{"id":1699,"date":"2022-02-03T17:22:05","date_gmt":"2022-02-03T08:22:05","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=1699"},"modified":"2024-08-28T10:10:03","modified_gmt":"2024-08-28T01:10:03","slug":"%e8%a3%9c%e8%b6%b3%ef%bc%9amaxima%e3%81%a7%e8%a7%92%e5%be%84%e8%b7%9d%e9%9b%a2%e3%81%ae%e3%82%b0%e3%83%a9%e3%83%95%e3%82%92%e6%8f%8f%e3%81%8f","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e4%b8%80%e8%88%ac%e7%9b%b8%e5%af%be%e8%ab%96%e7%9a%84%e5%ae%87%e5%ae%99%e8%ab%96\/%e8%a7%92%e5%be%84%e8%b7%9d%e9%9b%a2\/%e8%a3%9c%e8%b6%b3%ef%bc%9amaxima%e3%81%a7%e8%a7%92%e5%be%84%e8%b7%9d%e9%9b%a2%e3%81%ae%e3%82%b0%e3%83%a9%e3%83%95%e3%82%92%e6%8f%8f%e3%81%8f\/","title":{"rendered":"\u88dc\u8db3\uff1aMaxima \u3067\u89d2\u5f84\u8ddd\u96e2\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f"},"content":{"rendered":"<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u89d2\u5f84\u8ddd\u96e2\u306e\u5c0e\u51fa\u306e\u8a73\u7d30\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u3092\u53c2\u7167\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e4%b8%80%e8%88%ac%e7%9b%b8%e5%af%be%e8%ab%96%e7%9a%84%e5%ae%87%e5%ae%99%e8%ab%96\/%e8%a7%92%e5%be%84%e8%b7%9d%e9%9b%a2\/\">\u89d2\u5f84\u8ddd\u96e2<\/a><\/li>\n<\/ul>\n<p>\u3053\u3053\u3067\u306f\uff0cMaxima \u306e <code>plot2d()<\/code> \u304a\u3088\u3073 <code>draw2d()<\/code> \u3092\u4f7f\u3063\u3066\u89d2\u5f84\u8ddd\u96e2\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3002<!--more--><\/p>\n<h3 id=\"$\\Omega_{\\Lambda}-=-0$-\u306e\u5834\u5408\u306e\u89d2\u5f84\u8ddd\u96e2\">$\\Omega_{\\Lambda} = 0$ \u306e\u5834\u5408\u306e\u89d2\u5f84\u8ddd\u96e2<\/h3>\n<p>\\begin{eqnarray}<br \/>\nd_A<br \/>\n&amp;=&amp; \\frac{2}{H_0 \\Omega_{\\rm m}^2 (1+z)^2} \\left\\{2 &#8211; \\Omega_{\\rm m} + \\Omega_{\\rm m} z &#8211; (2-\\Omega_{\\rm m}) \\sqrt{1 + \\Omega_{\\rm m} z}\\right\\}<br \/>\n\\end{eqnarray}<\/p>\n<p>\u4ee5\u4e0b\u3067\u306f $H_0$ \u3092\uff08$H_0 = 1$ \u3068\u3057\u3066\uff09\u7701\u7565\u3057\uff0c\u8868\u8a18\u306e\u90fd\u5408\u4e0a $\\Omega_{\\rm m} \\rightarrow \\Omega$<\/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\">dA<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span>, <span class=\"nv\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> 2<span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"o\">**<\/span>2<span class=\"o\">*<\/span><span class=\"p\">(<\/span>1<span class=\"o\">+<\/span><span class=\"nv\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> \r\n             <span class=\"p\">(<\/span>2<span class=\"o\">-<\/span><span class=\"nv\">Omega<\/span><span class=\"o\">+<\/span> <span class=\"nv\">Omega<\/span><span class=\"o\">*<\/span><span class=\"nv\">z<\/span> <span class=\"o\">-<\/span> <span class=\"p\">(<\/span>2<span class=\"o\">-<\/span><span class=\"nv\">Omega<\/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\">Omega<\/span><span class=\"o\">*<\/span><span class=\"nv\">z<\/span><span class=\"p\">))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[1]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{1}$}{\\it dA}\\left(\\Omega , z\\right):=\\frac{2}{\\Omega^2\\,\\left(1+z\\right)^2}\\,\\left(2-\\Omega+\\Omega\\,z+\\left(-\\left(2-\\Omega\\right)\\right)\\,\\sqrt{1+\\Omega\\,z}\\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=\"$\\Omega_{\\rm-m}-+-\\Omega_{\\Lambda}-=-1$-\u306e\u5834\u5408\u306e\u89d2\u5f84\u8ddd\u96e2\">$\\Omega_{\\rm m} + \\Omega_{\\Lambda} = 1$ \u306e\u5834\u5408\u306e\u89d2\u5f84\u8ddd\u96e2<\/h3>\n<p>\\begin{eqnarray}<br \/>\nd_A<br \/>\n&amp;=&amp; \\frac{1}{H_0 (1+z)} \\int_0^z \\frac{dz}{\\sqrt{(1-\\Omega_{\\rm m}) + \\Omega_{\\rm m} (1+z)^3} }<br \/>\n\\end{eqnarray}<\/p>\n<p>\u89e3\u6790\u7684\u306b\u306f\u7a4d\u5206\u3067\u304d\u306a\u3044\u306e\u3067\uff0c\u6570\u5024\u7a4d\u5206 <code>romberg()<\/code> \u3092\u4f7f\u3063\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[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u88ab\u7a4d\u5206\u95a2\u6570\u306e\u5b9a\u7fa9 *\/<\/span>\r\n<span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span>, <span class=\"nv\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> 1<span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">((<\/span>1<span class=\"o\">-<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">Omega<\/span><span class=\"o\">*<\/span><span class=\"p\">(<\/span>1<span class=\"o\">+<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[2]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{2}$}f\\left(\\Omega , z\\right):=\\frac{1}{\\sqrt{1-\\Omega+\\Omega\\,\\left(1+x\\right)^3}}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">dAL1<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span>, <span class=\"nv\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> 1<span class=\"o\">\/<\/span><span class=\"p\">(<\/span>1<span class=\"o\">+<\/span><span class=\"nv\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"nf\">romberg<\/span><span class=\"p\">(<\/span><span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span>, <span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">z<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[3]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{3}$}{\\it dAL}_{1}\\left(\\Omega , z\\right):=\\frac{1}{1+z}\\,{\\it romberg}\\left(f\\left(\\Omega , x\\right) , x , 0 , z\\right)\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><code>quad_qags()<\/code> \u3067\u6570\u5024\u7a4d\u5206\u3059\u308b\u95a2\u6570\u3082\u5b9a\u7fa9\u3057\u3066\u304a\u304f\u3002<code>quad_qags()<\/code> \u306f4\u3064\u306e\u8981\u7d20<\/p>\n<p><code>[\u7a4d\u5206\u306e\u8fd1\u4f3c\u5024, \u8fd1\u4f3c\u306e\u7d76\u5bfe\u8aa4\u5dee, \u88ab\u7a4d\u5206\u95a2\u6570\u306e\u8a55\u4fa1\u6570, \u30a8\u30e9\u30fc\u30b3\u30fc\u30c9]<\/code><\/p>\n<p>\u304b\u3089\u306a\u308b\u30ea\u30b9\u30c8\u3092\u8fd4\u3059\u306e\u3067\uff0c\u7a4d\u5206\u8fd1\u4f3c\u5024\u306e\u307f\u3092\u51fa\u529b\u3055\u305b\u305f\u3044\u5834\u5408\u306b\u306f <code>[1]<\/code> \u3092\u3064\u3051\u3066\u30ea\u30b9\u30c8\u306e1\u756a\u76ee\u306e\u8981\u7d20\u306e\u307f\u3092\u51fa\u529b\u3059\u308b\u3088\u3046\u306b\u6307\u5b9a\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">dAL2<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span>, <span class=\"nv\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"p\">((<\/span>1<span class=\"o\">\/<\/span><span class=\"p\">(<\/span>1<span class=\"o\">+<\/span><span class=\"nv\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"nf\">quad_qags<\/span><span class=\"p\">(<\/span><span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span>, <span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">z<\/span><span class=\"p\">))[<\/span>1<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[4]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{4}$}{\\it dAL}_{2}\\left(\\Omega , z\\right):=\\left(\\frac{1}{1+z}\\,{\\it quad\\_qags}\\left(f\\left(\\Omega , x\\right) , x , 0 , z\\right)\\right)_{1}\\]<\/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>\u6570\u5024\u7a4d\u5206\u306e\u7cbe\u5ea6\u3092\u78ba\u8a8d\u3059\u308b\u305f\u3081\u306b\uff0c$\\Omega_m = 0.3, \\ z = 1$ \u306e\u5834\u5408\u306e $d_A$ \u306e\u5024\u3092\u51fa\u529b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">dAL1<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>;\r\n<span class=\"nf\">dAL2<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[5]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{5}$}0.3857136140379442\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[5]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{6}$}0.3857135332139056\\]<\/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>romberg()<\/code> \u3068 <code>quad_qags()<\/code> \u3067\u6570\u5024\u7a4d\u5206\u306e\u5024\u304c\u5fae\u5999\u306b\u7570\u306a\u308b\u306e\u306f\uff0c<code>romberg()<\/code> \u306e\u7cbe\u5ea6\u3092\u8a2d\u5b9a\u3059\u308b\u30d1\u30e9\u30e1\u30fc\u30bf <code>rombergtol<\/code> \u306e\u30c7\u30d5\u30a9\u30eb\u30c8\u5024\u304c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5c11\u3057\u5927\u304d\u3081\u3067\u3042\u308b\u3053\u3068\u306b\u3088\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">rombergtol<\/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[6]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{7}$}1.0 \\times 10^{-4}\\]<\/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>\u30d1\u30e9\u30e1\u30fc\u30bf <code>rombergtol<\/code> \u3092\uff0c\u3088\u308a\u5c0f\u3055\u3044\u5024\uff08\u4f8b\u3048\u3070 <code>rombergtol<\/code> $= 1.0\\times 10^{-10}$\uff09\u306b\u5909\u66f4\u3057\u3066\u307f\u308b\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[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">rombergtol<\/span><span class=\"o\">:<\/span> <span class=\"mf\">1.e-10<\/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{${\\it \\%o}_{8}$}1.0 \\times 10^{-10}\\]<\/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\">dAL1<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>;\r\n<span class=\"nf\">dAL2<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span>, <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[8]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{9}$}0.3857135332139057\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[8]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{10}$}0.3857135332139056\\]<\/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=\"plot2d()-\u3067\u30b0\u30e9\u30d5\u3092\u63cf\u304f\"><code>plot2d()<\/code> \u3067\u30b0\u30e9\u30d5\u3092\u63cf\u304f<\/h3>\n<p>\u4e0a\u8a18\u306e\u3088\u3046\u306b\u6570\u5024\u7a4d\u5206\u3092\u4f7f\u3063\u3066\u5b9a\u7fa9\u3057\u305f\u95a2\u6570 <code>dAL2(Omega, z)<\/code> \u3092\u76f4\u63a5<\/p>\n<div class=\"highlight\">\n<pre><span class=\"nf\">plot2d<\/span><span class=\"p\">(<\/span><span class=\"nf\">dAL2<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span>, <span class=\"nv\">z<\/span><span class=\"p\">)<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">z<\/span>, <span class=\"mi\">0<\/span>, 5<span class=\"p\">])<\/span>$\r\n<\/pre>\n<\/div>\n<p>\u306e\u3088\u3046\u306b\u3057\u3066\u30b0\u30e9\u30d5\u3092\u63cf\u3053\u3046\u3068\u3059\u308b\u3068\uff0c\u30a8\u30e9\u30fc\u3068\u306a\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">plot2d<\/span><span class=\"p\">(<\/span><span class=\"nf\">dAL2<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span>, <span class=\"nv\">z<\/span><span class=\"p\">)<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">z<\/span>, <span class=\"mi\">0<\/span>, 5<span class=\"p\">])<\/span>$\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>plot2d: expression (quad_qags(1\/sqrt(0.3*(x+1)^3+0.7),x,0,z,epsrel = 1.0e-8,\r\n                              epsabs = 0.0,limit = 200)\r\n                    \/(z+1))[\r\n                    1]\r\n\r\n    should  depend only on z, or be an expression of 2 variables\r\n    equal another expression of the same variables.\r\n\r\n\r\n -- an error. To debug this try: debugmode(true);\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>\u305d\u3053\u3067\uff0c\u6b21\u5584\u306e\u7b56\u3068\u3057\u3066\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u6570\u5024\u30ea\u30b9\u30c8\u3092\u4f5c\u308a\uff0c\u6570\u5024\u30c7\u30fc\u30bf\u3068\u3057\u3066 <code>[discrete, listdAL2(0.3)]<\/code> \u3067\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[10]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* z = 0 ~ 20 \u307e\u3067\u306e\u30ea\u30b9\u30c8\u3092\u4f5c\u308b\u95a2\u6570\u3002*\/<\/span>\r\n\r\n<span class=\"nf\">listdAL2<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span> <span class=\"o\">:=<\/span> \r\n    <span class=\"nf\">makelist<\/span><span class=\"p\">([<\/span><span class=\"nv\">i<\/span><span class=\"o\">*<\/span><span class=\"mf\">0.1<\/span>, <span class=\"nf\">dAL2<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span>,<span class=\"nv\">i<\/span><span class=\"o\">*<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">)]<\/span>, <span class=\"nv\">i<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">200<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[11]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">plot2d<\/span><span class=\"p\">([[<\/span><span class=\"nv\">discrete<\/span>, <span class=\"nf\">listdAL2<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span><span class=\"p\">)]<\/span>, \r\n        <span class=\"nf\">dA<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span>, <span class=\"nv\">z<\/span><span class=\"p\">)<\/span>, \r\n        <span class=\"nf\">dA<\/span><span class=\"p\">(<\/span><span class=\"mf\">1.0<\/span>, <span class=\"nv\">z<\/span><span class=\"p\">)]<\/span>, \r\n       <span class=\"p\">[<\/span><span class=\"nv\">z<\/span>, <span class=\"mi\">0<\/span>, 5<span class=\"p\">]<\/span>, \r\n       \r\n       <span class=\"cm\">\/* \u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n       <span class=\"p\">[<\/span><span class=\"nv\">y<\/span>, <span class=\"mi\">0<\/span>, 0<span class=\"o\">.<\/span>6<span class=\"p\">]<\/span>,                         \r\n\r\n       <span class=\"cm\">\/* \u5404\u66f2\u7dda\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\uff1a\u8272\uff0c\u7dda\u306e\u592a\u3055\uff0c\u51e1\u4f8b\u3002 *\/<\/span>\r\n       <span class=\"p\">[<\/span><span class=\"nv\">color<\/span>, <span class=\"nv\">blue<\/span>, \r\n               <span class=\"nv\">red<\/span>, \r\n               <span class=\"nv\">black<\/span><span class=\"p\">]<\/span>,                 \r\n       <span class=\"p\">[<\/span><span class=\"nv\">style<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">lines<\/span>, 2<span class=\"p\">]<\/span>, \r\n               <span class=\"p\">[<\/span><span class=\"nv\">lines<\/span>, 2<span class=\"p\">]<\/span>, \r\n               <span class=\"p\">[<\/span><span class=\"nv\">lines<\/span>, 3<span class=\"p\">]]<\/span>,         \r\n       <span class=\"p\">[<\/span><span class=\"nv\">legend<\/span>, <span class=\"s\">\"\u03a9_m =0.3,  \u03a9_\u039b =0.7\"<\/span>, \r\n                <span class=\"s\">\"\u03a9_m =0.3,  \u03a9_\u039b =0\"<\/span>, \r\n                <span class=\"s\">\"\u03a9_m =1,     \u03a9_\u039b =0\"<\/span><span class=\"p\">]<\/span>, \r\n\r\n       <span class=\"p\">[<\/span><span class=\"nv\">xlabel<\/span>, <span class=\"s\">\"z\"<\/span><span class=\"p\">]<\/span>, \r\n       <span class=\"p\">[<\/span><span class=\"nv\">ylabel<\/span>, <span class=\"s\">\"H_0 d_A(z)\"<\/span><span class=\"p\">]<\/span>, \r\n       <span class=\"p\">[<\/span><span class=\"nv\">title<\/span>, <span class=\"s\">\"\u89d2\u5f84\u8ddd\u96e2\"<\/span><span class=\"p\">]<\/span>, \r\n       \r\n       <span class=\"cm\">\/* \u51e1\u4f8b\u4f4d\u7f6e\u306f gnuplot \u6d41\u306b\u8a2d\u5b9a\u3002*\/<\/span>\r\n       <span class=\"p\">[<\/span><span class=\"nv\">gnuplot_preamble<\/span>, <span class=\"s\">\"set key Left reverse;\"<\/span><span class=\"p\">]<\/span>,\r\n       <span class=\"cm\">\/* \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba\u8a2d\u5b9a *\/<\/span>\r\n       <span class=\"p\">[<\/span><span class=\"nv\">gnuplot_svg_term_command<\/span>, <span class=\"s\">\"set term svg size 640,480 font \\\",14\\\"\"<\/span><span class=\"p\">]<\/span>,\r\n       <span class=\"cm\">\/* \u30b0\u30ea\u30c3\u30c9 *\/<\/span>\r\n        <span class=\"nv\">grid2d<\/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-9361\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/dA-Fig1-1-640x480.png\" alt=\"\" width=\"640\" height=\"480\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/dA-Fig1-1-640x480.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/dA-Fig1-1-300x225.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/dA-Fig1-1-750x563.png 750w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/dA-Fig1-1.png 1280w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/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=\"draw2d()-\u3067\u30b0\u30e9\u30d5\u3092\u63cf\u304f\"><code>draw2d()<\/code> \u3067\u30b0\u30e9\u30d5\u3092\u63cf\u304f<\/h3>\n<p>\u4ee5\u4e0b\u3067\u306f\uff0cMaxima \u306e <code>draw2d()<\/code> \u3092\u4f7f\u3063\u3066\u3082\u3046\u5c11\u3057 $z$ \u306e\u5927\u304d\u3044\u3068\u3053\u308d\u307e\u3067\u63cf\u3044\u3066\u307f\u308b\u3002<\/p>\n<p><code>draw2d()<\/code> \u3067\u306f\uff0c\u6570\u5024\u7a4d\u5206\u3067\u5b9a\u7fa9\u3057\u305f\u95a2\u6570 <code>dAL2(Omega, z)<\/code> \u3082\u6587\u53e5\u3092\u8a00\u308f\u308c\u308b\u3053\u3068\u306a\u304f\u76f4\u63a5<\/p>\n<div class=\"highlight\">\n<pre><span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span><span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">dAL2<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span>, <span class=\"nv\">z<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">z<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">20<\/span><span class=\"p\">))<\/span>$\r\n<\/pre>\n<\/div>\n<p>\u3067\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\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[12]:<\/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\">dimensions<\/span><span class=\"o\">=<\/span><span class=\"p\">[<\/span><span class=\"mi\">640<\/span>, 480<span class=\"p\">]<\/span>, <span class=\"cm\">\/* \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba\u306f\u4efb\u610f\u3067 *\/<\/span>\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"\u89d2\u5f84\u8ddd\u96e2\"<\/span>, \r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/Times z}\"<\/span>, \r\n  <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/Times H_0\\  d_A(z)}\"<\/span>,   \r\n\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>, 20<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>6<span class=\"p\">]<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u51e1\u4f8b\u4f4d\u7f6e\u7b49\u306f gnuplot \u6d41\u306b\u8a2d\u5b9a\u3002*\/<\/span>\r\n  <span class=\"nv\">user_preamble<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"s\">\"set key Left reverse;<\/span>\r\n<span class=\"s\">                    set xtics mirror; <\/span>\r\n<span class=\"s\">                    set ytics mirror;<\/span>\r\n<span class=\"s\">                    set mxtics 5; <\/span>\r\n<span class=\"s\">                    set grid;\"<\/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=\"s\">\"{\/Times \u03a9_m = 0.3,    \u03a9_\u039b= 0.7}\"<\/span>, \r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">blue<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">dAL2<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span>, <span class=\"nv\">z<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">z<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">20<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/Times \u03a9_m = 0.3,    \u03a9_\u039b= 0}\"<\/span>, \r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">red<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">dA<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span>, <span class=\"nv\">z<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">z<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">20<\/span><span class=\"p\">)<\/span>, \r\n  \r\n  <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/Times \u03a9_m = 1,       \u03a9_\u039b= 0}\"<\/span>, \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\">3<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">dA<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span>, <span class=\"nv\">z<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">z<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">20<\/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-9362\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/dA-Fig2-1-640x480.png\" alt=\"\" width=\"640\" height=\"480\" srcset=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/dA-Fig2-1-640x480.png 640w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/dA-Fig2-1-300x225.png 300w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/dA-Fig2-1-750x563.png 750w, https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/dA-Fig2-1.png 1280w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/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=\"$z-\\gg-1$-\u3067\u306e\u6f38\u8fd1\u5f62\">$z \\gg 1$ \u3067\u306e\u6f38\u8fd1\u5f62<\/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<h4 id=\"$\\Omega_{\\Lambda}-=-0$-\u306e\u5834\u5408\">$\\Omega_{\\Lambda} = 0$ \u306e\u5834\u5408<\/h4>\n<p>\\begin{eqnarray}<br \/>\nd_A<br \/>\n&amp;=&amp; \\frac{2}{H_0 \\Omega_{\\rm m}^2 (1+z)^2} \\left\\{2 &#8211; \\Omega_{\\rm m} + \\Omega_{\\rm m} z &#8211; (2-\\Omega_{\\rm m}) \\sqrt{1 + \\Omega_{\\rm m} z}\\right\\} \\\\<br \/>\n&amp;\\sim&amp; \\frac{2}{H_0 \\Omega_{\\rm m}^2 z^2} \\left\\{\\Omega_{\\rm m} z \\right\\} \\\\<br \/>\n&amp;=&amp; \\frac{2}{H_0\\, \\Omega_{\\rm m}\\, z}<br \/>\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"$\\Omega_{\\rm-m}-+-\\Omega_{\\Lambda}-=-1$-\u306e\u5834\u5408\">$\\Omega_{\\rm m} + \\Omega_{\\Lambda} = 1$ \u306e\u5834\u5408<\/h4>\n<p>\u7a4d\u5206\u90e8\u5206\u3092\u3044\u3063\u305f\u3093 $\\displaystyle t = \\frac{1}{1+z}, \\ dt = &#8211; \\frac{dz}{(1+z)^2}$ \u3068\u3057\u3066<\/p>\n<p>\\begin{eqnarray}<br \/>\nd_A<br \/>\n&amp;=&amp; \\frac{1}{H_0 (1+z)} \\int_0^z \\frac{dz}{\\sqrt{(1-\\Omega_{\\rm m}) + \\Omega_{\\rm m} (1+z)^3} } \\\\<br \/>\n&amp;=&amp; \\frac{1}{H_0 (1+z)} \\int_0^z<br \/>\n\\frac{dz}{(1+z)^2 \\sqrt{\\frac{\\Omega_{\\rm m}}{1+z} + \\frac{1-\\Omega_{\\rm m}}{(1+z)^4}} } \\\\<br \/>\n&amp;\\sim&amp; \\frac{1}{H_0 (1+z)} \\int_{\\frac{1}{1+z}}^1<br \/>\n\\frac{dt}{\\sqrt{\\Omega_{\\rm m} t}} \\\\<br \/>\n&amp;=&amp; \\frac{1}{H_0 (1+z)\\sqrt{\\Omega_{\\rm m}}} \\Bigl[2\\sqrt{t} \\Bigr]_{\\frac{1}{1+z}}^1 \\\\<br \/>\n&amp;\\sim&amp; \\frac{2}{H_0\\, \\sqrt{\\Omega_{\\rm m}}\\,z }<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066 $0 &lt; \\Omega_{\\rm m} &lt; 1$ \u306e\u5834\u5408\uff0c$z &lt; 1$ \u3067\u306f\u5b87\u5b99\u5b9a\u6570\u304c\u3042\u308b\u5834\u5408\u306e\u89d2\u5f84\u8ddd\u96e2\u304c\u5927\u304d\u3044\u5024\u3092\u51fa\u3059\u306b\u3082\u304b\u304b\u308f\u3089\u305a\uff0c$z \\gg 1$ \u3067\u306f\u5b87\u5b99\u5b9a\u6570\u304c\u3042\u308b\u5834\u5408\u306e\u307b\u3046\u304c\u89d2\u5f84\u8ddd\u96e2\u306f\u5c0f\u3055\u304f\u306a\u308b\u3002\u306a\u305c\u306a\u3089\uff0c<\/p>\n<p>$$ \\frac{1}{\\sqrt{\\Omega_{\\rm m}}} &lt; \\frac{1}{\\Omega_{\\rm m}}\\quad \\mbox{for}\\quad<br \/>\n0 &lt; \\Omega_{\\rm m} &lt; 1$$<\/p>\n<p>\u3067\u3042\u308b\u304b\u3089\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u89d2\u5f84\u8ddd\u96e2\u306e\u5c0e\u51fa\u306e\u8a73\u7d30\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u3092\u53c2\u7167\u3002<\/p>\n<ul>\n<li>\u89d2\u5f84\u8ddd\u96e2<\/li>\n<\/ul>\n<p>\u3053\u3053\u3067\u306f\uff0cMaxima \u306e plot2d() \u304a\u3088\u3073 draw2d() \u3092\u4f7f\u3063\u3066\u89d2\u5f84\u8ddd\u96e2\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e4%b8%80%e8%88%ac%e7%9b%b8%e5%af%be%e8%ab%96%e7%9a%84%e5%ae%87%e5%ae%99%e8%ab%96\/%e8%a7%92%e5%be%84%e8%b7%9d%e9%9b%a2\/%e8%a3%9c%e8%b6%b3%ef%bc%9amaxima%e3%81%a7%e8%a7%92%e5%be%84%e8%b7%9d%e9%9b%a2%e3%81%ae%e3%82%b0%e3%83%a9%e3%83%95%e3%82%92%e6%8f%8f%e3%81%8f\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":1551,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-1699","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\/1699","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=1699"}],"version-history":[{"count":11,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1699\/revisions"}],"predecessor-version":[{"id":9363,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1699\/revisions\/9363"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1551"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=1699"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}