{"id":9364,"date":"2024-08-28T15:07:15","date_gmt":"2024-08-28T06:07:15","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=9364"},"modified":"2024-08-28T16:09:09","modified_gmt":"2024-08-28T07:09:09","slug":"%e8%a3%9c%e8%b6%b3%ef%bc%9asympy-%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%9asympy-%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\uff1aSymPy \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\uff0cSymPy Plotting Backends \u3092\u4f7f\u3063\u3066\u89d2\u5f84\u8ddd\u96e2\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3002<!--more--><\/p>\n<h3 id=\"\u30e2\u30b8\u30e5\u30fc\u30eb\u306e-import-\u3068\u8a2d\u5b9a\">\u30e2\u30b8\u30e5\u30fc\u30eb\u306e import \u3068\u8a2d\u5b9a<\/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[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.abc<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n<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\">spb<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n\r\n<span class=\"c1\"># \u4ee5\u4e0b\u306f\u30b0\u30e9\u30d5\u3092 SVG \u3067 Notebook \u306b\u30a4\u30f3\u30e9\u30a4\u30f3\u8868\u793a\u3055\u305b\u308b\u8a2d\u5b9a<\/span>\r\n<span class=\"o\">%<\/span><span class=\"k\">config<\/span> InlineBackend.figure_formats = ['svg']\r\n\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<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">rcParams<\/span><span class=\"p\">[<\/span><span class=\"s1\">'mathtext.fontset'<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'cm'<\/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\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[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"k\">def<\/span> <span class=\"nf\">dA<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/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=\"n\">Omega<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">+<\/span><span class=\"n\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"o\">-<\/span><span class=\"n\">Omega<\/span><span class=\"o\">+<\/span><span class=\"n\">Omega<\/span><span class=\"o\">*<\/span><span class=\"n\">z<\/span><span class=\"o\">-<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"o\">-<\/span><span class=\"n\">Omega<\/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\">Omega<\/span><span class=\"o\">*<\/span><span class=\"n\">z<\/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=\"$\\Omega_{\\rm-m}-+-\\Omega_{\\Lambda}-=-1$-\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<code>.evalf()<\/code> \u3067\u6570\u5024\u7a4d\u5206\u306b\u3002\uff08\u6fc0\u9045\u3060\u3051\u3069\u697d\u3061\u3093\u3002\uff09<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"k\">def<\/span> <span class=\"nf\">dAL<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/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\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"n\">integrate<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/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\">Omega<\/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=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">))<\/span><span class=\"o\">.<\/span><span class=\"n\">evalf<\/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=\"$0-\\leq-z-\\leq-5$-\u307e\u3067\u306e\u30b0\u30e9\u30d5\">$0 \\leq z \\leq 5$ \u307e\u3067\u306e\u30b0\u30e9\u30d5<\/h3>\n<p>\u521d\u3081\u3066 <code>dAL(0.3, z)<\/code> \u3092 <code>plot()<\/code> \u3059\u308b\u969b\u306b\u306f\u3044\u308d\u3044\u308d\u6587\u53e5\u3092\u8a00\u308f\u308c\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u304c\uff0c\u306a\u3093\u3068\u304b\u30b0\u30e9\u30d5\u306f\u63cf\u3044\u3066\u304f\u308c\u308b\u3002\u3082\u306e\u3059\u3054\u304f\u6642\u9593\u304c\u304b\u304b\u308b\u306e\u3067\uff0c\u8f9b\u62b1\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-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">plot<\/span><span class=\"p\">((<\/span><span class=\"n\">dAL<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'$\\Omega_<\/span><span class=\"si\">{m}<\/span><span class=\"s1\">=0.3,\\, \\Omega_{\\Lambda}=0.7$'<\/span><span class=\"p\">),<\/span> \r\n     <span class=\"p\">(<\/span><span class=\"n\">dA<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'$\\Omega_<\/span><span class=\"si\">{m}<\/span><span class=\"s1\">=0.3,\\, \\Omega_{\\Lambda}=0$'<\/span><span class=\"p\">),<\/span> \r\n     <span class=\"p\">(<\/span><span class=\"n\">dA<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'$\\Omega_<\/span><span class=\"si\">{m}<\/span><span class=\"s1\">=1,\\, \\ \\ \\,\\Omega_{\\Lambda}=0$'<\/span><span class=\"p\">),<\/span> \r\n     <span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span> \r\n     <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">),<\/span> <span class=\"n\">title<\/span><span class=\"o\">=<\/span><span class=\"s1\">'\u89d2\u5f84\u8ddd\u96e2'<\/span><span class=\"p\">,<\/span>\r\n     <span class=\"n\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'$H_0\\, d_A(z)$'<\/span><span class=\"p\">)<\/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_stderr output_text\">\n<pre>\/usr\/local\/lib\/python3.8\/dist-packages\/spb\/series.py:1087: UserWarning: NumPy is unable to evaluate with complex numbers some of the functions included in this symbolic expression: [hyper]. Hence, the evaluation will use real numbers. If you believe the resulting plot is incorrect, change the evaluation module by setting the `modules` keyword argument.\r\n\/usr\/local\/lib\/python3.8\/dist-packages\/spb\/series.py:262: UserWarning: The evaluation with NumPy\/SciPy failed.\r\nNameError: name 'hyper' is not defined\r\nTrying to evaluate the expression with Sympy, but it might be a slow operation.\r\n<\/pre>\n<\/div>\n<\/div>\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><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spb-dA-fig1.svg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-9365\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spb-dA-fig1.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/a><\/p>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 12.9 s, sys: 1.41 s, total: 14.3 s\r\nWall time: 11.8 s\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=\"$-0-\\leq-z-\\leq-20$-\u307e\u3067\u306e\u30b0\u30e9\u30d5\">$ 0 \\leq z \\leq 20$ \u307e\u3067\u306e\u30b0\u30e9\u30d5<\/h3>\n<p>$z$ \u306e\u7bc4\u56f2\u3092\u5909\u3048\uff0c\u82e5\u5e72\u306e\u7d30\u304b\u306a\u8a2d\u5b9a\u3092\u8ffd\u52a0\u3057\u3066\u307f\u305f\u3002\u3042\u3044\u304b\u308f\u3089\u305a\u4f55\u304b\u8b66\u544a\u304c\u51fa\u308b\u304c\uff0c\u6c17\u306b\u305b\u305a\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-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot<\/span><span class=\"p\">((<\/span><span class=\"n\">dAL<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'$\\Omega_<\/span><span class=\"si\">{m}<\/span><span class=\"s1\">=0.3,\\, \\Omega_{\\Lambda}=0.7$'<\/span><span class=\"p\">),<\/span> \r\n         <span class=\"p\">(<\/span><span class=\"n\">dA<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'$\\Omega_<\/span><span class=\"si\">{m}<\/span><span class=\"s1\">=0.3,\\, \\Omega_{\\Lambda}=0$'<\/span><span class=\"p\">),<\/span> \r\n         <span class=\"p\">(<\/span><span class=\"n\">dA<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'$\\Omega_<\/span><span class=\"si\">{m}<\/span><span class=\"s1\">=1,\\, \\ \\ \\,\\Omega_{\\Lambda}=0$'<\/span><span class=\"p\">),<\/span> \r\n         <span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">20<\/span><span class=\"p\">),<\/span> \r\n         <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">20<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">),<\/span> <span class=\"n\">title<\/span><span class=\"o\">=<\/span><span class=\"s1\">'\u89d2\u5f84\u8ddd\u96e2'<\/span><span class=\"p\">,<\/span>\r\n         <span class=\"n\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'$H_0\\ d_A(z)$'<\/span><span class=\"p\">,<\/span> <span class=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">ax<\/span>\r\n\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/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<span class=\"c1\"># x \u306e\u4e3b\u76ee\u76db\u3092 5 \u523b\u307f\u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">([<\/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\">0<\/span><span class=\"p\">,<\/span><span class=\"mi\">21<\/span><span class=\"p\">,<\/span><span class=\"mi\">5<\/span><span class=\"p\">)])<\/span>\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<span class=\"c1\"># x \u306e\u526f\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">([<\/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\">20<\/span><span class=\"p\">)],<\/span> <span class=\"n\">minor<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># y \u306e\u526f\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/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\">0.05<\/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\">10<\/span><span class=\"p\">)],<\/span> <span class=\"n\">minor<\/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=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stderr output_text\">\n<pre>\/usr\/local\/lib\/python3.8\/dist-packages\/spb\/series.py:1087: UserWarning: NumPy is unable to evaluate with complex numbers some of the functions included in this symbolic expression: [hyper]. Hence, the evaluation will use real numbers. If you believe the resulting plot is incorrect, change the evaluation module by setting the `modules` keyword argument.\r\n<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre>CPU times: user 10.9 s, sys: 91.7 ms, total: 11 s\r\nWall time: 10.8 s\r\n<\/pre>\n<\/div>\n<\/div>\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><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spb-dA-fig2.svg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-9366\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spb-dA-fig2.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/a><\/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=\"\u6570\u5024\u30ea\u30b9\u30c8\u306b\u3057\u3066-plot_list()-\u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u3092\u63cf\u304f\">\u6570\u5024\u30ea\u30b9\u30c8\u306b\u3057\u3066 <code>plot_list()<\/code> \u3092\u4f7f\u3063\u3066\u30b0\u30e9\u30d5\u3092\u63cf\u304f<\/h3>\n<p>\uff08NumPy \u3092\u4f7f\u308f\u305a\u306b\uff09<code>dAL(Omega, z)<\/code> \u306e\u6570\u5024\u30ea\u30b9\u30c8\u3092\u4f5c\u6210\u3057\uff0c<code>plot_list()<\/code> \u3067\u6570\u5024\u30c7\u30fc\u30bf\u3092\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u308b\u3002<code>.evalf()<\/code> \u306f\u5909\u308f\u3089\u306a\u3044\u306e\u3067 <code>list_dAL<\/code> \u3092\u6c42\u3081\u308b\u306e\u306f\u6fc0\u9045\u306e\u307e\u307e\u3060\u304c\uff0c\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u969b\u306b\uff0c\u306a\u3093\u3060\u304b\u3093\u3060\u3068\u6587\u53e5\u306f\u3064\u3051\u3089\u308c\u306a\u304f\u306a\u308b\u306e\u3067\uff0c\u5c11\u3057\u3060\u3051\u7cbe\u795e\u7684\u306b\u697d\u304b\u306a\u3068\u3002\uff08\u305d\u308c\u306b\u3057\u3066\u3082 SymPy \u306e\u6570\u5024\u7a4d\u5206\u306f\u9045\u3044\u3002\uff09<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">list_z<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/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\">201<\/span><span class=\"p\">)]<\/span>\r\n<span class=\"n\">list_dAL<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">dAL<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"o\">*<\/span><span class=\"n\">i<\/span><span class=\"p\">)<\/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\">201<\/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>CPU times: user 2min 25s, sys: 206 ms, total: 2min 25s\r\nWall time: 2min 25s\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<h4 id=\"\u53c2\u8003\uff1ascipy.integrate.quad()-\u3092\u4f7f\u3046\">\u53c2\u8003\uff1a\u6570\u5024\u7a4d\u5206\u3068\u3057\u3066<code>scipy.integrate.quad()<\/code> \u3092\u4f7f\u3046<\/h4>\n<p><code>.evalf()<\/code> \u3092\u4f7f\u3063\u305f SymPy \u306e\u6570\u5024\u7a4d\u5206\u304c\u3042\u307e\u308a\u306b\u3082\u9045\u3059\u304e\u3066\u7cbe\u795e\u885b\u751f\u4e0a\u3088\u308d\u3057\u304f\u306a\u3044\u306e\u3067\uff0cSymPy\uff08\u306e\u307f\uff09\u3092\u4f7f\u3046\u3068\u3044\u3046\u672c\u7a3f\u306e\u65b9\u91dd\u304b\u3089\u306f\u9038\u8131\u3059\u308b\u304c\uff0cSciPy \u306e\u6570\u5024\u7a4d\u5206 <code>quad()<\/code> \u3092\u4f7f\u3063\u3066\u307f\u308b\u3002<\/p>\n<p><code>quad()<\/code> \u3092\u4f7f\u3046\u969b\u306b\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\uff0c\u6c7a\u3081\u4e8b\u306b\u305d\u3063\u3066\u88ab\u7a4d\u5206\u95a2\u6570\u3092\u5b9a\u7fa9\u3057\u3066\u3084\u308b\u3002<\/p>\n<ul>\n<li>\u88ab\u7a4d\u5206\u95a2\u6570\u306f\u539f\u5247 $x$ \u306e1\u5909\u6570\u95a2\u6570\u306e\u6c7a\u3081\u6253\u3061\u3067\u3002<\/li>\n<li>$x$ \u4ee5\u5916\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u3082\u4f9d\u5b58\u3059\u308b\u5834\u5408\u306f\uff0c$x$ \u306e\u5f8c\u306b\u5f15\u6570\u3068\u3057\u3066\u4e26\u3079\u308b\u3002<\/li>\n<li><code>quad()<\/code> \u3092\u547c\u3073\u51fa\u3059\u969b\u306b\u306f\uff0c$x$ \u4ee5\u5916\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306f <code>args<\/code> \u306b\u5165\u308c\u308b\u3002<\/li>\n<li><code>quad()<\/code> \u306f <code>(\u7a4d\u5206\u5024, \u63a8\u5b9a\u8aa4\u5dee)<\/code> \u3092\u8fd4\u3059\u306e\u3067\uff0c\u7a4d\u5206\u5024\u306e\u307f\u3092\u77e5\u308a\u305f\u3044\u3068\u304d\u306f\u305d\u306e\u3088\u3046\u306b\u3002<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[7]:<\/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\">scipy.integrate<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">quad<\/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[8]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"k\">def<\/span> <span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">Omega<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"mi\">1<\/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\">Omega<\/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=\"mi\">3<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"k\">def<\/span> <span class=\"nf\">dAL2<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">tmp<\/span> <span class=\"o\">=<\/span> <span class=\"n\">quad<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"n\">args<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"n\">Omega<\/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\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"n\">tmp<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span>\r\n    <span class=\"c1\"># \u5225\u89e3<\/span>\r\n    <span class=\"c1\"># ans, err = quad(f, 0, z, args=(Omega))<\/span>\r\n    <span class=\"c1\"># return 1\/(1+z)* ans<\/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[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">%%time<\/span>\r\n\r\n<span class=\"n\">list_z<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/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\">201<\/span><span class=\"p\">)]<\/span>\r\n<span class=\"n\">list_dAL2<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">dAL2<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.1<\/span><span class=\"o\">*<\/span><span class=\"n\">i<\/span><span class=\"p\">)<\/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\">201<\/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>CPU times: user 2.09 s, sys: 7.97 ms, total: 2.1 s\r\nWall time: 2.1 s\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>&#8230; \u3068\u3044\u3046\u3053\u3068\u3067\uff0cSciPy \u306e\u6570\u5024\u7a4d\u5206 <code>quad()<\/code> \u3067\u8a08\u7b97\u3057\u305f $d_A(\\Omega, z)$ \u306f\u7d0470\u500d\u9ad8\u901f\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308b\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<h4 id=\"$0-\\leq-z-\\leq-5$-\u307e\u3067\u306e\u30b0\u30e9\u30d5\">$0 \\leq z \\leq 5$ \u307e\u3067\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[10]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">p1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot_list<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"n\">list_z<\/span><span class=\"p\">,<\/span> <span class=\"n\">list_dAL2<\/span><span class=\"p\">,<\/span> \r\n        <span class=\"s1\">'$\\Omega_<\/span><span class=\"si\">{m}<\/span><span class=\"s1\">=0.3,\\, \\Omega_{\\Lambda}=0.7$'<\/span><span class=\"p\">,<\/span> \r\n        <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">),<\/span>\r\n        <span class=\"n\">title<\/span><span class=\"o\">=<\/span><span class=\"s1\">'\u89d2\u5f84\u8ddd\u96e2'<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'$z$'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'$H_0\\, d_A(z)$'<\/span><span class=\"p\">,<\/span> \r\n        <span class=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">p2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"p\">(<\/span><span class=\"n\">dA<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'$\\Omega_<\/span><span class=\"si\">{m}<\/span><span class=\"s1\">=0.3,\\, \\Omega_{\\Lambda}=0$'<\/span><span class=\"p\">),<\/span> \r\n        <span class=\"p\">(<\/span><span class=\"n\">dA<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'$\\Omega_<\/span><span class=\"si\">{m}<\/span><span class=\"s1\">=1,\\, \\ \\ \\,\\Omega_{\\Lambda}=0$'<\/span><span class=\"p\">),<\/span> \r\n        <span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span> <span class=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p1<\/span> <span class=\"o\">+<\/span> <span class=\"n\">p2<\/span>\r\n\r\n<span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">show<\/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><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spb-dA-fig3.svg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-9367\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spb-dA-fig3.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/a><\/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<h4 id=\"$0-\\leq-z-\\leq-20$-\u307e\u3067\u306e\u30b0\u30e9\u30d5\">$0 \\leq z \\leq 20$ \u307e\u3067\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[11]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">p1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot_list<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"n\">list_z<\/span><span class=\"p\">,<\/span> <span class=\"n\">list_dAL2<\/span><span class=\"p\">,<\/span> \r\n        <span class=\"s1\">'$\\Omega_<\/span><span class=\"si\">{m}<\/span><span class=\"s1\">=0.3,\\, \\Omega_{\\Lambda}=0.7$'<\/span><span class=\"p\">,<\/span> \r\n        <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">20<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">),<\/span>\r\n        <span class=\"n\">title<\/span><span class=\"o\">=<\/span><span class=\"s1\">'\u89d2\u5f84\u8ddd\u96e2'<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'$z$'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'$H_0\\, d_A(z)$'<\/span><span class=\"p\">,<\/span> \r\n        <span class=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">p2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"p\">(<\/span><span class=\"n\">dA<\/span><span class=\"p\">(<\/span><span class=\"mf\">0.3<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'$\\Omega_<\/span><span class=\"si\">{m}<\/span><span class=\"s1\">=0.3,\\, \\Omega_{\\Lambda}=0$'<\/span><span class=\"p\">),<\/span> \r\n        <span class=\"p\">(<\/span><span class=\"n\">dA<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'$\\Omega_<\/span><span class=\"si\">{m}<\/span><span class=\"s1\">=1,\\, \\ \\ \\,\\Omega_{\\Lambda}=0$'<\/span><span class=\"p\">),<\/span> \r\n        <span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">20<\/span><span class=\"p\">),<\/span> <span class=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p1<\/span> <span class=\"o\">+<\/span> <span class=\"n\">p2<\/span>\r\n\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">ax<\/span>\r\n\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/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<span class=\"c1\"># x \u306e\u4e3b\u76ee\u76db\u3092 5 \u523b\u307f\u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">([<\/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\">0<\/span><span class=\"p\">,<\/span><span class=\"mi\">21<\/span><span class=\"p\">,<\/span><span class=\"mi\">5<\/span><span class=\"p\">)])<\/span>\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<span class=\"c1\"># x \u306e\u526f\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">([<\/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\">20<\/span><span class=\"p\">)],<\/span> <span class=\"n\">minor<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># y \u306e\u526f\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/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\">0.05<\/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\">10<\/span><span class=\"p\">)],<\/span> <span class=\"n\">minor<\/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=\"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><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spb-dA-fig4.svg\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-9368\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spb-dA-fig4.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/a><\/p>\n<\/div>\n<\/div>\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\uff0cSymPy Plotting Backends \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%9asympy-%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":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-9364","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\/9364","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=9364"}],"version-history":[{"count":6,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/9364\/revisions"}],"predecessor-version":[{"id":9374,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/9364\/revisions\/9374"}],"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=9364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}