{"id":5164,"date":"2023-12-18T10:40:05","date_gmt":"2023-12-18T01:40:05","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=5164"},"modified":"2025-01-15T10:35:21","modified_gmt":"2025-01-15T01:35:21","slug":"maxima-%e3%81%a6%e3%82%99%e7%a9%ba%e6%b0%97%e6%8a%b5%e6%8a%97%e3%81%8c%e3%81%82%e3%82%8b%e5%a0%b4%e5%90%88%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%82%92%e8%aa%bf%e3%81%b9%e3%82%8b","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8f%82%e8%80%83%ef%bc%9amaxima-%e7%b7%a8\/maxima-%e3%81%a6%e3%82%99%e7%a9%ba%e6%b0%97%e6%8a%b5%e6%8a%97%e3%81%8c%e3%81%82%e3%82%8b%e5%a0%b4%e5%90%88%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%82%92%e8%aa%bf%e3%81%b9%e3%82%8b\/","title":{"rendered":"Maxima \u3066\u3099\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u3092\u8abf\u3079\u308b"},"content":{"rendered":"<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u8ecc\u9053\u3092\uff0cMaxima \u3092\u4f7f\u3063\u3066\u8abf\u3079\u308b\u3002<\/p>\n<p>\u8a73\u7d30\u306f\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e7%a9%ba%e6%b0%97%e6%8a%b5%e6%8a%97%e3%81%8c%e3%81%82%e3%82%8b%e5%a0%b4%e5%90%88%e3%81%ae%e6%96%9c%e6%96%b9%e6%8a%95%e5%b0%84%e3%82%92%e8%aa%bf%e3%81%b9%e3%82%8b%e6%ba%96%e5%82%99\/#i-5\">\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u3092\u8abf\u3079\u308b\u6e96\u5099<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<p><!--more--><\/p>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u89e3\">\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u89e3<\/h3>\n<p>\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u659c\u65b9\u6295\u5c04\u306e\u89e3\u306f\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\nX &amp;=&amp; \\frac{1-e^{-b T}}{b} \\, \\cos\\theta \\\\<br \/>\nY &amp;=&amp; H + \\frac{1-e^{-b T}}{b} \\, \\sin\\theta + \\frac{1 &#8211; b T -e^{-b T}}{b^2}<br \/>\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5ea6\u3092\u30e9\u30b8\u30a2\u30f3\u306b\u5909\u63db\u3059\u308b\u95a2\u6570\u3092\u6e96\u5099\u3057\u3066\u304a\u304f *\/<\/span>\r\n<span class=\"nf\">radians<\/span><span class=\"p\">(<\/span><span class=\"nv\">deg<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">deg<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span>180$\r\n\r\n<span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">th<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"p\">(<\/span><span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"nf\">exp<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"nv\">b<\/span><span class=\"o\">*<\/span><span class=\"nv\">T<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"nv\">b<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nf\">radians<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span><span class=\"p\">))<\/span>$\r\n<span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">th<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">H<\/span> <span class=\"o\">+<\/span> <span class=\"p\">(<\/span><span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"nf\">exp<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"nv\">b<\/span><span class=\"o\">*<\/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=\"nf\">radians<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span><span class=\"p\">))<\/span>\r\n                   <span class=\"o\">+<\/span> <span class=\"p\">(<\/span><span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">b<\/span><span class=\"o\">*<\/span><span class=\"nv\">T<\/span> <span class=\"o\">-<\/span> <span class=\"nf\">exp<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"nv\">b<\/span><span class=\"o\">*<\/span><span class=\"nv\">T<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nv\">b<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u6ede\u7a7a\u6642\u9593-$T_1$\">\u6ede\u7a7a\u6642\u9593 $T_1$<\/h3>\n<p>$T = 0$ \u3067\u6253\u3061\u51fa\u3055\u308c\u305f\u7c92\u5b50\u304c\u5730\u9762 $Y=0$ \u306b\u843d\u3061\u308b\u307e\u3067\u306e\u6ede\u7a7a\u6642\u9593 $T_1$ \u306f\u4ee5\u4e0b\u3092\u6e80\u305f\u3059\u3002<\/p>\n<p>\\begin{eqnarray}<br \/>\nY(T_1, \\theta, H, b) &amp;=&amp; H + \\frac{1-e^{-b T_1}}{b} \\, \\sin\\theta + \\frac{1 &#8211; b T_1 -e^{-b T_1}}{b^2} = 0<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3053\u306e\u5f0f\u306f $T_1$ \u306b\u3064\u3044\u3066\u8d85\u8d8a\u65b9\u7a0b\u5f0f\u3067\u3042\u308a\uff0c\u89e3\u6790\u7684\u306b\u89e3\u3092\u6c42\u3081\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002<\/p>\n<p>\u305d\u3053\u3067 Maxima \u3067\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u3092\u6c42\u3081\u308b\u305f\u3081\u306b\uff0c<code>find_root()<\/code> \u3092\u4f7f\u3046\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u3069\u306e\u7bc4\u56f2\u3067 find_root \u3059\u308b\u304b\u3002\u3053\u3053\u3067\u306f 0.1 ~ 3.0 \u3068\u5e83\u3081\u306b *\/<\/span>\r\n<span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">find_root<\/span><span class=\"p\">(<\/span><span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">th<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">=<\/span><span class=\"mi\">0<\/span>, <span class=\"nv\">T<\/span>, <span class=\"mf\">0.1<\/span>, <span class=\"mf\">3.0<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u6c34\u5e73\u5230\u9054\u8ddd\u96e2-$L$\">\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L$<\/h3>\n<p>$Y(T_1, \\theta, H, b) =0$ \u306e\u6570\u5024\u89e3 $T_1(\\theta, H, b)$ \u304c\u6c42\u307e\u3063\u305f\u3089\uff0c\u3053\u306e\u6ede\u7a7a\u6642\u9593\u306e\u9593\u306e\u6c34\u5e73\u65b9\u5411\u306e\u5230\u9054\u8ddd\u96e2 $L$ \u306f\uff0c<\/p>\n<p>$$L = X(T_1(\\theta, H, b), \\theta, b)$$<\/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\">L<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">th<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"$H-=-0$-\u306e\u5834\u5408\u306e\u8ecc\u9053\">$H = 0$ \u306e\u5834\u5408\u306e\u8ecc\u9053<\/h3>\n<p>\u7a7a\u6c17\u62b5\u6297\u306e\u4fc2\u6570 $b=0.5$ \u306e\u5834\u5408\u306b\uff0c$\\theta = 45^{\\circ}$ \u524d\u5f8c\u306e\u89d2\u5ea6\u3067\u306e\u659c\u65b9\u6295\u5c04\u306e\u8ecc\u9053\u3092\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3002<\/p>\n<p>\u3068\u308a\u3042\u3048\u305a\u306f $\\theta = 45^{\\circ}$ \u306e\u5834\u5408\u30921\u672c\uff0c\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">th1<\/span><span class=\"o\">:<\/span> 45$\r\n<span class=\"nv\">H1<\/span><span class=\"o\">:<\/span> 0$\r\n<span class=\"nv\">b1<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>5$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">th1<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">th1<\/span>, <span class=\"nv\">H1<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">)<\/span>, \r\n             <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"nv\">th1<\/span>, <span class=\"nv\">H1<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"p\">)<\/span>$\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-7510\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Mbtosha01a.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/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>\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3057\u3066\u305d\u308c\u3089\u3057\u3044\u30b0\u30e9\u30d5\u306b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">th1<\/span><span class=\"o\">:<\/span> 45$\r\n<span class=\"nv\">H1<\/span><span class=\"o\">:<\/span> 0$\r\n<span class=\"nv\">b1<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>5$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"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\u3068\u30b0\u30ea\u30c3\u30c9\u7dda *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>8<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>4<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"cm\">\/* \u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"X\"<\/span>, <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Y\"<\/span>, \r\n  <span class=\"cm\">\/* x\u8ef8 y\u8ef8\u306e\u76ee\u76db *\/<\/span>\r\n  <span class=\"nv\">xtics<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>, <span class=\"nv\">ytics<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/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=\"cm\">\/* \u6570\u5024\u3092\u53d6\u308a\u8fbc\u3093\u3060\u30bf\u30a4\u30c8\u30eb\u306e\u8a2d\u5b9a *\/<\/span>\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">false<\/span>, <span class=\"s\">\"b = ~,1f, H = ~,1f \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\"<\/span>, <span class=\"nv\">b1<\/span>, <span class=\"nv\">H1<\/span><span class=\"p\">)<\/span>,\r\n\r\n  <span class=\"cm\">\/* \u6570\u5024\u3092\u53d6\u308a\u8fbc\u3093\u3060\u51e1\u4f8b\u306e\u8a2d\u5b9a *\/<\/span>\r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">false<\/span>, <span class=\"s\">\"\u03b8 = ~2d\u00b0\"<\/span>, <span class=\"nv\">th1<\/span><span class=\"p\">)<\/span>, \r\n\r\n  <span class=\"cm\">\/* \u5a92\u4ecb\u5909\u6570\u8868\u793a\u3067\u66f2\u7dda\u3092\u63cf\u304f *\/<\/span>\r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">th1<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">th1<\/span>, <span class=\"nv\">H1<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">)<\/span>, \r\n             <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"nv\">th1<\/span>, <span class=\"nv\">H1<\/span>, <span class=\"nv\">b1<\/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-7511\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Mbtosha02.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/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>$\\theta$ \u306e\u5024\u3092 $38^{\\circ}$ \u304b\u3089 $45^{\\circ}$ \u307e\u3067 $1^{\\circ}$ \u523b\u307f\u3067\u5909\u3048\u3066\uff0c\u8907\u6570\u306e\u66f2\u7dda\u3092\u4e00\u5ea6\u306b\u63cf\u304f\u4f8b\u3002<\/p>\n<p>\u3042\u3089\u304b\u3058\u3081 <code>makelist()<\/code> \u3067\u30b0\u30e9\u30d5\u306b\u3059\u308b\u30ea\u30b9\u30c8\u3092\u4f5c\u3063\u3066\u304a\u304d\u307e\u3059\u3002\u3002<\/p>\n<p>\u306a\u304a\uff0c\u7d30\u304b\u3044\u3053\u3068\u3067\u3059\u304c\uff0c\u30b0\u30e9\u30d5\u306e\u6700\u9ad8\u70b9\u306f $\\theta$ \u306e\u5024\u304c\u5927\u304d\u3044\u3068\u304d\u3067\u3059\u306e\u3067\uff0c\u5148\u306b $45^{\\circ}$ \u304b\u3089\u63cf\u304d\u306f\u3058\u3081\u3066\uff0c$1^{\\circ}$ \u305a\u3064\u6e1b\u3089\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[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">H1<\/span><span class=\"o\">:<\/span> 0$\r\n<span class=\"nv\">b1<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>5$\r\n\r\n<span class=\"cm\">\/* \u8907\u6570\u306e\u30b0\u30e9\u30d5\u3092\u4e00\u5ea6\u306b\u63cf\u304f\u5834\u5408\u306f... *\/<\/span>\r\n<span class=\"cm\">\/* \u6700\u521d\u306b makelist \u3067\u4f5c\u3063\u3066\u304a\u304f\u3068\u3044\u3044\u304b\u3082 *\/<\/span>\r\n<span class=\"nv\">thmax<\/span><span class=\"o\">:<\/span> 45$\r\n<span class=\"nv\">thmin<\/span><span class=\"o\">:<\/span> 38$\r\n\r\n<span class=\"nv\">lines<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"p\">[<\/span><span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">false<\/span>, <span class=\"s\">\"\u03b8 = ~2d\u00b0\"<\/span>, <span class=\"nv\">th<\/span><span class=\"p\">)<\/span>,\r\n   <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">mod<\/span><span class=\"p\">(<\/span><span class=\"nv\">thmax<\/span>, <span class=\"nv\">th<\/span><span class=\"p\">)<\/span>, \r\n   <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">th<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">th<\/span>, <span class=\"nv\">H1<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">)<\/span>, \r\n             <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H1<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">))<\/span>\r\n  <span class=\"p\">]<\/span>, \r\n  <span class=\"nv\">th<\/span>, <span class=\"nv\">thmax<\/span>, <span class=\"nv\">thmin<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">)<\/span>$\r\n\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\">\/* \u8868\u793a\u7bc4\u56f2\u3068\u30b0\u30ea\u30c3\u30c9\u7dda *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>8<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>4<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"cm\">\/* \u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"X\"<\/span>, <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Y\"<\/span>, \r\n  <span class=\"cm\">\/* x\u8ef8 y\u8ef8\u306e\u76ee\u76db *\/<\/span>\r\n  <span class=\"nv\">xtics<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>, <span class=\"nv\">ytics<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>,\r\n  <span class=\"cm\">\/* \u6570\u5024\u3092\u53d6\u308a\u8fbc\u3093\u3060\u30bf\u30a4\u30c8\u30eb\u306e\u8a2d\u5b9a *\/<\/span>\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">false<\/span>, <span class=\"s\">\"b = ~,1f, H = ~,1f \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\"<\/span>, <span class=\"nv\">b1<\/span>, <span class=\"nv\">H1<\/span><span class=\"p\">)<\/span>,\r\n\r\n  <span class=\"cm\">\/* \u7dda\u306e\u6570\u3060\u3051\u7f85\u5217\u3059\u308b\u5fc5\u8981\u306a\u304f\uff0c\u4f5c\u6210\u6e08\u307f\u306e\u30ea\u30b9\u30c8\u3092\u66f8\u304f\u3060\u3051 *\/<\/span>\r\n  <span class=\"nv\">lines<\/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-7512\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Mbtosha03.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/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>\u843d\u4e0b\u70b9\u4ed8\u8fd1\u3092\u62e1\u5927\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u7740\u5730\u70b9\u4ed8\u8fd1\u3092\u62e1\u5927\u8868\u793a *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u843d\u4e0b\u70b9\u4ed8\u8fd1\u3092\u62e1\u5927\u8868\u793a *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mf\">0.66<\/span>, 0<span class=\"o\">.<\/span>682<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>01<span class=\"p\">]<\/span>, \r\n  <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"X\"<\/span>, <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Y\"<\/span>, \r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">false<\/span>, <span class=\"s\">\"b = ~,1f, H = ~,1f \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\"<\/span>, <span class=\"nv\">b1<\/span>, <span class=\"nv\">H1<\/span><span class=\"p\">)<\/span>,\r\n\r\n  <span class=\"nv\">lines<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-7513\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Mbtosha04.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$b = 0.5$ \u306e\u5834\u5408\uff0c\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3068\u306a\u308b\u306e\u306f $\\theta$ \u304c 39\u00b0 \u304b\u3089 40\u00b0 \u304f\u3089\u3044\u306e\u6642\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u3082\u3046\u5c11\u3057\u5b9a\u91cf\u7684\u306b\u6c42\u3081\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u6c34\u5e73\u5230\u9054\u8ddd\u96e2-$L$-\u306e\u30b0\u30e9\u30d5\">\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 $L$ \u306e\u30b0\u30e9\u30d5<\/h3>\n<p>\u5b9a\u91cf\u7684\u306b\u8abf\u3079\u308b\u305f\u3081\u306b\uff0c\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 <code>L(b, th, H)<\/code> \u3092\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[8]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>, \r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u6253\u3061\u51fa\u3057\u89d2\u5ea6 \u03b8 (\u00b0)\"<\/span>, \r\n  <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u898f\u683c\u5316\u3055\u308c\u305f\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 L\"<\/span>,\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">false<\/span>, \r\n          <span class=\"s\">\"b = ~,1f, H = ~,1f \u306e\u5834\u5408\u306e\u6295\u5c04\u89d2\u5ea6\u3068\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span>, <span class=\"nv\">b1<\/span>, <span class=\"nv\">H1<\/span><span class=\"p\">)<\/span>,\r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>,  \r\n\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H1<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">th<\/span>, <span class=\"mi\">38<\/span>, <span class=\"mi\">42<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-7514\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Mbtosha05.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3068\u306a\u308b\u89d2\u5ea6-$\\theta_{\\rm-max}$-\u3092\u6570\u5024\u5fae\u5206\u3067\u6c42\u3081\u308b\">\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3068\u306a\u308b\u89d2\u5ea6 $\\theta_{\\rm max}$ \u3092\u6570\u5024\u5fae\u5206\u3067\u6c42\u3081\u308b<\/h3>\n<p>$L(\\theta, H, b)$ \u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f $\\displaystyle \\frac{d L}{d \\theta} = 0$ \u3068\u306a\u308b\u89d2\u5ea6\u306e\u3068\u304d\u3067\u3059\u3002<\/p>\n<p>$L(\\theta, H, b)$ \u306f\u89e3\u6790\u7684\u306a\u95a2\u6570\u3068\u3057\u3066\u4e0e\u3048\u3089\u308c\u3066\u3044\u306a\u3044\u306e\u3067\uff0c\u3053\u3053\u3067\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u6570\u5024\u5fae\u5206\u3067\u6c42\u3081\u308b\u3053\u3068\u306b\u3057\u307e\u3059\u3002<\/p>\n<p>$$\\frac{d L}{d \\theta} \\simeq \\frac{L(\\theta+\\delta, H, b)-L(\\theta-\\delta, H, b)}{2 \\delta}$$<\/p>\n<p>$\\displaystyle \\frac{d L}{d \\theta} = 0$ \u3068\u306a\u308b\u89d2\u5ea6 $\\theta$ \u3092\u65b9\u7a0b\u5f0f\u306e\u89e3\u3092\u6570\u5024\u7684\u306b\u89e3\u304f <code>find_root()<\/code> \u3092\u4f7f\u3063\u3066\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[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">dL<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span>, <span class=\"nv\">delta<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> \r\n  <span class=\"p\">(<\/span><span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span><span class=\"o\">+<\/span><span class=\"nv\">delta<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span> <span class=\"o\">-<\/span> <span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span><span class=\"o\">-<\/span><span class=\"nv\">delta<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">))<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span>2<span class=\"o\">*<\/span><span class=\"nv\">delta<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[10]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3 *\/<\/span>\r\n<span class=\"cm\">\/* h \u3092\u5909\u3048\u3066\u307f\u308b *\/<\/span>\r\n<span class=\"k\">for<\/span> <span class=\"nv\">delta<\/span> <span class=\"nv\">in<\/span> <span class=\"p\">[<\/span><span class=\"mf\">1.e-3<\/span>, <span class=\"mf\">1.e-4<\/span>, <span class=\"mf\">1.e-5<\/span>, <span class=\"mf\">1.e-6<\/span>, 1<span class=\"o\">.<\/span><span class=\"nv\">e<\/span><span class=\"o\">-<\/span>7<span class=\"p\">]<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nf\">print<\/span><span class=\"p\">(<\/span><span class=\"nf\">find_root<\/span><span class=\"p\">(<\/span><span class=\"nf\">dL<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H1<\/span>, <span class=\"nv\">b1<\/span>, <span class=\"nv\">delta<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"nv\">th<\/span>, <span class=\"mi\">38<\/span>, <span class=\"mi\">45<\/span><span class=\"p\">))<\/span>\r\n<span class=\"p\">)<\/span>$\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_latex output_subarea \">\\(39.48760970738729\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(39.48760970505247\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(39.48760969486192\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(39.48760979510863\\)<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\(39.48760887562081\\)<\/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\u7d50\u679c\u304b\u3089\uff0c<code>delta = 1e-4<\/code> \u306b\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u95a2\u6570\u3092\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[11]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">thmax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">find_root<\/span><span class=\"p\">(<\/span><span class=\"nf\">dL<\/span><span class=\"p\">(<\/span><span class=\"nv\">th<\/span>, <span class=\"nv\">H<\/span>, <span class=\"nv\">b<\/span>, <span class=\"mf\">1e-4<\/span><span class=\"p\">)<\/span><span class=\"o\">=<\/span><span class=\"mi\">0<\/span>, <span class=\"nv\">th<\/span>, <span class=\"mi\">10<\/span>, <span class=\"mi\">45<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"$H=0,-b-=-0.5$-\u306e\u5834\u5408\">$H=0, b = 0.5$ \u306e\u5834\u5408<\/h3>\n<h4 id=\"\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3068\u6295\u5c04\u89d2\u5ea6\">\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u3068\u6295\u5c04\u89d2\u5ea6<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[12]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">H1<\/span><span class=\"o\">:<\/span> 0$\r\n<span class=\"nv\">b1<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>5$\r\n\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>,<span class=\"s\">\"b = ~,1f, H = ~,1f \u306e\u3068\u304d\uff0c~%\"<\/span>, <span class=\"nv\">b1<\/span>, <span class=\"nv\">H1<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>,<span class=\"s\">\"L \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6 \u03b8max \u306f ~9,6f\u00b0~%\"<\/span>, <span class=\"nf\">thmax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H1<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">))<\/span>$\r\n<span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">true<\/span>,<span class=\"s\">\"\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 Lmax \u306f ~,6f\"<\/span>, <span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"nf\">thmax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H1<\/span>,<span class=\"nv\">b1<\/span><span class=\"p\">)<\/span>,<span class=\"nv\">H1<\/span>,<span class=\"nv\">b1<\/span><span class=\"p\">))<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>b = 0.5, H = 0.0 \u306e\u3068\u304d\uff0c\r\nL \u304c\u6700\u5927\u3068\u306a\u308b\u89d2\u5ea6 \u03b8max \u306f 39.487610\u00b0\r\n\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2 Lmax \u306f 0.679421<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u8ecc\u9053\u306e\u30b0\u30e9\u30d5\">\u8ecc\u9053\u306e\u30b0\u30e9\u30d5<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[13]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">H1<\/span><span class=\"o\">:<\/span> 0$\r\n<span class=\"nv\">b1<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>5$\r\n\r\n<span class=\"nv\">thMax<\/span><span class=\"o\">:<\/span> <span class=\"nf\">thmax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H1<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">)<\/span>$\r\n\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\">\/* \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>, 0<span class=\"o\">.<\/span>8<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>4<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"nv\">xtics<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>, <span class=\"nv\">ytics<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>,\r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"X\"<\/span>, <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Y\"<\/span>,\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">false<\/span>, <span class=\"s\">\"H = ~1d \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span>,<span class=\"nv\">H1<\/span><span class=\"p\">)<\/span>,\r\n\r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>,\r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">false<\/span>, \r\n               <span class=\"s\">\"b = ~,1f, \u03b8_{max} = ~,4f\u00b0, L_{max} = ~,4f\"<\/span>, \r\n                <span class=\"nv\">b1<\/span>,       <span class=\"nv\">thMax<\/span>,           <span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"nv\">thMax<\/span>,<span class=\"nv\">H1<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">))<\/span>,\r\n  <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">thMax<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">thMax<\/span>, <span class=\"nv\">H1<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">)<\/span>, \r\n             <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"nv\">thMax<\/span>, <span class=\"nv\">H1<\/span>, <span class=\"nv\">b1<\/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-7515\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Mbtosha06.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/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=\"\u554f\u984c-1\">\u554f\u984c 1<\/h3>\n<p>\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u9ad8\u3055 $H=0$ \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u6253\u3061\u51fa\u3057\u89d2\u5ea6\u3068\uff0c\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u308f\u304b\u308b\u3088\u3046\u306a\u30b0\u30e9\u30d5\u3092\u6b21\u306e\u898f\u683c\u5316\u3055\u308c\u305f\u62b5\u6297\u4fc2\u6570 $b$ \u306e\u5834\u5408\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u3066\u63cf\u3051\u3002<\/p>\n<p>$$ b = 0.5, \\ 1.0, \\ 1.5, \\ 2.0$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u89e3\u7b54\u4f8b\">\u89e3\u7b54\u4f8b<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[14]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">bl<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span><span class=\"nf\">float<\/span><span class=\"p\">(<\/span>5<span class=\"o\">*<\/span><span class=\"nv\">i<\/span><span class=\"o\">\/<\/span><span class=\"mi\">10<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">i<\/span>, <span class=\"mi\">1<\/span>, <span class=\"mi\">4<\/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[14]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{34}$}\\left[ 0.5 , 1.0 , 1.5 , 2.0 \\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[15]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u4e00\u6642\u7684\u306b6\u6841\u3067 thml \u3092\u8868\u793a\u3059\u308b\u3002*\/<\/span>\r\n<span class=\"nv\">fpprintprec<\/span><span class=\"o\">:<\/span> 6$\r\n<span class=\"nv\">thml<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nf\">thmax<\/span><span class=\"p\">(<\/span><span class=\"nv\">H1<\/span>, <span class=\"nv\">bl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">])<\/span>, <span class=\"nv\">i<\/span>, <span class=\"mi\">1<\/span>, <span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">bl<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[15]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{36}$}\\left[ 39.4876 , 35.5897 , 32.6181 , 30.245 \\right] \\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[16]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">H1<\/span><span class=\"o\">:<\/span> 0$\r\n\r\n<span class=\"cm\">\/* \u5148\u306b\u63cf\u304f\u7dda\u3092\u30ea\u30b9\u30c8\u306b\u3057\u3066\u304a\u304f *\/<\/span>\r\n<span class=\"nv\">lines<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"p\">[<\/span><span class=\"nv\">color<\/span><span class=\"o\">=<\/span><span class=\"nv\">i<\/span>, \r\n   <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">false<\/span>, \r\n                <span class=\"s\">\"b = ~,1f, \u03b8_{max} = ~,4f\u00b0, L_{max} = ~,4f\"<\/span>, \r\n                 <span class=\"nv\">bl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>,    <span class=\"nv\">thml<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>,         <span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"nv\">thml<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>,<span class=\"nv\">H1<\/span>,<span class=\"nv\">bl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]))<\/span>,\r\n   <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">thml<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">bl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">])<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">thml<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">H1<\/span>, <span class=\"nv\">bl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">])<\/span>, \r\n              <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"nv\">thml<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">H1<\/span>, <span class=\"nv\">bl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]))<\/span>\r\n  <span class=\"p\">]<\/span>, \r\n  <span class=\"nv\">i<\/span>, <span class=\"mi\">1<\/span>, <span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">bl<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/span>,\r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>8<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>4<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"nv\">xtics<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>, <span class=\"nv\">ytics<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>, \r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"X\"<\/span>, <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Y\"<\/span>,\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">false<\/span>, <span class=\"s\">\"H = ~1d \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span>,<span class=\"nv\">H1<\/span><span class=\"p\">)<\/span>,\r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>,\r\n  <span class=\"nv\">lines<\/span>\r\n<span class=\"p\">)<\/span>$\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-7516\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Mbtosha07.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/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=\"\u554f\u984c-2\">\u554f\u984c 2<\/h3>\n<p>\u554f\u984c 1 \u3067\uff0c$H = 0$ \u306e\u5834\u5408\uff0c\u7a7a\u6c17\u62b5\u6297\u304c\u306a\u3044\u3068\u304d\uff0c\u3064\u307e\u308a $b=0$ \u306e\u3068\u304d\u306b\u306f $\\theta=45^{\\circ}$ \u306e\u3068\u304d\u306b\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u306b\u306a\u308b\u304c\uff0c\u3053\u306e\u307e\u307e\u3067\u306f <code>b=0<\/code> \u306e\u5834\u5408\u306e\u30b0\u30e9\u30d5\u3092\u8ffd\u52a0\u3057\u3088\u3046\u3068\u3059\u308b\u3068\u30a8\u30e9\u30fc\u306b\u306a\u308b\u306f\u305a\u3067\u3042\u308b\u3002<\/p>\n<p>\u305d\u306e\u539f\u56e0\u3092\u3064\u304d\u3068\u3081\uff0c\u6539\u5584\u3057\uff0c$b = 0, 0.5, 1.0, 1.5$ \u306e\u5834\u5408\u306e\u30b0\u30e9\u30d5\u3092\u307e\u3068\u3081\u3066\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<h3 id=\"\u554f\u984c-3\">\u554f\u984c 3<\/h3>\n<p>\u7a7a\u6c17\u62b5\u6297 $b = 0.5$ \u306e\u5834\u5408\u306e\u9ad8\u3055 $H$ \u304b\u3089\u306e\u659c\u65b9\u6295\u5c04\u306e\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u6700\u5927\u3068\u306a\u308b\u6253\u3061\u51fa\u3057\u89d2\u5ea6\u3068\uff0c\u305d\u306e\u3068\u304d\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\u304c\u308f\u304b\u308b\u3088\u3046\u306a\u30b0\u30e9\u30d5\u3092\u6b21\u306e $H$ \u306e\u5834\u5408\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u3066\u63cf\u3051\u3002<\/p>\n<p>$$ H = 0.0, 0.2, 0.4, 0.6, 0.8, 1.0$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u89e3\u7b54\u4f8b\">\u89e3\u7b54\u4f8b<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[17]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">Hl<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span><span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nv\">i<\/span><span class=\"o\">\/<\/span><span class=\"mi\">10<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">i<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">10<\/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[17]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{40}$}\\left[ 0.0 , 0.2 , 0.4 , 0.6 , 0.8 , 1.0 \\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[18]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">b1<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>5$\r\n\r\n<span class=\"cm\">\/* \u4e00\u6642\u7684\u306b6\u6841\u3067 thml \u3092\u8868\u793a\u3059\u308b\u3002*\/<\/span>\r\n<span class=\"nv\">fpprintprec<\/span><span class=\"o\">:<\/span> 6$\r\n<span class=\"nv\">thml<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nf\">thmax<\/span><span class=\"p\">(<\/span><span class=\"nv\">Hl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">i<\/span>, <span class=\"mi\">1<\/span>, <span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">Hl<\/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 output_prompt\">Out[18]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{43}$}\\left[ 39.4876 , 32.0487 , 26.956 , 23.1965 , 20.2851 , 17.9536 \\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[19]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5148\u306b\u63cf\u304f\u7dda\u3092\u30ea\u30b9\u30c8\u306b\u3057\u3066\u304a\u304f *\/<\/span>\r\n<span class=\"nv\">lines<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"p\">[<\/span><span class=\"nv\">color<\/span><span class=\"o\">=<\/span><span class=\"nv\">i<\/span>, \r\n   <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">printf<\/span><span class=\"p\">(<\/span><span class=\"no\">false<\/span>, \r\n                <span class=\"s\">\"H = ~,1f, \u03b8_{max} = ~,4f\u00b0, L_{max} = ~,4f\"<\/span>, \r\n                 <span class=\"nv\">Hl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>,    <span class=\"nv\">thml<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>,         <span class=\"nf\">L<\/span><span class=\"p\">(<\/span><span class=\"nv\">thml<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>,<span class=\"nv\">Hl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>,<span class=\"nv\">b1<\/span><span class=\"p\">))<\/span>,\r\n   <span class=\"nf\">parametric<\/span><span class=\"p\">(<\/span><span class=\"nf\">X<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">thml<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"nv\">T<\/span>, <span class=\"nv\">thml<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">Hl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">)<\/span>, \r\n              <span class=\"nv\">T<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"nv\">thml<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">Hl<\/span><span class=\"p\">[<\/span><span class=\"nv\">i<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">b1<\/span><span class=\"p\">))<\/span>\r\n  <span class=\"p\">]<\/span>, \r\n  <span class=\"nv\">i<\/span>, <span class=\"nf\">length<\/span><span class=\"p\">(<\/span><span class=\"nv\">Hl<\/span><span class=\"p\">)<\/span>, <span class=\"mi\">1<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">1<\/span>\r\n<span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4\u3002*\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">xy<\/span>,\r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 2<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 1<span class=\"o\">.<\/span>2<span class=\"p\">]<\/span>, <span class=\"nv\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>, \r\n  <span class=\"nv\">xtics<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.2<\/span>, <span class=\"nv\">ytics<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.2<\/span>,\r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"X\"<\/span>, <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Y\"<\/span>,\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">concat<\/span><span class=\"p\">(<\/span><span class=\"s\">\"\u7a7a\u6c17\u62b5\u6297 b = \"<\/span>, <span class=\"nv\">b1<\/span>,\r\n                 <span class=\"s\">\" \u306e\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u6700\u5927\u6c34\u5e73\u5230\u9054\u8ddd\u96e2\"<\/span><span class=\"p\">)<\/span>, \r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>,\r\n  <span class=\"nv\">lines<\/span>\r\n  ,<span class=\"nv\">file_name<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">Mbtosha08<\/span>,<span class=\"nv\">terminal<\/span> <span class=\"o\">=<\/span> <span class=\"o\">'<\/span><span class=\"nv\">svg<\/span>\r\n<span class=\"p\">)<\/span>$\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-7517\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Mbtosha08.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u7a7a\u6c17\u62b5\u6297\u304c\u3042\u308b\u5834\u5408\u306e\u659c\u65b9\u6295\u5c04\u306e\u8ecc\u9053\u3092\uff0cMaxima \u3092\u4f7f\u3063\u3066\u8abf\u3079\u308b\u3002<\/p>\n<p>\u8a73\u7d30\u306f\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8<\/p><p><a class=\"more-link btn\" 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