{"id":7536,"date":"2024-02-04T10:10:04","date_gmt":"2024-02-04T01:10:04","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=7536"},"modified":"2024-03-27T13:08:03","modified_gmt":"2024-03-27T04:08:03","slug":"%e8%a3%9c%e8%b6%b3%ef%bc%9asympy-%e3%81%a8-spb-%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%9asympy-%e3%81%a8-spb-%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\uff1aSymPy \u3068 SPB \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\uff0cPython \u306e <a href=\"https:\/\/sympy-plot-backends.readthedocs.io\/en\/latest\/overview.html\">SymPy Plotting Backends<\/a> \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 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-ipython3\">\n<pre><span class=\"kn\">from<\/span> <span class=\"nn\">sympy<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">sympy.abc<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n<span class=\"c1\"># \u865a\u6570\u5358\u4f4d\uff0c\u5186\u5468\u7387\uff0c\u30cd\u30a4\u30d4\u30a2\u6570<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">sympy<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">I<\/span><span class=\"p\">,<\/span> <span class=\"n\">pi<\/span><span class=\"p\">,<\/span> <span class=\"n\">E<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">spb<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30e9\u30d5\u3092 SVG \u3067 Notebook \u306b\u30a4\u30f3\u30e9\u30a4\u30f3\u8868\u793a<\/span>\r\n<span class=\"o\">%<\/span><span class=\"k\">config<\/span> InlineBackend.figure_formats = ['svg']\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[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u30b0\u30e9\u30d5\u3092\u63cf\u304f\u305f\u3081\u3067\u306f\u306a\u304f\u30c7\u30d5\u30a9\u30eb\u30c8\u8a2d\u5b9a\u306e\u305f\u3081<\/span>\r\n<span class=\"kn\">import<\/span> <span class=\"nn\">matplotlib.pyplot<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">plt<\/span>\r\n\r\n<span class=\"n\">config<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{<\/span>\r\n    <span class=\"s1\">'axes.labelsize'<\/span><span class=\"p\">:<\/span> <span class=\"s1\">'x-large'<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"s1\">'mathtext.fontset'<\/span><span class=\"p\">:<\/span> <span class=\"s1\">'cm'<\/span>\r\n<span class=\"p\">}<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">rcParams<\/span><span class=\"o\">.<\/span><span class=\"n\">update<\/span><span class=\"p\">(<\/span><span class=\"n\">config<\/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=\"$\\Omega_{\\Lambda}-=-0$-\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[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># Omega &gt; 1<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">t1<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"p\">((<\/span><span class=\"n\">x<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span> <span class=\"o\">*<\/span> <span class=\"n\">atan<\/span><span class=\"p\">(<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"c1\"># Omega &lt; 1<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">t2<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"mi\">1<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span> <span class=\"o\">-<\/span> <span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"p\">((<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">x<\/span><span class=\"p\">))<\/span> <span class=\"o\">*<\/span> <span class=\"n\">atanh<\/span><span class=\"p\">(<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">x<\/span><span class=\"p\">))<\/span>\r\n<span class=\"c1\"># Omega = 1<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">t0<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"mi\">2<\/span><span class=\"o\">\/<\/span><span class=\"mi\">3<\/span>\r\n\r\n<span class=\"k\">def<\/span> <span class=\"nf\">t<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">if<\/span> <span class=\"n\">Omega<\/span> <span class=\"o\">&gt;<\/span> <span class=\"mi\">1<\/span><span class=\"p\">:<\/span>\r\n        <span class=\"k\">return<\/span> <span class=\"n\">t1<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">elif<\/span> <span class=\"n\">Omega<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">1<\/span><span class=\"p\">:<\/span>\r\n        <span class=\"k\">return<\/span> <span class=\"n\">t0<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\r\n        <span class=\"k\">return<\/span> <span class=\"n\">t2<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/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=\"$\\Omega_{\\Lambda}-=-1---\\Omega_{\\rm-m}$-\u3059\u306a\u308f\u3061-$k-=-0$-\u306e\u5834\u5408\">$\\Omega_{\\Lambda} = 1 &#8211; \\Omega_{\\rm m}$ \u3059\u306a\u308f\u3061 $k = 0$ \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[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># Omega &gt; 1<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"mi\">2<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"o\">*<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span> <span class=\"o\">*<\/span> <span class=\"n\">atan<\/span><span class=\"p\">(<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span>\r\n<span class=\"c1\"># Omega &lt; 1<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">T2<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"mi\">2<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"o\">*<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">Omega<\/span><span class=\"p\">))<\/span> <span class=\"o\">*<\/span> <span class=\"n\">atanh<\/span><span class=\"p\">(<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">Omega<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"k\">def<\/span> <span class=\"nf\">T<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">if<\/span> <span class=\"n\">Omega<\/span> <span class=\"o\">&gt;<\/span> <span class=\"mi\">1<\/span><span class=\"p\">:<\/span>\r\n        <span class=\"k\">return<\/span> <span class=\"n\">T1<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">elif<\/span> <span class=\"n\">Omega<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">1<\/span><span class=\"p\">:<\/span>\r\n        <span class=\"k\">return<\/span> <span class=\"n\">t0<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\r\n        <span class=\"k\">return<\/span> <span class=\"n\">T2<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/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=\"SymPy-Plotting-Backends-\u3067\u5c11\u3057\u8fbc\u307f\u5165\u3063\u305f\u95a2\u6570\u3092-plot()-\u3059\u308b\u3068\u304d\u306e\u5c0f\u6280\">SymPy Plotting Backends \u3067\u5c11\u3057\u8fbc\u307f\u5165\u3063\u305f\u95a2\u6570\u3092 <code>plot()<\/code> \u3059\u308b\u3068\u304d\u306e\u5c0f\u6280<\/h3>\n<p>\u901a\u5e38\u306a\u3089\u3070<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">T<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.001<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">))<\/span>\r\n<\/pre>\n<\/div>\n<p>\u3068\u3059\u308b\u3068\u3053\u308d\u3060\u304c\uff0c\u95a2\u6570 <code>T(Omega)<\/code> \u306e\u5b9a\u7fa9\u304c\u5c11\u3057\u8fbc\u307f\u5165\u3063\u3066\u3044\u3066 <code>if<\/code> \u6587\u304c\u3042\u308b\u5834\u5408\uff0c\u3053\u308c\u3060\u3068\u30a8\u30e9\u30fc\u306b\u306a\u308b\u3002<\/p>\n<p>\u5bfe\u7b56\u306f\uff0c<\/p>\n<ul>\n<li>\u95a2\u6570\u540d\u306e\u307f\u306b\u3059\u308b\uff08\u304b\u3063\u3053\u3084\u5f15\u6570\u306f\u7701\u7565\u3059\u308b\uff09<\/li>\n<li><code>force_real_eval=True<\/code> \u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u3064\u3051\u308b<\/li>\n<\/ul>\n<p>\u3064\u307e\u308a\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3059\u308c\u3070\u3088\u3044\u3002<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">T<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.001<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> <span class=\"n\">force_real_eval<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\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=\"\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3057\u3066-plot-\u3059\u308b\">\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3057\u3066 <code>plot()<\/code> \u3059\u308b<\/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-ipython3\">\n<pre><span class=\"n\">var<\/span><span class=\"p\">(<\/span><span class=\"s1\">'Omega'<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"p\">(<\/span><span class=\"n\">T<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.001<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> \r\n     <span class=\"sa\">r<\/span><span class=\"s2\">\"$\\Omega_{\\Lambda} = 1 - \\Omega_{\\rm m}$\"<\/span><span class=\"p\">,<\/span> \r\n     <span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'red'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'linewidth'<\/span><span class=\"p\">:<\/span><span class=\"mi\">2<\/span><span class=\"p\">}),<\/span> \r\n    <span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.001<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> \r\n     <span class=\"sa\">r<\/span><span class=\"s2\">\"$\\Omega_{\\Lambda} = 0$\"<\/span><span class=\"p\">,<\/span> \r\n     <span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'black'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'linewidth'<\/span><span class=\"p\">:<\/span><span class=\"mi\">2<\/span><span class=\"p\">}),<\/span>\r\n    <span class=\"n\">force_real_eval<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">,<\/span> <span class=\"n\">show<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span>\r\n<span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5404\u7a2e\u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u8a2d\u5b9a<\/span>\r\n<span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">ax<\/span>\r\n\r\n<span class=\"c1\">#\u30b0\u30e9\u30d5\u306e\u4e0a\u4e0b\u5de6\u53f3\u306b\u76ee\u76db\u7dda\u3092\u4ed8\u3051\u308b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">yaxis<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ticks_position<\/span><span class=\"p\">(<\/span><span class=\"s1\">'both'<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">xaxis<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ticks_position<\/span><span class=\"p\">(<\/span><span class=\"s1\">'both'<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># tick \u306e\u5411\u304d\u3092\u5185\u5074\u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">tick_params<\/span><span class=\"p\">(<\/span><span class=\"n\">which<\/span> <span class=\"o\">=<\/span><span class=\"s2\">\"both\"<\/span><span class=\"p\">,<\/span><span class=\"n\">direction<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'in'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u306e\u8868\u793a\u7bc4\u56f2<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlim<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">])<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylim<\/span><span class=\"p\">([<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.5<\/span><span class=\"p\">])<\/span>\r\n\r\n<span class=\"c1\"># x \u306e\u4e3b\u76ee\u76db<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">([<\/span><span class=\"mf\">0.2<\/span><span class=\"o\">*<\/span><span class=\"n\">i<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span><span class=\"mi\">11<\/span><span class=\"p\">)])<\/span>\r\n<span class=\"c1\"># y \u306e\u4e3b\u76ee\u76db<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_yticks<\/span><span class=\"p\">([<\/span><span class=\"mf\">0.5<\/span><span class=\"o\">+<\/span><span class=\"mf\">0.1<\/span><span class=\"o\">*<\/span><span class=\"n\">i<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">11<\/span><span class=\"p\">)])<\/span>\r\n\r\n<span class=\"c1\"># \u526f\u76ee\u76db\u3082\u8868\u793a<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">minorticks_on<\/span><span class=\"p\">()<\/span>\r\n<span class=\"c1\"># \u526f\u76ee\u76db\u306b\u306f grid \u3092\u3064\u3051\u306a\u3044<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span> <span class=\"n\">which<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"minor\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u4e3b\u76ee\u76db\u306e grid \u3092\u7d30\u3044\u70b9\u7dda\u3067<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"kc\">True<\/span><span class=\"p\">,<\/span> <span class=\"n\">which<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"major\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s1\">'dotted'<\/span><span class=\"p\">);<\/span>\r\n\r\n<span class=\"c1\"># \u30bf\u30a4\u30c8\u30eb<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_title<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"\u5b87\u5b99\u5e74\u9f62 $t_0$ \u306e\u5bc6\u5ea6\u30d1\u30e9\u30e1\u30fc\u30bf\u4f9d\u5b58\u6027\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># \u8ef8\u306e\u30e9\u30d9\u30eb<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlabel<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"$\\Omega_{\\rm m}$\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylabel<\/span><span class=\"p\">(<\/span><span class=\"sa\">r<\/span><span class=\"s2\">\"$H_0\\ t_0$\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u51e1\u4f8b\u306e\u8868\u793a\u30b5\u30a4\u30ba<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/span><span class=\"p\">(<\/span><span class=\"n\">prop<\/span><span class=\"o\">=<\/span><span class=\"p\">{<\/span><span class=\"s2\">\"size\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"x-large\"<\/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_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-7537\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/SPB-t-fig01.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<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>\u5b87\u5b99\u8ad6\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u5b87\u5b99\u5e74\u9f62<\/li>\n<\/ul>\n<p>\u3053\u3053\u3067\u306f\uff0cPython \u306e SymPy Plotting Backends \u3092\u4f7f\u3063\u3066\u5b87\u5b99\u5e74\u9f62\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u3044\u3066\u307f\u308b\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\/%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%9asympy-%e3%81%a8-spb-%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":19,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-7536","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\/7536","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=7536"}],"version-history":[{"count":3,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/7536\/revisions"}],"predecessor-version":[{"id":8229,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/7536\/revisions\/8229"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/1483"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=7536"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}