{"id":5306,"date":"2023-02-03T12:04:36","date_gmt":"2023-02-03T03:04:36","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=5306"},"modified":"2023-02-03T12:04:36","modified_gmt":"2023-02-03T03:04:36","slug":"%e8%a3%9c%e8%b6%b3%ef%bc%9amaxima-%e3%81%a7%e5%ae%87%e5%ae%99%e5%b9%b4%e9%bd%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\/%e5%ae%87%e5%ae%99%e8%ab%96%e3%83%91%e3%83%a9%e3%83%a1%e3%83%bc%e3%82%bf%e3%81%a8%e5%ae%87%e5%ae%99%e5%b9%b4%e9%bd%a2\/%e8%a3%9c%e8%b6%b3%ef%bc%9amaxima-%e3%81%a7%e5%ae%87%e5%ae%99%e5%b9%b4%e9%bd%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\u5b87\u5b99\u5e74\u9f62\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>\u5b87\u5b99\u5e74\u9f62\u306e\u8868\u5f0f\u306e\u5c0e\u51fa\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\/%e5%ae%87%e5%ae%99%e8%ab%96%e3%83%91%e3%83%a9%e3%83%a1%e3%83%bc%e3%82%bf%e3%81%a8%e5%ae%87%e5%ae%99%e5%b9%b4%e9%bd%a2\/\">\u5b87\u5b99\u8ad6\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u5b87\u5b99\u5e74\u9f62<\/a><\/li>\n<\/ul>\n<p>\u3053\u3053\u3067\u306f\uff0cMaxima \u3092\u4f7f\u3063\u3066\u5b87\u5b99\u5e74\u9f62\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u3044\u3066\u307f\u308b\u3002<\/p>\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=\"$\\Omega_{\\Lambda}-=-0$-\u306e\u5834\u5408\">$\\Omega_{\\Lambda} = 0$ \u306e\u5834\u5408<\/h3>\n<p>$$H_0 t_0 = -\\frac{1}{\\Omega_{\\rm m} -1}+\\frac{\\Omega_{\\rm m}}{(\\Omega_{\\rm m}-1)^{\\frac{3}{2}} }<br \/>\n\\tan^{-1}\\sqrt{\\Omega_{\\rm m}-1} \\quad \\mbox{for}\\ \\ \\Omega_{\\rm m} &gt; 1$$$$H_0 t_0 = \\frac{1}{1-\\Omega_{\\rm m}}-\\frac{\\Omega_{\\rm m}}{(1-\\Omega_{\\rm m})^{\\frac{3}{2}} }<br \/>\n\\tanh^{-1}\\sqrt{1-\\Omega_{\\rm m}} \\quad \\mbox{for}\\ \\ \\Omega_{\\rm m} &lt; 1$$<\/p>\n<p>$\\Omega_{\\rm m} \\rightarrow \\Omega$ \u3068\u3057\u3066&#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[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* Omega &gt; 1 *\/<\/span>\r\n<span class=\"nf\">t1<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"o\">-<\/span>1<span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">Omega<\/span><span class=\"o\">\/<\/span><span class=\"p\">((<\/span><span class=\"nv\">Omega<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">atan<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span>;\r\n<span class=\"cm\">\/* Omega &lt; 1 *\/<\/span>\r\n<span class=\"nf\">t2<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/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\">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\">Omega<\/span><span class=\"p\">)<\/span><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=\"nf\">atanh<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span>1<span class=\"o\">-<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">))<\/span>;\r\n<span class=\"cm\">\/* Omega = 1 *\/<\/span>\r\n<span class=\"nf\">t0<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> 2<span class=\"o\">\/<\/span><span class=\"mi\">3<\/span>;\r\n\r\n<span class=\"nf\">t<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"k\">if<\/span> <span class=\"nv\">Omega<\/span> <span class=\"o\">&gt;<\/span> <span class=\"mi\">1<\/span> <span class=\"k\">then<\/span> <span class=\"nf\">t1<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span> <span class=\"k\">elseif<\/span> <span class=\"nv\">Omega<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span> <span class=\"k\">then<\/span> <span class=\"nf\">t0<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span> <span class=\"k\">else<\/span> <span class=\"nf\">t2<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/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{${\\it \\%o}_{1}$}t_{1}\\left(\\Omega\\right):=\\frac{-1}{\\Omega-1}+\\frac{\\Omega}{\\left(\\Omega-1\\right)\\,\\sqrt{\\Omega-1}}\\,\\arctan \\sqrt{\\Omega-1}\\]<\/div>\n<\/div>\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{${\\it \\%o}_{2}$}t_{2}\\left(\\Omega\\right):=\\frac{1}{1-\\Omega}-\\frac{\\Omega}{\\left(1-\\Omega\\right)\\,\\sqrt{1-\\Omega}}\\,{\\rm atanh}\\; \\sqrt{1-\\Omega}\\]<\/div>\n<\/div>\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{${\\it \\%o}_{3}$}t_{0}\\left(\\Omega\\right):=\\frac{2}{3}\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[1]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{4}$}t\\left(\\Omega\\right):=\\mathbf{if}\\;\\Omega&gt;1\\;\\mathbf{then}\\;t_{1}\\left(\\Omega\\right)\\;\\mathbf{elseif}\\;\\Omega=1\\;\\mathbf{then}\\;t_{0}\\left(\\Omega\\right)\\;\\mathbf{else}\\;t_{2}\\left(\\Omega\\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=\"$k-=-0$-\u306e\u5834\u5408\">$k = 0$ \u306e\u5834\u5408<\/h3>\n<p>$$H_0 t_0 = \\frac{2}{3\\sqrt{\\Omega_{\\rm m} -1}}\\tan^{-1} \\sqrt{\\Omega_{\\rm m} -1} \\quad \\mbox{for}\\ \\ \\Omega_{\\rm m} &gt; 1$$$$H_0 t_0 = \\frac{2}{3\\sqrt{1-\\Omega_{\\rm m} }}\\tanh^{-1} \\sqrt{1-\\Omega_{\\rm m} } \\quad \\mbox{for}\\ \\ \\Omega_{\\rm m} &lt; 1$$<\/p>\n<p>$\\Omega_{\\rm m} \\rightarrow \\Omega$ \u3068\u3057\u3066&#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[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* Omega &gt; 1 *\/<\/span>\r\n<span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> 2<span class=\"o\">\/<\/span><span class=\"p\">(<\/span>3<span class=\"o\">*<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">atan<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span>;\r\n<span class=\"cm\">\/* Omega &lt; 1 *\/<\/span>\r\n<span class=\"nf\">T2<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> 2<span class=\"o\">\/<\/span><span class=\"p\">(<\/span>3<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=\"nf\">atanh<\/span><span class=\"p\">(<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span>1<span class=\"o\">-<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">))<\/span>;\r\n\r\n<span class=\"nf\">T<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"k\">if<\/span> <span class=\"nv\">Omega<\/span> <span class=\"o\">&gt;<\/span> <span class=\"mi\">1<\/span> <span class=\"k\">then<\/span> <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span> <span class=\"k\">elseif<\/span> <span class=\"nv\">Omega<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span> <span class=\"k\">then<\/span> <span class=\"nf\">t0<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span> <span class=\"k\">else<\/span> <span class=\"nf\">T2<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/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{${\\it \\%o}_{5}$}T_{1}\\left(\\Omega\\right):=\\frac{2}{3\\,\\sqrt{\\Omega-1}}\\,\\arctan \\sqrt{\\Omega-1}\\]<\/div>\n<\/div>\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{${\\it \\%o}_{6}$}T_{2}\\left(\\Omega\\right):=\\frac{2}{3\\,\\sqrt{1-\\Omega}}\\,{\\rm atanh}\\; \\sqrt{1-\\Omega}\\]<\/div>\n<\/div>\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{${\\it \\%o}_{7}$}T\\left(\\Omega\\right):=\\mathbf{if}\\;\\Omega&gt;1\\;\\mathbf{then}\\;T_{1}\\left(\\Omega\\right)\\;\\mathbf{elseif}\\;\\Omega=1\\;\\mathbf{then}\\;t_{0}\\left(\\Omega\\right)\\;\\mathbf{else}\\;T_{2}\\left(\\Omega\\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=\"plot2d()-\u3067\u63cf\u304f\u4f8b\"><code>plot2d()<\/code> \u3067\u63cf\u304f\u4f8b<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/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>\r\n  <span class=\"p\">[<\/span><span class=\"nf\">T<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">t<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)]<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">Omega<\/span>, <span class=\"mf\">0.01<\/span>, 2<span class=\"p\">]<\/span>, \r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"p\">[<\/span><span class=\"nv\">y<\/span>, <span class=\"mf\">0.5<\/span>, 1<span class=\"o\">.<\/span>5<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><span class=\"nv\">gnuplot_preamble<\/span>, <span class=\"s\">\"set xtics 0.2; set mxtics 2;<\/span>\r\n<span class=\"s\">                      set ytics 0.1; set mytics 2;\"<\/span><span class=\"p\">]<\/span>,\r\n  \r\n  <span class=\"cm\">\/* \u51e1\u4f8b *\/<\/span>\r\n  <span class=\"p\">[<\/span><span class=\"nv\">legend<\/span>, <span class=\"s\">\"\u03a9_\u039b = 1 - \u03a9_m\"<\/span>, <span class=\"s\">\"\u03a9_\u039b = 0\"<\/span><span class=\"p\">]<\/span>, \r\n  <span class=\"cm\">\/* \u7dda\u306e\u592a\u3055\u3068\u8272 *\/<\/span>\r\n  <span class=\"p\">[<\/span><span class=\"nv\">style<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">lines<\/span>, <span class=\"mi\">2<\/span>, <span class=\"nv\">red<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">lines<\/span>, <span class=\"mi\">2<\/span>, <span class=\"nv\">black<\/span><span class=\"p\">]]<\/span>, \r\n  <span class=\"cm\">\/* \u5ea7\u6a19\u8ef8\u306e\u30e9\u30d9\u30eb *\/<\/span>\r\n  <span class=\"p\">[<\/span><span class=\"nv\">xlabel<\/span>, <span class=\"s\">\"\u03a9_m\"<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">ylabel<\/span>, <span class=\"s\">\"H_0 t_0\"<\/span><span class=\"p\">]<\/span>, \r\n  <span class=\"cm\">\/* \u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb *\/<\/span>\r\n  <span class=\"p\">[<\/span><span class=\"nv\">title<\/span>, <span class=\"s\">\"\u5b87\u5b99\u5e74\u9f62\u306e\u5bc6\u5ea6\u30d1\u30e9\u30e1\u30fc\u30bf\u4f9d\u5b58\u6027\"<\/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-full wp-image-5307\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/mpt-fig1.svg\" alt=\"\" width=\"600\" height=\"480\" \/><\/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\u63cf\u304f\u4f8b\"><code>draw2d()<\/code> \u3067\u63cf\u304f\u4f8b<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">font<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"Arial\"<\/span>, <span class=\"nv\">font_size<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">14<\/span>, \r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/=16 \u5b87\u5b99\u5e74\u9f62\u306e\u5bc6\u5ea6\u30d1\u30e9\u30e1\u30fc\u30bf\u4f9d\u5b58\u6027}\"<\/span>, \r\n  <span class=\"nv\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/Times=16 \u03a9_m}\"<\/span>, \r\n  <span class=\"nv\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/jsMath-cmti10=16 H}_0 {\/jsMath-cmti10=16 t}_0\"<\/span>, \r\n  <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mf\">0.5<\/span>, 1<span class=\"o\">.<\/span>5<span class=\"p\">]<\/span>,\r\n  <span class=\"nv\">user_preamble<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"set xtics 0.2; set mxtics 2; <\/span>\r\n<span class=\"s\">                   set ytics 0.1; set mytics 2;<\/span>\r\n<span class=\"s\">                   set xtics mirror; set ytics mirror; set grid;\"<\/span>,\r\n\r\n  \r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>, \r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"red\"<\/span>, <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/Times=16 \u03a9_\u039b = 1 - \u03a9_m}\"<\/span>,\r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">T<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">Omega<\/span>, <span class=\"mf\">0.01<\/span>, <span class=\"mi\">2<\/span><span class=\"p\">)<\/span>, \r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"black\"<\/span>, <span class=\"nv\">key<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/Times=16 \u03a9_\u039b = 0}\"<\/span>, \r\n  <span class=\"nf\">explicit<\/span><span class=\"p\">(<\/span><span class=\"nf\">t<\/span><span class=\"p\">(<\/span><span class=\"nv\">Omega<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">Omega<\/span>, <span class=\"mf\">0.01<\/span>, <span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div 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-full wp-image-5308\" 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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\/%e5%ae%87%e5%ae%99%e8%ab%96%e3%83%91%e3%83%a9%e3%83%a1%e3%83%bc%e3%82%bf%e3%81%a8%e5%ae%87%e5%ae%99%e5%b9%b4%e9%bd%a2\/%e8%a3%9c%e8%b6%b3%ef%bc%9amaxima-%e3%81%a7%e5%ae%87%e5%ae%99%e5%b9%b4%e9%bd%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":1483,"menu_order":22,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-5306","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.0.1 - aioseo.com -->\n\t<meta name=\"description\" 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