3067\u6955\u5186\u306e\u9762\u7a4d\u30fb\u5468\uff0c\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\u7a4d\u30fb\u4f53\u7a4d<\/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=\"\u5857\u308a\u3064\u3076\u3057\u305f\u6955\u5186\">\u5857\u308a\u3064\u3076\u3057\u305f\u6955\u5186<\/h3>\n<p>Maxima \u3067\u9577\u534a\u5f84 $a$\uff0c\u5358\u534a\u5f84 $b$ \u306e\u6955\u5186\u3092\u63cf\u304f\u4f8b\u3002<code>ellipse()<\/code> \u3092\u4f7f\u3063\u3066\u307f\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<pre><code>? ellipse;\r\n\r\n-- Graphic object: ellipse (&lt;xc&gt;, &lt;yc&gt;, &lt;a&gt;, &lt;b&gt;, &lt;ang1&gt;, &lt;ang2&gt;)\r\n     Draws ellipses and circles in 2D.\r\n\r\n     2D\r\n\r\n     'ellipse (&lt;xc&gt;, &lt;yc&gt;, &lt;a&gt;, &lt;b&gt;, &lt;ang1&gt;, &lt;ang2&gt;)' plots an ellipse\r\n     centered at '[&lt;xc&gt;, &lt;yc&gt;]' with horizontal and vertical semi axis\r\n     &lt;a&gt; and &lt;b&gt;, respectively, starting at angle &lt;ang1&gt; with an\r\n     amplitude equal to angle &lt;ang2&gt;.<\/code><\/pre>\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=\"nv\">a<\/span><span class=\"o\">:<\/span> 2$\r\n<span class=\"nv\">b<\/span><span class=\"o\">:<\/span> 1$\r\n<span class=\"nv\">xlim<\/span><span class=\"o\">:<\/span> <span class=\"nv\">a<\/span><span class=\"o\">+<\/span>0<span class=\"o\">.<\/span>5$\r\n<span class=\"nv\">ylim<\/span><span class=\"o\">:<\/span> <span class=\"nv\">b<\/span><span class=\"o\">+<\/span>0<span class=\"o\">.<\/span>5$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">font_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">14<\/span>, <span class=\"nv\">dimensions<\/span><span class=\"o\">=<\/span><span class=\"p\">[<\/span><span class=\"mi\">640<\/span>, 400<span class=\"p\">]<\/span>,\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/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=\"o\">-<\/span><span class=\"nv\">xlim<\/span>, <span class=\"nv\">xlim<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"nv\">ylim<\/span>, <span class=\"nv\">ylim<\/span><span class=\"p\">]<\/span>,\r\n\r\n  <span class=\"cm\">\/* x \u8ef8 y \u8ef8\u306e\u8868\u793a *\/<\/span>\r\n  <span class=\"nv\">xaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>, <span class=\"nv\">yaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"nv\">xtics<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{[<\/span><span class=\"s\">\"-a\"<\/span>, <span class=\"o\">-<\/span><span class=\"nv\">a<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"s\">\"a\"<\/span>, <span class=\"nv\">a<\/span><span class=\"p\">]}<\/span>,\r\n  <span class=\"nv\">ytics<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{[<\/span><span class=\"s\">\"-b\"<\/span>, <span class=\"o\">-<\/span><span class=\"nv\">b<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"s\">\"b\"<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">]}<\/span>, \r\n  <span class=\"nv\">user_preamble<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"set grid front;\"<\/span>,\r\n\r\n  <span class=\"nv\">transparent<\/span> <span class=\"o\">=<\/span> <span class=\"no\">false<\/span>, <span class=\"nv\">fill_color<\/span>  <span class=\"o\">=<\/span> <span class=\"nv\">yellow<\/span>,\r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>,\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">dark<\/span><span class=\"o\">-<\/span><span class=\"nv\">blue<\/span>,\r\n  <span class=\"nf\">ellipse<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">a<\/span>, <span class=\"nv\">b<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">360<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \"><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-7840\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdaen-01.svg\" alt=\"\" width=\"640\" height=\"400\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u5857\u308a\u3064\u3076\u3057\u7121\u3057\u306e\u6955\u5186\">\u5857\u308a\u3064\u3076\u3057\u7121\u3057\u306e\u6955\u5186<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">a<\/span><span class=\"o\">:<\/span> 2$\r\n<span class=\"nv\">b<\/span><span class=\"o\">:<\/span> 1$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">font_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">14<\/span>, <span class=\"nv\">dimensions<\/span><span class=\"o\">=<\/span><span class=\"p\">[<\/span><span class=\"mi\">640<\/span>, 400<span class=\"p\">]<\/span>,\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/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=\"o\">-<\/span><span class=\"nv\">xlim<\/span>, <span class=\"nv\">xlim<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"nv\">ylim<\/span>, <span class=\"nv\">ylim<\/span><span class=\"p\">]<\/span>,\r\n\r\n  <span class=\"cm\">\/* x \u8ef8 y \u8ef8\u306e\u8868\u793a *\/<\/span>\r\n  <span class=\"nv\">xaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>, <span class=\"nv\">yaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"nv\">xtics<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{[<\/span><span class=\"s\">\"-a\"<\/span>, <span class=\"o\">-<\/span><span class=\"nv\">a<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"s\">\"a\"<\/span>, <span class=\"nv\">a<\/span><span class=\"p\">]}<\/span>,\r\n  <span class=\"nv\">ytics<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{[<\/span><span class=\"s\">\"-b\"<\/span>, <span class=\"o\">-<\/span><span class=\"nv\">b<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"s\">\"b\"<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">]}<\/span>, \r\n  <span class=\"nv\">user_preamble<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"set grid front;\"<\/span>,\r\n\r\n  <span class=\"nv\">transparent<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>,\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">dark<\/span><span class=\"o\">-<\/span><span class=\"nv\">blue<\/span>,\r\n  <span class=\"nf\">ellipse<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">a<\/span>, <span class=\"nv\">b<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">360<\/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_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-7841\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdaen-02.svg\" alt=\"\" width=\"640\" height=\"400\" \/><\/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=\"\u9577\u8ef8\u306e\u5468\u308a\u306b\u56de\u8ee2\u3057\u305f\u56de\u8ee2\u6955\u5186\u4f53\">\u9577\u8ef8\u306e\u5468\u308a\u306b\u56de\u8ee2\u3057\u305f\u56de\u8ee2\u6955\u5186\u4f53<\/h3>\n<p>$\\displaystyle y = b \\sqrt{1-\\frac{x^2}{a^2}} $ \u3092 $x$ \u306e\u5468\u308a\u306b\u56de\u8ee2\u3057\u3066\u3067\u304d\u308b\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\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-maxima\">\n<pre><span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">font_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">14<\/span>, <span class=\"nv\">dimensions<\/span><span class=\"o\">=<\/span><span class=\"p\">[<\/span><span class=\"mi\">640<\/span>, 400<span class=\"p\">]<\/span>,\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/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=\"o\">-<\/span><span class=\"nv\">xlim<\/span>, <span class=\"nv\">xlim<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"nv\">ylim<\/span>, <span class=\"nv\">ylim<\/span><span class=\"p\">]<\/span>,\r\n  \r\n  <span class=\"cm\">\/* x \u8ef8 y \u8ef8\u306e\u8868\u793a *\/<\/span>\r\n  <span class=\"nv\">xaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>, <span class=\"nv\">yaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"nv\">xtics<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{[<\/span><span class=\"s\">\"-a\"<\/span>, <span class=\"o\">-<\/span><span class=\"nv\">a<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"s\">\"a\"<\/span>, <span class=\"nv\">a<\/span><span class=\"p\">]}<\/span>,\r\n  <span class=\"nv\">ytics<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{[<\/span><span class=\"s\">\"-b\"<\/span>, <span class=\"o\">-<\/span><span class=\"nv\">b<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"s\">\"b\"<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">]}<\/span>, <span class=\"nv\">user_preamble<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"set grid front;\"<\/span>,\r\n\r\n  <span class=\"nv\">transparent<\/span> <span class=\"o\">=<\/span> <span class=\"no\">false<\/span>,\r\n  <span class=\"nv\">fill_color<\/span>  <span class=\"o\">=<\/span> <span class=\"nv\">light-blue<\/span>,\r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>,\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">dark<\/span><span class=\"o\">-<\/span><span class=\"nv\">blue<\/span>,\r\n  <span class=\"cm\">\/* \u4e0a\u534a\u5206\u306e\u6955\u5186\u3092\u63cf\u304f *\/<\/span>\r\n  <span class=\"nf\">ellipse<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">a<\/span>, <span class=\"nv\">b<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">180<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">blue<\/span>, <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"nv\">xlim<\/span>, <span class=\"nv\">xlim<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \"><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-7842\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Maxdaen-03a.svg\" alt=\"\" width=\"640\" height=\"400\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">b<\/span><span class=\"o\">*<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span>1<span class=\"o\">-<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span>2<span class=\"o\">\/<\/span><span class=\"nv\">a<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nv\">a<\/span><span class=\"o\">:<\/span> 2$\r\n<span class=\"nv\">b<\/span><span class=\"o\">:<\/span> 1$\r\n<span class=\"nv\">xlim<\/span><span class=\"o\">:<\/span> <span class=\"nv\">a<\/span><span class=\"o\">+<\/span>0<span class=\"o\">.<\/span>5$\r\n<span class=\"nv\">ylim<\/span><span class=\"o\">:<\/span> <span class=\"nv\">b<\/span><span class=\"o\">+<\/span>0<span class=\"o\">.<\/span>5$\r\n\r\n<span class=\"nf\">draw3d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">dimensions<\/span><span class=\"o\">=<\/span><span class=\"p\">[<\/span><span class=\"mi\">640<\/span>, 640<span class=\"p\">]<\/span>, <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xyz<\/span>, \r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"nv\">xlim<\/span>, <span class=\"nv\">xlim<\/span><span class=\"p\">]<\/span>,\r\n  <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"nv\">xlim<\/span>, <span class=\"nv\">xlim<\/span><span class=\"p\">]<\/span>, \r\n  <span class=\"nv\">zrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"nv\">xlim<\/span>, <span class=\"nv\">xlim<\/span><span class=\"p\">]<\/span>, \r\n\r\n  <span class=\"cm\">\/* \u56de\u8ee2\u4f53\u306e\u8868\u9762 *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">blue<\/span>, \r\n  <span class=\"nv\">line_width<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span>, <span class=\"nv\">xu_grid<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">40<\/span>, <span class=\"nv\">yv_grid<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">30<\/span>,\r\n  <span class=\"nf\">parametric_surface<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/span>, \r\n                     <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"nv\">a<\/span>, <span class=\"nv\">a<\/span>, <span class=\"nv\">t<\/span>, <span class=\"mi\">0<\/span>, 2<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span>,\r\n\r\n  <span class=\"nv\">surface_hide<\/span> <span class=\"o\">=<\/span><span class=\"no\">true<\/span>, <span class=\"nv\">view<\/span><span class=\"o\">=<\/span><span class=\"p\">[<\/span><span class=\"mi\">60<\/span>, 10<span class=\"p\">]<\/span>, \r\n  <span class=\"nv\">axis_3d<\/span> <span class=\"o\">=<\/span> <span class=\"no\">false<\/span>, \r\n\r\n  <span class=\"cm\">\/* x \u8ef8 *\/<\/span>\r\n  <span class=\"nv\">color<\/span><span class=\"o\">=<\/span><span class=\"nv\">blue<\/span>, <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>,\r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mf\">2.2<\/span>, <span class=\"mf\">2.2<\/span><span class=\"p\">)<\/span>, \r\n\r\n  <span class=\"cm\">\/* \u3044\u308f\u3086\u308b\u300cy = y(x)\u300d\uff0c\u5b9f\u306f z = z(x) *\/<\/span>\r\n  <span class=\"nv\">nticks<\/span><span class=\"o\">=<\/span><span class=\"mi\">100<\/span>, <span class=\"nv\">color<\/span><span class=\"o\">=<\/span><span class=\"nv\">dark<\/span><span class=\"o\">-<\/span><span class=\"nv\">blue<\/span>, <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>,\r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nv\">a<\/span><span class=\"o\">*<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">b<\/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=\"nv\">t<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \"><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-7843\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdaen-04.svg\" alt=\"\" width=\"640\" height=\"640\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u77ed\u8ef8\u306e\u5468\u308a\u306b\u56de\u8ee2\u3057\u305f\u56de\u8ee2\u6955\u5186\u4f53\">\u77ed\u8ef8\u306e\u5468\u308a\u306b\u56de\u8ee2\u3057\u305f\u56de\u8ee2\u6955\u5186\u4f53<\/h3>\n<p>$\\displaystyle x = a \\sqrt{1-\\frac{y^2}{b^2}} $ \u3092 $y$ \u306e\u5468\u308a\u306b\u56de\u8ee2\u3057\u3066\u3067\u304d\u308b\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\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[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">font_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">14<\/span>, <span class=\"nv\">dimensions<\/span><span class=\"o\">=<\/span><span class=\"p\">[<\/span><span class=\"mi\">640<\/span>, 400<span class=\"p\">]<\/span>,\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/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=\"o\">-<\/span><span class=\"nv\">xlim<\/span>, <span class=\"nv\">xlim<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"nv\">ylim<\/span>, <span class=\"nv\">ylim<\/span><span class=\"p\">]<\/span>,\r\n  \r\n  <span class=\"cm\">\/* x \u8ef8 y \u8ef8\u306e\u8868\u793a *\/<\/span>\r\n  <span class=\"nv\">xaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>, <span class=\"nv\">yaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"nv\">xtics<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{[<\/span><span class=\"s\">\"-a\"<\/span>, <span class=\"o\">-<\/span><span class=\"nv\">a<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"s\">\"a\"<\/span>, <span class=\"nv\">a<\/span><span class=\"p\">]}<\/span>,\r\n  <span class=\"nv\">ytics<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{[<\/span><span class=\"s\">\"-b\"<\/span>, <span class=\"o\">-<\/span><span class=\"nv\">b<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"s\">\"b\"<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">]}<\/span>, \r\n  <span class=\"nv\">user_preamble<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"set grid front;\"<\/span>,\r\n\r\n  <span class=\"nv\">transparent<\/span> <span class=\"o\">=<\/span> <span class=\"no\">false<\/span>,\r\n  <span class=\"nv\">fill_color<\/span>  <span class=\"o\">=<\/span> <span class=\"nv\">light-pink<\/span>,\r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>,\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">dark<\/span><span class=\"o\">-<\/span><span class=\"nv\">red<\/span>,\r\n  <span class=\"cm\">\/* \u53f3\u534a\u5206\u306e\u6955\u5186\u3092\u63cf\u304f *\/<\/span>\r\n  <span class=\"nf\">ellipse<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">a<\/span>, <span class=\"nv\">b<\/span>, <span class=\"mi\">90<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">180<\/span><span class=\"p\">)<\/span>,  \r\n  \r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">red<\/span>, <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>,\r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span>, <span class=\"nv\">y<\/span>, <span class=\"nv\">y<\/span>, <span class=\"o\">-<\/span><span class=\"nv\">ylim<\/span>, <span class=\"nv\">ylim<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \"><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-7844\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Maxdaen-05.svg\" alt=\"\" width=\"640\" height=\"400\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">g<\/span><span class=\"p\">(<\/span><span class=\"nv\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">a<\/span><span class=\"o\">*<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span>1<span class=\"o\">-<\/span><span class=\"nv\">z<\/span><span class=\"o\">**<\/span>2<span class=\"o\">\/<\/span><span class=\"nv\">b<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">draw3d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">dimensions<\/span><span class=\"o\">=<\/span><span class=\"p\">[<\/span><span class=\"mi\">640<\/span>, 640<span class=\"p\">]<\/span>, <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xyz<\/span>, \r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"nv\">a<\/span>, <span class=\"nv\">a<\/span><span class=\"p\">]<\/span>,\r\n  <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"nv\">a<\/span>, <span class=\"nv\">a<\/span><span class=\"p\">]<\/span>, \r\n  <span class=\"nv\">zrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"nv\">a<\/span>, <span class=\"nv\">a<\/span><span class=\"p\">]<\/span>, \r\n       \r\n  <span class=\"cm\">\/* \u56de\u8ee2\u4f53\u306e\u8868\u9762 *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">red<\/span>,\r\n  <span class=\"nv\">line_width<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span>, <span class=\"nv\">xu_grid<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">40<\/span>, <span class=\"nv\">yv_grid<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">30<\/span>,\r\n  <span class=\"nf\">parametric_surface<\/span><span class=\"p\">(<\/span><span class=\"nf\">g<\/span><span class=\"p\">(<\/span><span class=\"nv\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">g<\/span><span class=\"p\">(<\/span><span class=\"nv\">z<\/span><span class=\"p\">)<\/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=\"nv\">z<\/span>, \r\n                     <span class=\"nv\">z<\/span>, <span class=\"o\">-<\/span><span class=\"nv\">b<\/span>, <span class=\"nv\">b<\/span>, <span class=\"nv\">t<\/span>, <span class=\"mi\">0<\/span>, 2<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span>,\r\n\r\n  <span class=\"nv\">surface_hide<\/span><span class=\"o\">=<\/span><span class=\"no\">true<\/span>, <span class=\"nv\">view<\/span><span class=\"o\">=<\/span><span class=\"p\">[<\/span><span class=\"mi\">70<\/span>, 20<span class=\"p\">]<\/span>, \r\n  <span class=\"nv\">axis_3d<\/span> <span class=\"o\">=<\/span> <span class=\"no\">false<\/span>, \r\n    \r\n  <span class=\"cm\">\/* \u3044\u308f\u3086\u308b\u300cy \u8ef8\u300d\uff0c\u5b9f\u306f z \u8ef8 *\/<\/span>\r\n  <span class=\"nv\">color<\/span><span class=\"o\">=<\/span><span class=\"nv\">red<\/span>, <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>,\r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">z<\/span>, <span class=\"nv\">z<\/span>, <span class=\"o\">-<\/span><span class=\"nv\">xlim<\/span>, <span class=\"nv\">xlim<\/span><span class=\"p\">)<\/span>, \r\n\r\n  <span class=\"cm\">\/* \u3044\u308f\u3086\u308b\u300cx = x(y)\u300d\uff0c\u5b9f\u306f x = x(z) *\/<\/span>\r\n  <span class=\"nv\">nticks<\/span><span class=\"o\">=<\/span><span class=\"mi\">100<\/span>, <span class=\"nv\">color<\/span><span class=\"o\">=<\/span><span class=\"nv\">dark<\/span><span class=\"o\">-<\/span><span class=\"nv\">red<\/span>, <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span>,\r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nv\">a<\/span><span class=\"o\">*<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">b<\/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=\"nv\">t<\/span>, <span class=\"o\">-<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span>, <span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/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 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