{"id":4539,"date":"2023-12-18T10:36:35","date_gmt":"2023-12-18T01:36:35","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=4539"},"modified":"2023-12-18T10:39:01","modified_gmt":"2023-12-18T01:39:01","slug":"maxima-%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%82%99%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90-draw2d-%e7%b7%a8","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%ab%e3%82%88%e3%82%8b%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/maxima-%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%82%99%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90-draw2d-%e7%b7%a8\/","title":{"rendered":"Maxima \u3067\u30af\u3099\u30e9\u30d5\u4f5c\u6210 draw2d \u7de8"},"content":{"rendered":"<p>Maxima \u306e2\u6b21\u5143\u30b0\u30e9\u30d5\u4f5c\u6210\u306f <code>plot2d()<\/code> \u3067\u3082\u3067\u304d\u307e\u3059\u304c\uff0c\u3053\u3053\u3067\u306f\uff0c<code>draw2d()<\/code> \u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<!--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<p>Maxima \u3092\u4f7f\u3063\u3066\uff0c\u95a2\u6570\u306e\u30af\u3099\u30e9\u30d5\u3092\u63cf\u304f\u3053\u3068\u304b\u3099\u3066\u3099\u304d\u307e\u3059\u3002\u307e\u305f\uff0c\u6570\u5024\u30c6\u3099\u30fc\u30bf\u3082\u30af\u3099\u30e9\u30d5\u306b\u3059\u308b\u3053\u3068\u304b\u3099\u3066\u3099\u304d\u307e\u3059\u3002<\/p>\n<p>Maxima \u306e2\u6b21\u5143\u30b0\u30e9\u30d5\u4f5c\u6210\u306f <code>plot2d()<\/code> \u3067\u3082\u3067\u304d\u307e\u3059\u304c\uff0c\u3053\u3053\u3067\u306f\uff0c<code>draw2d()<\/code> \u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<br \/>\n<code>draw2d()<\/code> \u3067\u30d7\u30ed\u30c3\u30c8\u3067\u304d\u308b\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u967d\u95a2\u6570 $y = f(x)$:\n<ul>\n<li><code>explicit(f(x), x, xmin, xmax)<\/code><\/li>\n<\/ul>\n<\/li>\n<li>\u9670\u95a2\u6570 $f(x, y) = 0$:\n<ul>\n<li><code>implicit(f(x, y) = 0, x, xmin, xmax, y, ymin, ymax)<\/code><\/li>\n<\/ul>\n<\/li>\n<li>\u5a92\u4ecb\u5909\u6570\u8868\u793a $x(t), y(t)$:\n<ul>\n<li><code>parametric(x(t), y(t), t, tmin, tmax)<\/code><\/li>\n<\/ul>\n<\/li>\n<li>\u70b9\uff0c$x$ \u5ea7\u6a19 $y$ \u5ea7\u6a19\u306e\u6570\u5024\u30c7\u30fc\u30bf:\n<ul>\n<li><code>points([[x1, y1], [x2, y2], ... ])<\/code><br \/>\n\u307e\u305f\u306f <code>points([x1, x2, ... ], [y1, y2, ...])<\/code><\/li>\n<\/ul>\n<\/li>\n<li>\u30d9\u30af\u30c8\u30eb\uff0c\u59cb\u70b9 $x_0, y_0$ \u304b\u3089\u30d9\u30af\u30c8\u30eb\u6210\u5206 $v_x, v_y$:\n<ul>\n<li><code>vector([x0, y0], [vx, vy])<\/code><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u307e\u305f\uff0c2\u672c\u306e\u967d\u95a2\u6570\u3067\u631f\u307e\u308c\u305f\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3059\u3053\u3068\u3082\u3067\u304d\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<h2 id=\"\u967d\u95a2\u6570\u306e\u30b0\u30e9\u30d5\">\u967d\u95a2\u6570\u306e\u30b0\u30e9\u30d5<\/h2>\n<p>\u4f8b\u3068\u3057\u3066\uff0c$y = \\sin x$ \u306e\u30af\u3099\u30e9\u30d5\u3092 $\u22122\\pi \\leq x \\leq 2\\pi$ \u306e\u7bc4\u56f2\u3066\u3099\u63cf\u304d\u307e\u3059\u3002\u57fa\u672c\u7684\u306a\u5b9a\u6570\u306e\u4e00\u3064\u3066\u3099\u3042\u308b\u5186\u5468\u7387 $\\pi$ \u306f Maxima \u3066\u3099\u306f <code>%pi<\/code> \u3068\u66f8\u304f\u306e\u3066\u3099\u3057\u305f\u306d\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=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span>2<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span>, 2<span class=\"o\">*<\/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 \">\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-4540\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw01.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\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[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u8a2d\u5b9a\u4f8b *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u30d5\u30a9\u30f3\u30c8\u8a2d\u5b9a *\/<\/span>\r\n  <span class=\"nv\">font<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Arial\"<\/span>, \r\n  <span class=\"nv\">font_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">16<\/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=\"mi\">10<\/span>, 10<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mf\">1.1<\/span>, 1<span class=\"o\">.<\/span>1<span class=\"p\">]<\/span>,\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=\"cm\">\/* \u30b0\u30ea\u30c3\u30c9 *\/<\/span>\r\n  <span class=\"nv\">grid<\/span><span class=\"o\">=<\/span><span class=\"no\">true<\/span>,\r\n\r\n  <span class=\"cm\">\/* \u51e1\u4f8b *\/<\/span>\r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u6b63\u5f26\u95a2\u6570\"<\/span>, \r\n  <span class=\"cm\">\/* \u8272 *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">red<\/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  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span>2<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span>, 2<span class=\"o\">*<\/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 \">\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-4541\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw02.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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<h2 id=\"\u9670\u95a2\u6570\u306e\u30b0\u30e9\u30d5\">\u9670\u95a2\u6570\u306e\u30b0\u30e9\u30d5<\/h2>\n<p>\u4f8b\u3068\u3057\u3066\uff0c$x^2 + y^2 = 1$ \u306e\u30af\u3099\u30e9\u30d5\u3092\u63cf\u304d\u307e\u3059\u3002$y$ \u306b\u3064\u3044\u3066\u89e3\u3044\u3066\u967d\u95a2\u6570\u306e\u5f62\u306b\u3057\u305f\u308a\uff0c\u4ee5\u4e0b\u3067\u8ff0\u3079\u308b\u3088\u3046\u306a\u5a92\u4ecb\u5909\u6570\u8868\u793a\u306b\u3057\u306a\u304f\u3066\u3082\uff0c\u9670\u95a2\u6570\u306e\u307e\u307e\uff0c\u30b0\u30e9\u30d5\u306b\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\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-maxima\">\n<pre><span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nf\">implicit<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mf\">1.2<\/span>, <span class=\"mf\">1.2<\/span>, <span class=\"nv\">y<\/span>, <span class=\"o\">-<\/span><span class=\"mf\">1.2<\/span>, <span class=\"mf\">1.2<\/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 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-4542\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw03.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\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[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u8a2d\u5b9a\u4f8b *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u30b0\u30ea\u30c3\u30c9\u3092\u591a\u3081\u306b *\/<\/span>\r\n  <span class=\"nv\">ip_grid<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">200<\/span>, 200<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\">\/* 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  \r\n  <span class=\"nf\">implicit<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mf\">1.5<\/span>, <span class=\"mf\">1.5<\/span>, <span class=\"nv\">y<\/span>, <span class=\"o\">-<\/span><span class=\"mf\">1.5<\/span>, <span class=\"mf\">1.5<\/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 \">\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-4543\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw04.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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<h2 id=\"\u5a92\u4ecb\u5909\u6570\u8868\u793a\u306e\u30b0\u30e9\u30d5\">\u5a92\u4ecb\u5909\u6570\u8868\u793a\u306e\u30b0\u30e9\u30d5<\/h2>\n<p>\u534a\u5f84 $1$ \u306e\u5186\u306e\u65b9\u7a0b\u5f0f\u306f $x^2 +y^2 = 1$ \u3066\u3099\u3059\u3002\u3053\u306e\u5186\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5a92\u4ecb\u5909\u6570\u8868\u793a\u306b\u3057\u3066\u63cf\u304d\u307e\u3059\u3002<\/p>\n<p>$$ x=\\cos t, \\quad y=\\sin t \\quad (0 \\leq t \\leq 2\\pi) $$<\/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=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/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>, 2<span class=\"o\">*<\/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 \">\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-4544\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw05.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\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[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u8a2d\u5b9a\u4f8b *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u591a\u3081\u306b *\/<\/span>\r\n  <span class=\"nv\">nticks<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>, \r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/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=\"mf\">1.1<\/span>, 1<span class=\"o\">.<\/span>1<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mf\">1.1<\/span>, 1<span class=\"o\">.<\/span>1<span class=\"p\">]<\/span>,\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  \r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/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>, 2<span class=\"o\">*<\/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 \">\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-4545\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw06.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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<h2 id=\"\u70b9\u30fb\u6570\u5024\u30c6\u3099\u30fc\u30bf\u306e\u30af\u3099\u30e9\u30d5\">\u70b9\u30fb\u6570\u5024\u30c6\u3099\u30fc\u30bf\u306e\u30af\u3099\u30e9\u30d5<\/h2>\n<p>\u4ee5\u4e0b\u306e\u4f8b\u3066\u3099\u306f\uff0c\u6700\u521d\uff08\u5de6\u5074\uff09\u306e\u6570\u5024\u3092 $x$ \u5ea7\u6a19\u306e\u5024\uff0c\u6b21\uff08\u53f3\u5074\uff09\u306e\u6570\u5024\u3092 $y$ \u5ea7\u6a19\u306e\u5024\u3068\u3057\u3066 6 \u500b\u306e\u70b9 \u304b\u3089\u306a\u308b\u30ea\u30b9\u30c8 <code>data<\/code> \u306e\u5404\u70b9\u3092\u3064\u306a\u3044\u305f\u3099\u6298\u308c\u7dda\u30af\u3099\u30e9\u30d5\u3092\u63cf\u304d\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[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">data<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">([<\/span><span class=\"nv\">i<\/span>, <span class=\"nv\">i<\/span><span class=\"o\">^<\/span>2<span class=\"p\">]<\/span>, <span class=\"nv\">i<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">5<\/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{${\\it \\%o}_{7}$}\\left[ \\left[ 0 , 0 \\right] , \\left[ 1 , 1 \\right] , \\left[ 2 , 4 \\right] , \\left[ 3 , 9 \\right] , \\left[ 4 , 16 \\right] , \\left[ 5 , 25 \\right] \\right] \\]<\/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[8]:<\/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=\"nf\">points<\/span><span class=\"p\">(<\/span><span class=\"nv\">data<\/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 \">\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-4546\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw7.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\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-maxima\">\n<pre><span class=\"cm\">\/* \u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u8a2d\u5b9a\u4f8b *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/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>, 5<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 28<span class=\"p\">]<\/span>,\r\n\r\n  <span class=\"cm\">\/* \u70b9\u3092\u5857\u308a\u3064\u3076\u3057\u305f\u4e38\u306b *\/<\/span>\r\n  <span class=\"nv\">point_type<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">7<\/span>,\r\n  <span class=\"cm\">\/* \u70b9\u306e\u5927\u304d\u3055 *\/<\/span>\r\n  <span class=\"nv\">point_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>,\r\n  <span class=\"cm\">\/* \u8272 *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">purple<\/span>,\r\n  <span class=\"nf\">points<\/span><span class=\"p\">(<\/span><span class=\"nv\">data<\/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 \">\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-4547\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw07.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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<p><code>point_type<\/code> \u306b\u306f\u4ee5\u4e0b\u306e\u7a2e\u985e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<pre><code>none (-1)\r\ndot (0)\r\nplus (1)\r\nmultiply (2)\r\nasterisk (3)\r\nsquare (4) \r\nfilled_square (5)\r\ncircle (6)\r\nfilled_circle (7)\r\nup_triangle (8)\r\nfilled_up_triangle (9)\r\ndown_triangle (10) \r\nfilled_down_triangle (11)\r\ndiamant (12)\r\nfilled_diamant (13)<\/code><\/pre>\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<h2 id=\"\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304f\">\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304f<\/h2>\n<p>\u539f\u70b9\u3092\u59cb\u70b9\u3068\u3057\uff0c$v_x = 0.5, v_y = 1$ \u306e\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304d\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[10]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u6307\u5b9a\u3057\u306a\u3044\u3068\u5909\u306a\u30d9\u30af\u30c8\u30eb\u306b... *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nf\">vector<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span>, 0<span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"mf\">0.5<\/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 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-4548\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw08.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\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-maxima\">\n<pre><span class=\"cm\">\/* \u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u8a2d\u5b9a\u4f8b *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/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=\"mf\">1.5<\/span>, 1<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mf\">1.5<\/span>, 1<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>,\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/span>,\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\r\n  <span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u306e\u77e2\u306e\u8a2d\u5b9a *\/<\/span>\r\n  <span class=\"nv\">head_length<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>,\r\n  <span class=\"nv\">head_angle<\/span>  <span class=\"o\">=<\/span> <span class=\"mi\">20<\/span>, \r\n\r\n  <span class=\"nf\">vector<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span>, 0<span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"mf\">0.5<\/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 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-4549\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw09.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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<p>\u8907\u6570\u306e\u30d9\u30af\u30c8\u30eb\u3084\u30d9\u30af\u30c8\u30eb\u5834\u306a\u3069\u3092\u63cf\u304f\u4f8b\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[12]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">x<\/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=\"o\">*<\/span> <span class=\"nv\">t<\/span>$\r\n<span class=\"nf\">y<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"mi\">2<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">t<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">t<\/span><span class=\"o\">**<\/span>2$\r\n\r\n<span class=\"nf\">vx<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> 2$\r\n<span class=\"nf\">vy<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"mi\">2<\/span> <span class=\"o\">-<\/span> 2<span class=\"o\">*<\/span><span class=\"nv\">t<\/span>$\r\n\r\n<span class=\"nv\">scaling<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>2$\r\n<span class=\"nv\">vecV<\/span><span class=\"o\">:<\/span> \r\n  <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"nf\">vector<\/span><span class=\"p\">(<\/span>1<span class=\"o\">.<\/span>0<span class=\"o\">*<\/span><span class=\"p\">[<\/span><span class=\"nf\">x<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">y<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">)]<\/span>, <span class=\"nv\">scaling<\/span><span class=\"o\">*<\/span><span class=\"p\">[<\/span><span class=\"nf\">vx<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">vy<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">)])<\/span>, <span class=\"nv\">t<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">4<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"k\">for<\/span> <span class=\"nv\">v<\/span> <span class=\"nv\">in<\/span> <span class=\"nv\">vecV<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span><span class=\"nf\">print<\/span><span class=\"p\">(<\/span><span class=\"nv\">v<\/span><span class=\"p\">))<\/span>$\r\n<span class=\"cm\">\/* \u4ee5\u4e0b\u306e\u3088\u3046\u306b vecV \u306f 5\u672c\u306e\u30d9\u30af\u30c8\u30eb\u306e\u30ea\u30b9\u30c8\u306b\u306a\u3063\u3066\u3044\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_latex output_subarea \">\\({\\it vector}\\left(\\left[ 0 , 0 \\right] , \\left[ 0.4 , 0.4 \\right] \\right)\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\({\\it vector}\\left(\\left[ 1.0 , 0.75 \\right] , \\left[ 0.4 , 0.2 \\right] \\right)\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\({\\it vector}\\left(\\left[ 2.0 , 1.0 \\right] , \\left[ 0.4 , 0 \\right] \\right)\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\({\\it vector}\\left(\\left[ 3.0 , 0.75 \\right] , \\left[ 0.4 , -0.2 \\right] \\right)\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\({\\it vector}\\left(\\left[ 4.0 , 0 \\right] , \\left[ 0.4 , -0.4 \\right] \\right)\\)<\/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[13]:<\/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=\"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=\"mf\">0.5<\/span>, 4<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.5<\/span>, 2<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\">\/* \u30b0\u30ea\u30c3\u30c9\u3002y \u8ef8\u306e\u76ee\u76db\u3092 1 \u3054\u3068\u306b *\/<\/span>\r\n  <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"nv\">ytics<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/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=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u306e\u77e2\u306e\u8a2d\u5b9a *\/<\/span>\r\n  <span class=\"nv\">head_length<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>,\r\n  <span class=\"nv\">head_angle<\/span>  <span class=\"o\">=<\/span> <span class=\"mi\">20<\/span>, \r\n  \r\n  <span class=\"nv\">vecV<\/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 \">\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-4550\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw10.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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<p>\u3055\u3089\u306b\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30d9\u30af\u30c8\u30eb\u5834\u306e\u30b0\u30e9\u30d5\u3082\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u53c2\u8003\u307e\u3067\u306b\u3002<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxvec-fig04.svg\" width=\"75%\" \/><\/p>\n<ul>\n<li>\u53c2\u8003\uff1a<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3934\/\">Maxima \u3067\u30d9\u30af\u30c8\u30eb\u5834\uff08\u96fb\u5834\u30fb\u78c1\u5834\uff09\u3092\u63cf\u304f<\/a><\/li>\n<\/ul>\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<h2 id=\"\u8907\u6570\u306e\u30af\u3099\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a\">\u8907\u6570\u306e\u30af\u3099\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a<\/h2>\n<p>\u8907\u6570\u306e\u30af\u3099\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a\u3059\u308b\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<p>$y = x^2 &#8211; 1$ \u3068 $y = 4 x &#8211; 5$ \u306e 2\u3064\u306e\u967d\u95a2\u6570\u306e\u30af\u3099\u30e9\u30d5\u3092\u91cd\u306d\u3066\u63cf\u304d\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[14]:<\/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=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">5<\/span>, <span class=\"mi\">5<\/span><span class=\"p\">)<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span>4<span class=\"o\">*<\/span><span class=\"nv\">x<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">5<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">5<\/span>, <span class=\"mi\">5<\/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 \">\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-4551\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw11.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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<p><code>plot2d()<\/code> \u306e\u5834\u5408\u3068\u9055\u3044\uff0c\u81ea\u52d5\u3067\u8272\u3092\u5909\u3048\u3066\u306f\u304f\u308c\u307e\u305b\u3093\u3002\u3044\u304f\u3064\u304b\u30aa\u30d5\u309a\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3057\u3066\u63cf\u304f\u4f8b\u3066\u3099\u3059\u3002\u305d\u308c\u305e\u308c\u306e\u95a2\u6570\u3092 <code>explicit()<\/code> \u3067\u63cf\u304f\u76f4\u524d\u306b\uff0c\u305d\u308c\u305e\u308c\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u6307\u5b9a\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[15]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u8a2d\u5b9a\u4f8b *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u30d5\u30a9\u30f3\u30c8\u8a2d\u5b9a *\/<\/span>\r\n  <span class=\"nv\">font<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Arial\"<\/span>, \r\n  <span class=\"nv\">font_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">16<\/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=\"mi\">5<\/span>, 5<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">5<\/span>, 10<span class=\"p\">]<\/span>,\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=\"cm\">\/* \u51e1\u4f8b\u306e\u4f4d\u7f6e *\/<\/span>\r\n  <span class=\"nv\">user_preamble<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"set key bottom\"<\/span>,\r\n\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=\"mi\">4<\/span>,\r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"x^2 - 1\"<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">5<\/span>, <span class=\"mi\">5<\/span><span class=\"p\">)<\/span>,\r\n  \r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">black<\/span>,\r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>,\r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"4 x - 5\"<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span>4<span class=\"o\">*<\/span><span class=\"nv\">x<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">5<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">1<\/span>, <span class=\"mi\">3<\/span><span class=\"p\">)<\/span>\r\n  <span class=\"cm\">\/* x \u306e\u7bc4\u56f2\u3082\u5225\u500b\u306b\u8a2d\u5b9a\u53ef\u80fd *\/<\/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 \">\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-4552\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw12.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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<p>\u4e0a\u306e\u30af\u3099\u30e9\u30d5\u3092\u307f\u308b\u3068\uff0c2 \u3064\u306e\u30af\u3099\u30e9\u30d5\u306f 1 \u70b9\u3066\u3099\u63a5\u3057\u3066\u3044\u308b\u3088\u3046\u306b\u898b\u3048\u307e\u3059\u3002<\/p>\n<p>\u5b9f\u969b\u306b $y = 4x &#8211; 5$ \u304b\u3099\u63a5\u7dda\u3066\u3099\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>$x^2 &#8211; 1 = 4 x &#8211; 5$ \u306e\u89e3\u304c1\u3064\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b\u3070\u5341\u5206\u3067\u3059\u306d\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[16]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">sol<\/span><span class=\"o\">:<\/span> <span class=\"nf\">solve<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">^<\/span><span class=\"mi\">2<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">=<\/span> 4<span class=\"o\">*<\/span><span class=\"nv\">x<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">5<\/span>, <span class=\"nv\">x<\/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[16]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{22}$}\\left[ x=2 \\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>$y = f(x)$ \u306e $x = x_1$ \u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f\uff0c<br \/>\n$$ y &#8211; f(x_1) = f'(x_1) \\,(x &#8211; x_1)$$ \u3067\u3059\u304b\u3089\uff0c$x = x_1$ \u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u3042\u304b\u3089\u3055\u307e\u306b\u66f8\u304f\u3068&#8230;<\/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[17]:<\/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\">x<\/span><span class=\"o\">^<\/span><span class=\"mi\">2<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span>;\r\n<span class=\"nf\">define<\/span><span class=\"p\">(<\/span><span class=\"nf\">df<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">diff<\/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=\"nv\">x<\/span><span class=\"p\">))<\/span>;\r\n\r\n<span class=\"nv\">x1<\/span><span class=\"o\">:<\/span> <span class=\"nf\">rhs<\/span><span class=\"p\">(<\/span><span class=\"nv\">sol<\/span><span class=\"p\">[<\/span>1<span class=\"p\">])<\/span>;\r\n<span class=\"nv\">y<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">df<\/span><span class=\"p\">(<\/span><span class=\"nv\">x1<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"p\">(<\/span><span class=\"nv\">x<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">x1<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">x1<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">ratsimp<\/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[17]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{23}$}f\\left(x\\right):=x^2-1\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[17]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{24}$}{\\it df}\\left(x\\right):=2\\,x\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[17]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{25}$}2\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[17]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{26}$}y=4\\,x-5\\]<\/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\u7fd2-4-1\">\u7df4\u7fd2 4-1<\/h3>\n<p>$y = f(x) = x^2 -1$ \u306e $x = 1$ \u306b\u304a\u3051\u308b\u63a5\u7dda\uff0c\u304a\u3088\u3073 $ x = 3$ \u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u3092\u6c42\u3081\uff0c\u3053\u308c\u30893\u672c\u306e\u7dda\u304a\u3088\u3073\u63a5\u70b9\u3092\u30b0\u30e9\u30d5\u306b\u63cf\u3051\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[18]:<\/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\">x<\/span><span class=\"o\">^<\/span><span class=\"mi\">2<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span>;\r\n<span class=\"nf\">define<\/span><span class=\"p\">(<\/span><span class=\"nf\">df<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">diff<\/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=\"nv\">x<\/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[18]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{27}$}f\\left(x\\right):=x^2-1\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[18]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{28}$}{\\it df}\\left(x\\right):=2\\,x\\]<\/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>$y = f(x)$ \u306e $x = x_1$ \u306b\u304a\u3051\u308b\u63a5\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f\uff0c<br \/>\n$$ y &#8211; f(x_1) = f'(x_1) \\,(x &#8211; x_1)$$ \u3067\u3059\u304b\u3089&#8230;<\/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[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><\/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[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><\/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<h2 id=\"\u6570\u5024\u30c6\u3099\u30fc\u30bf\u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u8fbc\u3080\">\u6570\u5024\u30c6\u3099\u30fc\u30bf\u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u8fbc\u3080<\/h2>\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>Maxima \u3066\u3099\u306f\uff0c\u3042\u3089\u304b\u3057\u3099\u3081\u4f5c\u6210\u3055\u308c\u305f\u6570\u5024\u30c6\u3099\u30fc\u30bf\u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u8fbc\u3093\u3066\u3099\u30af\u3099\u30e9\u30d5\u3092\u63cf\u304f\u3053\u3068\u3082\u3066\u3099\u304d\u307e\u3059\u3002<\/p>\n<p>\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5185\u5bb9\u306e\u30d5\u30a1\u30a4\u30eb <code>test.dat<\/code> \u304c\u30ab\u30ec\u30f3\u30c8\u30c6\u3099\u30a3\u30ec\u30af\u30c8\u30ea\u306b\u3042\u308b\u3068\u3057\u307e\u3059\u3002\uff08\u306a\u3044\u5834\u5408\u306f\uff0c\u5f18\u5927 JupyterHub \u306e Home \u3067\u300c\u65b0\u898f\u300d\u304b\u3089\u300c\u30c6\u30ad\u30b9\u30c8\u30d5\u30a1\u30a4\u30eb\u300d\u3092\u9078\u629e\u3057\uff0c\u4ee5\u4e0b\u306e\u6570\u5024\u3092\u30b3\u30d4\u30da\u3057\uff0c\u300ctest.dat\u300d\u306b\u30ea\u30cd\u30fc\u30e0\u3057\uff0c\u4fdd\u5b58\u3057\u3066\u304f\u3060\u3055\u3044\u3002\uff09<\/p>\n<pre><code>0   0\r\n1   1\r\n2   4\r\n3   9\r\n4   16\r\n5   25\r\n\r\n<\/code><\/pre>\n<p>\u30c6\u3099\u30fc\u30bf\u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u8fbc\u3080 Maxima \u306e\u95a2\u6570\u306f\uff0c<code>read_nested_list<\/code> \u3092\u4f7f\u3044\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[19]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">dat<\/span><span class=\"o\">:<\/span> <span class=\"nf\">read_nested_list<\/span><span class=\"p\">(<\/span><span class=\"s\">\"test.dat\"<\/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[19]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{29}$}\\left[ \\left[ 0 , 0 \\right] , \\left[ 1 , 1 \\right] , \\left[ 2 , 4 \\right] , \\left[ 3 , 9 \\right] , \\left[ 4 , 16 \\right] , \\left[ 5 , 25 \\right] \\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>\u30ea\u30b9\u30c8 <code>dat<\/code> \u306b\u8aad\u307f\u8fbc\u3093\u3060\u6570\u5024\u30c7\u30fc\u30bf\u3092 <code>plot2d()<\/code> \u3067\u30b0\u30e9\u30d5\u306b\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[20]:<\/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=\"nf\">points<\/span><span class=\"p\">(<\/span><span class=\"nv\">dat<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-4553\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw13.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[21]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u8a2d\u5b9a\u4f8b *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">user_preamble<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"set key top left\"<\/span>, \r\n  \r\n  <span class=\"nv\">point_type<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">7<\/span>, \r\n  <span class=\"nv\">point_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>,\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">red<\/span>, \r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u30c7\u30fc\u30bf\"<\/span>,\r\n  <span class=\"nf\">points<\/span><span class=\"p\">(<\/span><span class=\"nv\">dat<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\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 \">\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-4554\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw14.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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<h2 id=\"\u6570\u5024\u30c6\u3099\u30fc\u30bf\u3068\u7406\u8ad6\u66f2\u7dda\u3092\u91cd\u306d\u3066\u8868\u793a\">\u6570\u5024\u30c6\u3099\u30fc\u30bf\u3068\u7406\u8ad6\u66f2\u7dda\u3092\u91cd\u306d\u3066\u8868\u793a<\/h2>\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>\u524d\u7bc0\u306e\u6570\u5024\u30c6\u3099\u30fc\u30bf\u30d5\u30a1\u30a4\u30eb <code>test.dat<\/code> \u3068\u7406\u8ad6\u66f2\u7dda $y = x^2$ \u306e 2 \u3064\u306e\u30af\u3099\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a\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[22]:<\/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\">user_preamble<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"set key top left\"<\/span>,\r\n \r\n  <span class=\"cm\">\/* \u6570\u5024\u30c7\u30fc\u30bf\u3092\u70b9\u3067 *\/<\/span>\r\n  <span class=\"nv\">point_type<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">7<\/span>, \r\n  <span class=\"nv\">point_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>,\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>, \r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u30c7\u30fc\u30bf\"<\/span>,\r\n  <span class=\"nf\">points<\/span><span class=\"p\">(<\/span><span class=\"nv\">dat<\/span><span class=\"p\">)<\/span>, \r\n\r\n  <span class=\"cm\">\/* \u66f2\u7dda\u3092\u967d\u95a2\u6570\u3067 *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>,\r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u7406\u8ad6\u66f2\u7dda y = x^2\"<\/span>, \r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">5<\/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 \">\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-4555\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw15.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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=\"\u7df4\u7fd2-4-2\">\u7df4\u7fd2 4-2<\/h3>\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><strong>\u6955\u5186\u306e\u30af\u3099\u30e9\u30d5\uff08\u6955\u5186\u4e2d\u5fc3\u3092\u539f\u70b9\u306b\u3057\u3066\uff09<\/strong><\/p>\n<p>\u5a92\u4ecb\u5909\u6570\u8868\u793a\u306e\u30b0\u30e9\u30d5\u3092\u8907\u6570\u91cd\u306d\u3066\u8868\u793a\u3059\u308b\u4f8b\u3067\u3059\u3002<\/p>\n<p>\u539f\u70b9\u3092\u4e2d\u5fc3\u3068\u3057\uff0c\u9577\u534a\u5f84 $a$\uff0c\u5358\u534a\u5f84 $b$ \u306e\u6955\u5186\u306e\u5f0f\u306f<\/p>\n<p>$$\\frac{x^2}{a^2} + \\frac{y^2}{b^2} = 1$$<\/p>\n<p>\u5a92\u4ecb\u5909\u6570\u8868\u793a\u3066\u3099\u306f\uff0c$x=a \\cos t, \\ y=b \\sin t, \\ (0\\leq t\\leq 2\\pi)$\u3068\u66f8\u3051\u307e\u3059\u3002<br \/>\n$a$\uff0c$b$ \u306b\u9069\u5f53\u306a\u5024\u3092\u5165\u308c\u3066\u8907\u6570\u306e\u6955\u5186\u306e\u30af\u3099\u30e9\u30d5\u3092\u91cd\u306d\u3066\u63cf\u304d\u306a\u3055\u3044\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[23]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u30d2\u30f3\u30c8\uff1a\u5a92\u4ecb\u5909\u6570 t \u8868\u793a\u306e x, y \u3092\u95a2\u6570\u3068\u3057\u3066\u5b9a\u7fa9 *\/<\/span>\r\n<span class=\"nf\">x<\/span><span class=\"p\">(<\/span><span class=\"nv\">a<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/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>$\r\n<span class=\"nf\">y<\/span><span class=\"p\">(<\/span><span class=\"nv\">b<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">b<\/span><span class=\"o\">*<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">t<\/span><span class=\"p\">)<\/span>$\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[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><\/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<h2 id=\"\u6d77\u738b\u661f\u3068\u51a5\u738b\u661f\u306e\u8ecc\u9053\">\u6d77\u738b\u661f\u3068\u51a5\u738b\u661f\u306e\u8ecc\u9053<\/h2>\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=\"\u7126\u70b9\u3092\u539f\u70b9\u3068\u3057\u305f\u6955\u5186\u306e\u30af\u3099\u30e9\u30d5\">\u7126\u70b9\u3092\u539f\u70b9\u3068\u3057\u305f\u6955\u5186\u306e\u30af\u3099\u30e9\u30d5<\/h3>\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>\u592a\u967d\u304b\u3089\u306e\u4e07\u6709\u5f15\u529b\u3092\u53d7\u3051\u3066\u904b\u52d5\u3059\u308b\u60d1\u661f\u306f\uff0c\u592a\u967d\uff08\u4e8c\u4f53\u554f\u984c\u3066\u3099\u306f\u8cea\u91cf\u4e2d\u5fc3\uff09\u3092\u7126\u70b9\u306e\u4e00\u3064\u3068\u3057\u305f\u6955\u5186\u904b\u52d5\u3092\u63cf\u3044\u3066\u904b\u52d5\u3057\u307e\u3059\u3002<br \/>\n\u7126\u70b9\u306e\u4e00\u3064\u3092\u539f\u70b9\u3068\u3057\uff0c\u9577\u534a\u5f84 $a$\uff0c\u96e2\u5fc3\u7387 $e$ \u306e\u6955\u5186\u306e\u65b9\u7a0b\u5f0f\u306f\uff0c\u6975\u5ea7\u6a19 $r$\uff0c$\\varphi$ \u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304b\u3099\u3066\u3099\u304d\u307e\u3059\u3002<\/p>\n<p>$$ r= \\frac{a (1\u2212e^2)}{ 1 + e\\cos\\varphi}$$<\/p>\n<p>\u3055\u3066\uff0c\u304b\u3064\u3066\u306f\u7b2c9\u60d1\u661f\uff0c\u73fe\u5728\u3067\u306f\u6e96\u60d1\u661f\u306e\u4e00\u3064\u3067\u3042\u308b\u51a5\u738b\u661f\u3082\u6955\u5186\u8ecc\u9053\u3092\u63cf\u304d\u307e\u3059\u3002\u51a5\u738b\u661f\u306e\u8ecc\u9053\u9577\u534a\u5f84 $\ud835\udc4e_P=39.445 \\mbox{au}$\uff0c\u96e2\u5fc3\u7387 $\ud835\udc52_P=0.250$<br \/>\n\u3092\u4f7f\u3063\u3066\u51a5\u738b\u661f\u306e\u8ecc\u9053\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u53c2\u8003\uff1a<a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E5%86%A5%E7%8E%8B%E6%98%9F\">\u51a5\u738b\u661f &#8211; Wikipedia<\/a><\/li>\n<\/ul>\n<p>\u307e\u305a\uff0c\u6975\u5ea7\u6a19\u8868\u793a\u306e\u6955\u5186\u306e\u5f0f\u3092\u95a2\u6570\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[24]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">r<\/span><span class=\"p\">(<\/span><span class=\"nv\">a<\/span>, <span class=\"nv\">e<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">a<\/span><span class=\"o\">*<\/span><span class=\"p\">(<\/span>1<span class=\"o\">-<\/span><span class=\"nv\">e<\/span><span class=\"o\">^<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span>1<span class=\"o\">+<\/span><span class=\"nv\">e<\/span><span class=\"o\">*<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">phi<\/span><span class=\"p\">))<\/span>;\r\n<span class=\"nf\">x<\/span><span class=\"p\">(<\/span><span class=\"nv\">a<\/span>, <span class=\"nv\">e<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">r<\/span><span class=\"p\">(<\/span><span class=\"nv\">a<\/span>, <span class=\"nv\">e<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">phi<\/span><span class=\"p\">)<\/span>;\r\n<span class=\"nf\">y<\/span><span class=\"p\">(<\/span><span class=\"nv\">a<\/span>, <span class=\"nv\">e<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">r<\/span><span class=\"p\">(<\/span><span class=\"nv\">a<\/span>, <span class=\"nv\">e<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">phi<\/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[24]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{35}$}r\\left(a , e , \\varphi\\right):=\\frac{a\\,\\left(1-e^2\\right)}{1+e\\,\\cos \\varphi}\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[24]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{36}$}x\\left(a , e , \\varphi\\right):=r\\left(a , e , \\varphi\\right)\\,\\cos \\varphi\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[24]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{37}$}y\\left(a , e , \\varphi\\right):=r\\left(a , e , \\varphi\\right)\\,\\sin \\varphi\\]<\/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>\u51a5\u738b\u661f\u306e\u8ecc\u9053\u9577\u534a\u5f84\u3068\u96e2\u5fc3\u7387\uff1a<\/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[25]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">aP<\/span><span class=\"o\">:<\/span> 39<span class=\"o\">.<\/span>445$\r\n<span class=\"nv\">eP<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>250$\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[26]:<\/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=\"cm\">\/* \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u591a\u3081\u306b *\/<\/span>\r\n  <span class=\"nv\">nticks<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">200<\/span>, \r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/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=\"mi\">50<\/span>, 50<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">50<\/span>, 50<span class=\"p\">]<\/span>,\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\r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u51a5\u738b\u661f\"<\/span>,\r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">x<\/span><span class=\"p\">(<\/span><span class=\"nv\">aP<\/span>, <span class=\"nv\">eP<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">y<\/span><span class=\"p\">(<\/span><span class=\"nv\">aP<\/span>, <span class=\"nv\">eP<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">phi<\/span>, <span class=\"mi\">0<\/span>, 2<span class=\"o\">*<\/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 \">\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-4556\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw16.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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<p>\u3067\u306f\uff0c\u3053\u306e\u51a5\u738b\u661f\u306e\u8ecc\u9053\u3068\uff0c\u305d\u306e\u5185\u5074\u3092\u307e\u308f\u308b\u6d77\u738b\u661f\u306e\u8ecc\u9053\u3092\u91cd\u306d\u3066\u63cf\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u6d77\u738b\u661f\u306e\u8ecc\u9053\u9577\u534a\u5f84\u306f $a_N=30.181 \\mbox{au}$\uff0c\u96e2\u5fc3\u7387\u306f $e_N=0.0097$ \u3068\u5c0f\u3055\u3044\u306e\u3067\u7c21\u5358\u306e\u305f\u3081\u306b $e_N=0$ \u3068\u3057\u3066\u6271\u3044\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u53c2\u8003\uff1a<a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E6%B5%B7%E7%8E%8B%E6%98%9F\">\u6d77\u738b\u661f &#8211; Wikipedia<\/a><\/li>\n<\/ul>\n<p>\u5b9f\u969b\u306e2\u3064\u306e\u5929\u4f53\u306e\u8ecc\u9053\u306f\u540c\u3058\u5e73\u9762\u4e0a\u306b\u3042\u308a\u307e\u305b\u3093\u304c\uff0c\u592a\u967d\u304b\u3089\u306e\u8ddd\u96e2\u306e\u307f\u3092\u307f\u308b\u305f\u3081\u306b\uff0c\u3053\u3053\u3067\u306f\u540c\u4e00\u5e73\u9762\u4e0a\u306b\u63cf\u304d\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[27]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">aN<\/span><span class=\"o\">:<\/span> 30<span class=\"o\">.<\/span>181$\r\n<span class=\"nv\">eN<\/span><span class=\"o\">:<\/span> 0$\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[28]:<\/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=\"cm\">\/* \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u591a\u3081\u306b *\/<\/span>\r\n  <span class=\"nv\">nticks<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">200<\/span>, \r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/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=\"mi\">50<\/span>, 50<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">50<\/span>, 50<span class=\"p\">]<\/span>,\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\r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u51a5\u738b\u661f\"<\/span>,\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">blue<\/span>,\r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">x<\/span><span class=\"p\">(<\/span><span class=\"nv\">aP<\/span>, <span class=\"nv\">eP<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">y<\/span><span class=\"p\">(<\/span><span class=\"nv\">aP<\/span>, <span class=\"nv\">eP<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">phi<\/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\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u6d77\u738b\u661f\"<\/span>,\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">red<\/span>,\r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">x<\/span><span class=\"p\">(<\/span><span class=\"nv\">aN<\/span>, <span class=\"nv\">eN<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">y<\/span><span class=\"p\">(<\/span><span class=\"nv\">aN<\/span>, <span class=\"nv\">eN<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">phi<\/span>, <span class=\"mi\">0<\/span>, 2<span class=\"o\">*<\/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 \">\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-4557\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw17.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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<p>\u3055\u3066\uff0c\u3053\u306e\u51a5\u738b\u661f\u3068\u6d77\u738b\u661f\u306e\u8ecc\u9053\u306e\u30b0\u30e9\u30d5\u3092\u3044\u308b\u3068\uff0c\u8ecc\u9053\u304c\u4ea4\u5dee\u3057\u3066\u3044\u308b\u3088\u3046\u306b\u898b\u3048\u307e\u3059\u3002\u3053\u306e\u3053\u3068\u3092\u78ba\u304b\u3081\u307e\u3059\u3002<\/p>\n<p>\u8868\u793a\u3055\u308c\u308b\u9818\u57df\u3092\u5236\u9650\u3057\u3066\uff0c\u4ea4\u5dee\u3057\u3066\u3044\u308b\u3042\u305f\u308a\u3092\u62e1\u5927\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[29]:<\/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\">nticks<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">200<\/span>, \r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/span>,\r\n\r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2\u3092\u9069\u5b9c\u8abf\u6574\u3059\u308b\u3053\u3068 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">20<\/span>, 30<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">10<\/span>, 20<span class=\"p\">]<\/span>,\r\n\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\r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u51a5\u738b\u661f\"<\/span>,\r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">x<\/span><span class=\"p\">(<\/span><span class=\"nv\">aP<\/span>, <span class=\"nv\">eP<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">y<\/span><span class=\"p\">(<\/span><span class=\"nv\">aP<\/span>, <span class=\"nv\">eP<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">phi<\/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\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u6d77\u738b\u661f\"<\/span>,\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">red<\/span>,\r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">x<\/span><span class=\"p\">(<\/span><span class=\"nv\">aN<\/span>, <span class=\"nv\">eN<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">y<\/span><span class=\"p\">(<\/span><span class=\"nv\">aN<\/span>, <span class=\"nv\">eN<\/span>, <span class=\"nv\">phi<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">phi<\/span>, <span class=\"mi\">0<\/span>, 2<span class=\"o\">*<\/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 \">\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-4558\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw18.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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<p>\u6d77\u738b\u661f\u306e\u8ecc\u9053\u306f\u534a\u5f84 $a_N$ \u306e\u5186\u3068\u3057\u3066\u3044\u307e\u3059\u304b\u3089\uff0c\u4ee5\u4e0b\u306e\u5f0f\u3092\u6e80\u305f\u3059\u89d2\u5ea6 $\\varphi$<br \/>\n\u3092\u6c42\u3081\u308c\u3070\u3088\u3044\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>$$ r(a_P, e_P, \\varphi) = a_N$$<\/p>\n<p>$0 &lt; \\varphi &lt; \\pi\/2$<br \/>\n\u306e\u3069\u3053\u304b\u3067\u4ea4\u5dee\u3057\u3066\u3044\u308b\u3088\u3046\u3067\u3059\u304b\u3089\uff0c\u3053\u306e\u3042\u305f\u308a\u3067\u6570\u5024\u7684\u306b\u89e3\u3092\u6c42\u3081\u308b\u65b9\u6cd5\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\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[30]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">phi1<\/span><span class=\"o\">:<\/span> <span class=\"nf\">find_root<\/span><span class=\"p\">(<\/span><span class=\"nf\">r<\/span><span class=\"p\">(<\/span><span class=\"nv\">aP<\/span>, <span class=\"nv\">eP<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">aN<\/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<\/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[30]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{45}$}0.4485997043415258\\]<\/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>$ -\\pi\/2 &lt; \\varphi &lt; 0$ \u306e\u7bc4\u56f2\u3066\u3099\u3082\u4ea4\u5dee\u3057\u3066\u3044\u307e\u3059\u306d\u3002<br \/>\n\u5bfe\u79f0\u6027\u304b\u3089\u7b54\u3048\u306f <code>phi1<\/code> \u306b\u8ca0\u53f7\u3092\u3064\u3051\u305f\u3082\u306e\u306b\u306a\u308b\u306e\u306f\u660e\u3089\u304b\u3066\u3099\u3059\u304b\u3099\uff0c\u5ff5\u306e\u305f\u3081\u306b\u78ba\u304b\u3081\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[31]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">phi2<\/span><span class=\"o\">:<\/span> <span class=\"nf\">find_root<\/span><span class=\"p\">(<\/span><span class=\"nf\">r<\/span><span class=\"p\">(<\/span><span class=\"nv\">aP<\/span>, <span class=\"nv\">eP<\/span>, <span class=\"nv\">t<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">aN<\/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=\"mi\">0<\/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[31]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{46}$}-0.4485997043415258\\]<\/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>\u6c42\u3081\u305f\u89d2\u5ea6\u306f\u30e9\u30b7\u3099\u30a2\u30f3\u5358\u4f4d\u3066\u3099\u3059\u304b\u3089\uff0c\u5ea6\u306b\u76f4\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[32]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u4eca\u5f8c\u8868\u793a\u3059\u308b\u30b1\u30bf\u6570\u3092 4 \u306b *\/<\/span> \r\n<span class=\"nv\">fpprintprec<\/span><span class=\"o\">:<\/span> 4$ \r\n\r\n<span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nv\">phi1<\/span><span class=\"o\">*<\/span>180<span class=\"o\">\/<\/span><span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span>;\r\n<span class=\"nv\">%<\/span> <span class=\"o\">*<\/span> <span class=\"mi\">2<\/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[32]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{48}$}25.7\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[32]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{49}$}51.41\\]<\/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>\u3064\u307e\u308a\u4e00\u5468 360 \u5ea6\u306e\u3046\u3061\uff0c\u3053\u306e\u89d2\u5ea6\u306b\u3042\u305f\u308b\u5206\u306f\uff0c\u6d77\u738b\u661f\u306e\u307b\u3046\u304b\u3099\u51a5\u738b\u661f\u3088\u308a\u592a\u967d\u304b\u3089\u9060\u3044\u4f4d\u7f6e\u306b\u3042\u308b\u3053\u3068\u304b\u3099\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p>\u539f\u70b9\u3068 2 \u3064\u306e\u8ecc\u9053\u306e\u4ea4\u70b9\u3092\u7d50\u3075\u3099\u76f4\u7dda\u3092\u63cf\u304f\u65b9\u6cd5\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3066\u3099\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[33]:<\/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=\"cm\">\/* \u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u591a\u3081\u306b *\/<\/span>\r\n  <span class=\"nv\">nticks<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">200<\/span>, \r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/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=\"mi\">50<\/span>, 50<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">50<\/span>, 50<span class=\"p\">]<\/span>,\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\r\n  <span class=\"cm\">\/* \u70b9\u3068\u70b9\u3092\u7dda\u3067\u3064\u306a\u3050 *\/<\/span>\r\n  <span class=\"nv\">points_joined<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>, \r\n  <span class=\"cm\">\/* \u7aef\u70b9\u306b\u306f\u25cf\u306a\u3069\u3092\u3064\u3051\u306a\u3044 *\/<\/span>\r\n  <span class=\"nv\">point_type<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">none<\/span>,\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">black<\/span>,\r\n  <span class=\"nf\">points<\/span><span class=\"p\">([[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">aN<\/span><span class=\"o\">*<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">phi1<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">aN<\/span><span class=\"o\">*<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">phi1<\/span><span class=\"p\">)]])<\/span>,\r\n  <span class=\"nf\">points<\/span><span class=\"p\">([[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">aN<\/span><span class=\"o\">*<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">phi2<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">aN<\/span><span class=\"o\">*<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">phi2<\/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 \">\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-4559\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw19.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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=\"\u7df4\u7fd2-4-3\">\u7df4\u7fd2 4-3<\/h3>\n<p>\u539f\u70b9\u30682\u3064\u306e\u8ecc\u9053\u306e\u4ea4\u70b9\u3092\u7d50\u3076\u76f4\u7dda\u3092\u8ffd\u52a0\u3057\u3066\uff0c\u51a5\u738b\u661f\u3068\u6d77\u738b\u661f\u306e\u8ecc\u9053\u3092\u63cf\u3051\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[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><\/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<h2 id=\"\u6708\u5225\u5e73\u5e74\u6c17\u6e29\u306e\u95a2\u6570\u30d5\u30a3\u30c3\u30c8\">\u6708\u5225\u5e73\u5e74\u6c17\u6e29\u306e\u95a2\u6570\u30d5\u30a3\u30c3\u30c8<\/h2>\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>\u5f18\u524d\u5e02\u306e\u6708\u5225\u5e73\u5e74\u6c17\u6e29\u306e\u30c6\u3099\u30fc\u30bf\u3092\u4f7f\u3063\u3066\u30ea\u30b9\u30c8 <code>HiroT<\/code> \u3092\u4f5c\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u53c2\u8003\uff1a<a href=\"https:\/\/www.data.jma.go.jp\/obd\/stats\/etrn\/view\/nml_amd_ym.php?prec_no=31&amp;block_no=0166&amp;year=&amp;month=&amp;day=&amp;view=\">\u5f18\u524d\u3000\u5e73\u5e74\u5024\uff08\u5e74\u30fb\u6708\u3054\u3068\u306e\u5024\uff09\u3000\u4e3b\u306a\u8981\u7d20<\/a><\/li>\n<\/ul>\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[34]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">HiroT<\/span><span class=\"o\">:<\/span> <span class=\"p\">[<\/span>\r\n<span class=\"p\">[<\/span><span class=\"mi\">1<\/span>, <span class=\"o\">-<\/span>1<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>,\r\n<span class=\"p\">[<\/span><span class=\"mi\">2<\/span>, <span class=\"o\">-<\/span>1<span class=\"o\">.<\/span>0<span class=\"p\">]<\/span>,\r\n<span class=\"p\">[<\/span><span class=\"mi\">3<\/span>, 2<span class=\"o\">.<\/span>3<span class=\"p\">]<\/span>,\r\n<span class=\"p\">[<\/span><span class=\"mi\">4<\/span>, 8<span class=\"o\">.<\/span>6<span class=\"p\">]<\/span>,\r\n<span class=\"p\">[<\/span><span class=\"mi\">5<\/span>, 14<span class=\"o\">.<\/span>3<span class=\"p\">]<\/span>,\r\n<span class=\"p\">[<\/span><span class=\"mi\">6<\/span>, 18<span class=\"o\">.<\/span>3<span class=\"p\">]<\/span>,\r\n<span class=\"p\">[<\/span><span class=\"mi\">7<\/span>, 22<span class=\"o\">.<\/span>3<span class=\"p\">]<\/span>,\r\n<span class=\"p\">[<\/span><span class=\"mi\">8<\/span>, 23<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>,\r\n<span class=\"p\">[<\/span><span class=\"mi\">9<\/span>, 19<span class=\"o\">.<\/span>4<span class=\"p\">]<\/span>,\r\n<span class=\"p\">[<\/span><span class=\"mi\">10<\/span>, 12<span class=\"o\">.<\/span>9<span class=\"p\">]<\/span>,\r\n<span class=\"p\">[<\/span><span class=\"mi\">11<\/span>, 6<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>,\r\n<span class=\"p\">[<\/span><span class=\"mi\">12<\/span>, 0<span class=\"o\">.<\/span>8<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 output_prompt\">Out[34]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{51}$}\\left[ \\left[ 1 , -1.5 \\right] , \\left[ 2 , -1.0 \\right] , \\left[ 3 , 2.3 \\right] , \\left[ 4 , 8.6 \\right] , \\left[ 5 , 14.3 \\right] , \\left[ 6 , 18.3 \\right] , \\left[ 7 , 22.3 \\right] , \\left[ 8 , 23.5 \\right] , \\left[ 9 , 19.4 \\right] , \\left[ 10 , 12.9 \\right] , \\left[ 11 , 6.5 \\right] , \\left[ 12 , 0.8 \\right] \\right] \\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e\u30c6\u3099\u30fc\u30bf\u3092\u30af\u3099\u30e9\u30d5\u306b\u63cf\u3044\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[35]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">point_type<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">7<\/span>,  \r\n  <span class=\"nf\">points<\/span><span class=\"p\">(<\/span><span class=\"nv\">HiroT<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\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 \">\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-4560\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw20.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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<p>\u30af\u3099\u30e9\u30d5\u3092\u898b\u308b\u3068\uff0c\u6708\u5225\u5e73\u5e74\u6c17\u6e29\u306f 12 \u30f6\u6708\u5468\u671f\u306e\u4e09\u89d2\u95a2\u6570\u3067\u30d5\u30a3\u30c3\u30c8\u3067\u304d\u308b\u3088\u3046\u306b\u307f\u3048\u307e\u3059\u3002<\/p>\n<p>\u3066\u3099\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u95a2\u6570\u30d5\u30a3\u30c3\u30c8\u3092\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u307e\u3059\u3099\uff0c\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306e\u30cf\u309a\u30c3\u30b1\u30fc\u30b7\u3099 <code>lsquares<\/code> \u3092\u30ed\u30fc\u30c8\u3099\u3057\u307e\u3059.\u3053\u308c\u306f <code>lsquares_estimates<\/code> \u3092 \u521d\u3081\u3066\u4f7f\u3046\u969b\uff0c\u6700\u521d\u306b 1 \u56de\u305f\u3099\u3051\u884c\u3048\u306f\u3099\u3088\u3044\u3066\u3099\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[36]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">load<\/span><span class=\"p\">(<\/span><span class=\"nv\">lsquares<\/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 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>\u6b21\u306b\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u95a2\u6570\u3092\u5b9a\u7fa9\u3057\u3066\uff0c\u3046\u307e\u304f\u30d5\u30a3\u30c3\u30c8\u3059\u308b\u3088\u3046\u306b\u5b9a\u6570 <code>a0, a1, b1, a2, b2<\/code> \u3092\u6c42\u3081\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[37]:<\/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\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">a0<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">a1<\/span><span class=\"o\">*<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span>2<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">*<\/span><span class=\"nv\">x<\/span><span class=\"o\">\/<\/span><span class=\"mi\">12<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">b1<\/span><span class=\"o\">*<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span>2<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">*<\/span><span class=\"nv\">x<\/span><span class=\"o\">\/<\/span><span class=\"mi\">12<\/span><span class=\"p\">)<\/span> \r\n            <span class=\"o\">+<\/span> <span class=\"nv\">a2<\/span><span class=\"o\">*<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span>4<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">*<\/span><span class=\"nv\">x<\/span><span class=\"o\">\/<\/span><span class=\"mi\">12<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">b2<\/span><span class=\"o\">*<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span>4<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">*<\/span><span class=\"nv\">x<\/span><span class=\"o\">\/<\/span><span class=\"mi\">12<\/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[37]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{54}$}g\\left(x\\right):=\\frac{a_{0}}{2}+a_{1}\\,\\cos \\left(\\frac{2\\,\\pi\\,x}{12}\\right)+b_{1}\\,\\sin \\left(\\frac{2\\,\\pi\\,x}{12}\\right)+a_{2}\\,\\cos \\left(\\frac{4\\,\\pi\\,x}{12}\\right)+b_{2}\\,\\sin \\left(\\frac{4\\,\\pi\\,x}{12}\\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<h3 id=\"\u53c2\u8003\uff1a\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\">\u53c2\u8003\uff1a\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b<\/h3>\n<p>\u4e00\u822c\u306b\u5468\u671f $2L$ \u306e\u5468\u671f\u95a2\u6570\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\u3067\u304d\u308b\u306e\u3067\u3042\u3063\u305f\u3002\u3057\u305f\u304c\u3063\u3066\uff0c\u3053\u3053\u3067\u3084\u3063\u3066\u3044\u308b\u3053\u3068\u306f\uff0c12\u30f6\u6708\u5206\u306e\u6708\u5e73\u5e74\u6c17\u6e29\u3068\u3044\u3046\u6570\u5024\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\uff0c\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u5c55\u958b\u307f\u305f\u3044\u306a\u3053\u3068\u3092\u6570\u5024\u7684\u306b\u884c\u3063\u3066\u3044\u308b\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n<p>$$ f(x) = \\frac{a_0}{2} + \\sum_{n=1}^{\\infty} \\bigl( a_n \\cos \\left(n \\frac{\\pi}{L} {x}\\right) + b_n \\sin \\left(n\\frac{\\pi}{L} {x}\\right) \\bigr) $$<\/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>\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3092\u884c\u3046\u95a2\u6570 <code>lsquares_estimates<\/code> \u306b\u306f\u6570\u5024\u30c6\u3099\u30fc\u30bf\u3092<strong>\u884c\u5217<\/strong>\u3068\u3057\u3066\u5165\u308c\u3066\u3084\u308b\u5fc5\u8981\u304b\u3099\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u305f\u3081\u306b\u30ea\u30b9\u30c8 <code>HiroT<\/code> \u3092\u884c\u5217 <code>M<\/code> \u306b\u5909\u63db\u3057\u307e\u3059\u3002\uff08\u30ea\u30b9\u30c8\u3068\u884c\u5217\u3067\u306f\u8868\u793a\u304c\u7570\u306a\u308a\u307e\u3059\u3002\u884c\u5217\u306f\u884c\u5217\u3089\u3057\u304f\u8868\u793a\u3055\u308c\u3066\u3044\u307e\u3059\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[38]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u30ea\u30b9\u30c8 HiroT \u3092\u884c\u5217 M \u306b\u5909\u63db\u3059\u308b *\/<\/span>\r\n<span class=\"nv\">M<\/span><span class=\"o\">:<\/span> <span class=\"nf\">apply<\/span><span class=\"p\">(<\/span><span class=\"o\">'<\/span><span class=\"nv\">matrix<\/span>, <span class=\"nv\">HiroT<\/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[38]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{55}$}\\begin{pmatrix}1 &amp; -1.5 \\\\ 2 &amp; -1.0 \\\\ 3 &amp; 2.3 \\\\ 4 &amp; 8.6 \\\\ 5 &amp; 14.3 \\\\ 6 &amp; 18.3 \\\\ 7 &amp; 22.3 \\\\ 8 &amp; 23.5 \\\\ 9 &amp; 19.4 \\\\ 10 &amp; 12.9 \\\\ 11 &amp; 6.5 \\\\ 12 &amp; 0.8 \\\\ \\end{pmatrix}\\]<\/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[39]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u6700\u5c0f\u4e8c\u4e57\u6cd5\u3067 a0, a1, ... \u3092\u6c42\u3081\u308b *\/<\/span>\r\n<span class=\"nf\">lsquares_estimates<\/span><span class=\"p\">(<\/span><span class=\"nv\">M<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">y<\/span><span class=\"o\">=<\/span><span class=\"nf\">g<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">a0<\/span>, <span class=\"nv\">a1<\/span>, <span class=\"nv\">b1<\/span>, <span class=\"nv\">a2<\/span>, <span class=\"nv\">b2<\/span><span class=\"p\">])<\/span>$\r\n<span class=\"cm\">\/* \u76f4\u524d\u306e\u7b54\u3048 a0, a1, ... \u3092\u4e0d\u52d5\u5c0f\u6570\u70b9\u8868\u793a\u3059\u308b *\/<\/span>\r\n<span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nv\">%<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[39]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{57}$}\\left[ \\left[ a_{0}=21.07 , a_{1}=-9.161 , b_{1}=-8.34 , a_{2}=-0.6333 , b_{2}=0.1443 \\right] \\right] \\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306b\u3088\u3063\u3066\u6c42\u3081\u305f <code>a0, a1, b1, a2, b2<\/code> \u306e\u5024\u3092 <code>gfit<\/code> \u306b\u4ee3\u5165\u3057\uff0c\u3053\u306e\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[40]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">gfit<\/span><span class=\"o\">:<\/span> <span class=\"nf\">ev<\/span><span class=\"p\">(<\/span><span class=\"nf\">g<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">%<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[40]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{58}$}0.1443\\,\\sin \\left(\\frac{\\pi\\,x}{3}\\right)-0.6333\\,\\cos \\left(\\frac{\\pi\\,x}{3}\\right)-8.34\\,\\sin \\left(\\frac{\\pi\\,x}{6}\\right)-9.161\\,\\cos \\left(\\frac{\\pi\\,x}{6}\\right)+10.53\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[41]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mf\">0.5<\/span>, 12<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">5<\/span>, 28<span class=\"p\">]<\/span>,\r\n  <span class=\"nv\">xaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>, <span class=\"nv\">yaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>, \r\n  <span class=\"nv\">user_preamble<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"set xtics 1\"<\/span>, \r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u6708\"<\/span>, \r\n  <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u6708\u5225\u5e73\u5e74\u6c17\u6e29\"<\/span>,\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u5f18\u524d\u5e02\u306e\u6708\u5225\u5e73\u5e74\u6c17\u6e29\"<\/span>,\r\n  \r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nv\">gfit<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">1<\/span>, <span class=\"mi\">12<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\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 \">\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-4561\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw21.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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=\"\u7df4\u7fd2-4-4\">\u7df4\u7fd2 4-4<\/h3>\n<ol>\n<li>\u6708\u5225\u5e73\u5e74\u6c17\u6e29\u306e\u6570\u5024\u30c6\u3099\u30fc\u30bf\u3068\u30d5\u30a3\u30c3\u30c8\u66f2\u7dda\u306e\u30b0\u30e9\u30d5\u3092\u91cd\u306d\u3066\u63cf\u3051\u3002<\/li>\n<\/ol>\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[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><\/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<h2 id=\"\u9818\u57df\u306e\u5857\u308a\u3064\u3076\u3057\">\u9818\u57df\u306e\u5857\u308a\u3064\u3076\u3057<\/h2>\n<p>$y = f(x)$ \u3068 $y = g(x)$ \uff08$f(x) \\geq g(x)$\uff09\u3067\u56f2\u307e\u308c\u305f\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3059\u4f8b\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[42]:<\/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> 0<span class=\"o\">.<\/span>6<span class=\"o\">*<\/span><span class=\"nv\">x<\/span> <span class=\"o\">+<\/span> 0<span class=\"o\">.<\/span>4<span class=\"o\">*<\/span><span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">g<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> 0$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">0<\/span>, 2<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.2<\/span>,1<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>,\r\n  <span class=\"nv\">xaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"cm\">\/* \u5857\u308a\u3064\u3076\u3059\u8272\u306e\u6307\u5b9a\u3002*\/<\/span>\r\n  <span class=\"nv\">fill_color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">yellow<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u4e0a\u306e\u7dda\u3002*\/<\/span>\r\n  <span class=\"nv\">filled_func<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u4e0b\u306e\u7dda\u3068\u7bc4\u56f2\u306e\u6307\u5b9a\u3002*\/<\/span>\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">g<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mf\">0.5<\/span>, <span class=\"mi\">2<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u5857\u308a\u6f70\u3057\u7d42\u4e86 *\/<\/span>\r\n  <span class=\"nv\">filled_func<\/span> <span class=\"o\">=<\/span> <span class=\"no\">false<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u3042\u3089\u305f\u3081\u3066 y = f(x) \u3092\u63cf\u304f *\/<\/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=\"mi\">2<\/span>, \r\n  <span class=\"nf\">explicit<\/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=\"nv\">x<\/span>, <span class=\"mf\">0.25<\/span>, <span class=\"mf\">2.25<\/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 \">\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-4562\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw22.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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=\"\u7df4\u7fd2-4-5\">\u7df4\u7fd2 4-5<\/h3>\n<p>\u534a\u5f84 $1$ \u306e\u5186\u306b\u304a\u3044\u3066\uff0c\u4ee5\u4e0b\u306e\u6247\u5f62\u306e\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3059\u3002<\/p>\n<ol>\n<li>\u4e2d\u5fc3\u304b\u3089 $\\theta = -15^{\\circ}$ \u3068 $\\theta = 15^{\\circ}$ \u306e\u76f4\u7dda\u3067\u56f2\u307e\u308c\u305f\u9818\u57df<\/li>\n<li>\u4e2d\u5fc3\u304b\u3089 $\\theta = 100^{\\circ}$ \u3068 $\\theta = 130^{\\circ}$ \u306e\u76f4\u7dda\u3067\u56f2\u307e\u308c\u305f\u9818\u57df<\/li>\n<\/ol>\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>\u5186\u306e\u30b0\u30e9\u30d5\u306e\u63cf\u304d\u65b9\u306b\u306f\u3044\u308d\u3044\u308d\u3042\u308a\u307e\u3059\u304c\uff0c\u4eca\u56de\u306f\u5857\u308a\u3064\u3076\u3057\u306a\u306e\u3067\uff0c\u967d\u95a2\u6570\u3067\u8868\u73fe\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\\begin{eqnarray}<br \/>\nx^2 + y^2 &amp;=&amp; 1 \\\\<br \/>\ny &amp;=&amp; \\pm \\sqrt{1 &#8211; x^2}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u307e\u305f\uff0c\u539f\u70b9\uff08\u5186\u306e\u4e2d\u5fc3\uff09\u3068\u5186\u4e0a\u306e\u70b9 $(\\cos\\theta, \\sin\\theta)$ \u3092\u7d50\u3076\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u306f<\/p>\n<p>$$y = \\tan\\theta \\cdot x$$<\/p>\n<p>\u3053\u306e\u554f\u984c\u3067\u306f\u89d2\u5ea6\u3092\u5ea6\u3067\u3042\u3089\u308f\u3057\u3066\u3044\u308b\u306e\u3067\uff0c\u30e9\u30b8\u30a2\u30f3\u306b\u63db\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\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[43]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5186\u306e\u65b9\u7a0b\u5f0f\uff1a\u4e0a\u534a\u5206 *\/<\/span>\r\n<span class=\"nf\">yu<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>;\r\n<span class=\"cm\">\/* \u5186\u306e\u65b9\u7a0b\u5f0f\uff1a\u4e0b\u534a\u5206 *\/<\/span>\r\n<span class=\"nf\">yd<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"o\">-<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>;\r\n\r\n<span class=\"cm\">\/* \u4e2d\u5fc3\u3068\u5186\u4e0a\u306e\u70b9\u3092\u7d50\u3076\u76f4\u7dda\u306e\u65b9\u7a0b\u5f0f\u3002theta \u306f\u5ea6\u3067 *\/<\/span>\r\n<span class=\"nf\">yl<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">theta<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">tan<\/span><span class=\"p\">(<\/span><span class=\"nv\">theta<\/span><span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">180<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">x<\/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[43]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{63}$}{\\it yu}\\left(x\\right):=\\sqrt{1-x^2}\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[43]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{64}$}{\\it yd}\\left(x\\right):=-\\sqrt{1-x^2}\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[43]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{65}$}{\\it yl}\\left(x , \\vartheta\\right):=\\tan \\left(\\frac{\\vartheta\\,\\pi}{180}\\right)\\,x\\]<\/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[44]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5186\u3068 theta = 15\u00b0, 15\u00b0 \u306e\u76f4\u7dda *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/span>,\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\r\n  <span class=\"cm\">\/* \u5186 *\/<\/span>\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yu<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">1<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yd<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">1<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u539f\u70b9\u304b\u3089\u306e\u76f4\u7dda *\/<\/span>\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yl<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"mi\">15<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span>15<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">180<\/span><span class=\"p\">))<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yl<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">15<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span>15<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">180<\/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 \">\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-4563\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw23.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\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[45]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5857\u308a\u3064\u3076\u3057 1 *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u5ea7\u6a19\u8ef8\u304c\u5857\u308a\u3064\u3076\u3055\u308c\u306a\u3044\u3088\u3046\u306b *\/<\/span>\r\n  <span class=\"nv\">user_preamble<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"set grid front; unset grid;\"<\/span>,\r\n  \r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/span>,\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  \r\n  <span class=\"cm\">\/* \u5857\u308a\u3064\u3076\u3059\u8272\u306e\u6307\u5b9a\u3002*\/<\/span>\r\n  <span class=\"nv\">fill_color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">yellow<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u4e0a\u306e\u7dda\u3002*\/<\/span>\r\n  <span class=\"nv\">filled_func<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">yl<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"mi\">15<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u4e0b\u306e\u7dda\u3068\u7bc4\u56f2\u306e\u6307\u5b9a\u3002*\/<\/span>\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yl<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">15<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span>15<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">180<\/span><span class=\"p\">))<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u5857\u308a\u6f70\u3057\u7d42\u4e86 *\/<\/span>\r\n  <span class=\"nv\">filled_func<\/span> <span class=\"o\">=<\/span> <span class=\"no\">false<\/span>, \r\n\r\n  <span class=\"cm\">\/* \u5186 *\/<\/span>\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yu<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">1<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yd<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">1<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u539f\u70b9\u304b\u3089\u306e\u76f4\u7dda *\/<\/span>\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yl<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"mi\">15<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span>15<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">180<\/span><span class=\"p\">))<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yl<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">15<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span>15<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">180<\/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 \">\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-4564\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw24.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\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[46]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5857\u308a\u3064\u3076\u3057 2 *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u5ea7\u6a19\u8ef8\u304c\u5857\u308a\u3064\u3076\u3055\u308c\u306a\u3044\u3088\u3046\u306b *\/<\/span>\r\n  <span class=\"nv\">user_preamble<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"set grid front; unset grid;\"<\/span>,\r\n  \r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/span>,\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  \r\n  <span class=\"cm\">\/* \u5857\u308a\u3064\u3076\u3059\u8272\u306e\u6307\u5b9a\u3002*\/<\/span>\r\n  <span class=\"nv\">fill_color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">yellow<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u4e0a\u306e\u7dda\u3002*\/<\/span>\r\n  <span class=\"nv\">filled_func<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">yl<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"mi\">15<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u4e0b\u306e\u7dda\u3068\u7bc4\u56f2\u306e\u6307\u5b9a\u3002*\/<\/span>\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yl<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">15<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span>15<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">180<\/span><span class=\"p\">))<\/span>, \r\n\r\n  <span class=\"cm\">\/* \u5857\u308a\u6b8b\u3057\u305f\u90e8\u5206 *\/<\/span>\r\n  <span class=\"cm\">\/* \u4e0a\u306e\u7dda\u3002*\/<\/span>\r\n  <span class=\"nv\">filled_func<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">yu<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u4e0b\u306e\u7dda\u3068\u7bc4\u56f2\u306e\u6307\u5b9a\u3002*\/<\/span>\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yd<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span>15<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">180<\/span><span class=\"p\">)<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>, \r\n\r\n  <span class=\"cm\">\/* \u5857\u308a\u6f70\u3057\u7d42\u4e86 *\/<\/span>\r\n  <span class=\"nv\">filled_func<\/span> <span class=\"o\">=<\/span> <span class=\"no\">false<\/span>, \r\n\r\n  <span class=\"cm\">\/* \u5186 *\/<\/span>\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yu<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">1<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yd<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">1<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u539f\u70b9\u304b\u3089\u306e\u76f4\u7dda *\/<\/span>\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yl<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"mi\">15<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span>15<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">180<\/span><span class=\"p\">))<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yl<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">15<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span>15<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">180<\/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 \">\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-4565\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw25.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/p>\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[47]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5186\u3068 theta = 100\u00b0, 130\u00b0 \u306e\u76f4\u7dda *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/span>,\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\r\n  <span class=\"cm\">\/* \u5186 *\/<\/span>\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yu<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">1<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yd<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">1<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u539f\u70b9\u304b\u3089\u306e\u76f4\u7dda *\/<\/span>\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yl<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"mi\">100<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span>100<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">180<\/span><span class=\"p\">)<\/span>, <span class=\"mi\">0<\/span><span class=\"p\">)<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">yl<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"mi\">130<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span>130<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">180<\/span><span class=\"p\">)<\/span>, <span class=\"mi\">0<\/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 \">\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-4566\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxdraw26.svg\" alt=\"\" width=\"640\" height=\"533\" \/><\/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<p>\u53c2\u8003\uff1a<\/p>\n<p>\u3053\u306e\u7df4\u7fd2\u554f\u984c\u3067\u306f\u5186\u3067\u3059\u304c\uff0c\u5929\u6587\u5b66\u306b\u304a\u3051\u308b\u30b1\u30d7\u30e9\u30fc\u306e\u6cd5\u5247\u304b\u3089\uff0c\u5929\u4f53\u306e\u8ecc\u9053\u306f\u6955\u5186\u3067\u3042\u308a\uff0c\u9762\u7a4d\u901f\u5ea6\u304c\u4e00\u5b9a\u3067\u3059\u3002\u6247\u5f62\u306e\u90e8\u5206\u3092\u5857\u308a\u3064\u3076\u3059\u3068\u3044\u3046\u3053\u3068\u306f\uff0c\u30b1\u30d7\u30e9\u30fc\u306e\u7b2c2\u6cd5\u5247\u3092\u8996\u899a\u7684\u306b\u8868\u3059\u969b\u306b\u3068\u3066\u3082\u91cd\u8981\u306a\u3093\u3067\u3059\u3088\u3002<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/109.png\" alt=\"kep2\" width=\"75%\" \/><\/p>\n<ul>\n<li>\u53c2\u8003\uff1a<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/4052\/\">Maxima \u3066\u3099\u30b1\u30d5\u309a\u30e9\u30fc\u65b9\u7a0b\u5f0f\u3092\u9010\u6b21\u8fd1\u4f3c\u7684\u306b\u89e3\u3044\u3066 draw2d \u3067\u63cf\u3044\u3066\u30d1\u30e9\u30d1\u30e9\u30a2\u30cb\u30e1\u306b\u3059\u308b<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Maxima \u306e2\u6b21\u5143\u30b0\u30e9\u30d5\u4f5c\u6210\u306f plot2d() \u3067\u3082\u3067\u304d\u307e\u3059\u304c\uff0c\u3053\u3053\u3067\u306f\uff0cdraw2d() \u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/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%ab%e3%82%88%e3%82%8b%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/maxima-%e3%81%ab%e3%82%88%e3%82%8b%e3%82%af%e3%82%99%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90-draw2d-%e7%b7%a8\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":4506,"menu_order":20,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-4539","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\/4539","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=4539"}],"version-history":[{"count":7,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4539\/revisions"}],"predecessor-version":[{"id":4985,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4539\/revisions\/4985"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4506"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=4539"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}