{"id":9701,"date":"2024-11-25T11:26:19","date_gmt":"2024-11-25T02:26:19","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=9701"},"modified":"2024-12-04T14:20:00","modified_gmt":"2024-12-04T05:20:00","slug":"sympy-plotting-backends-%e3%81%a7%e3%82%b0%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90%ef%bc%9athe-graphic-module-%e7%b7%a8","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/python-%e3%81%a7%e3%82%b0%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90\/sympy-plotting-backends-%e3%81%a7%e3%82%b0%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90%ef%bc%9athe-graphic-module-%e7%b7%a8\/","title":{"rendered":"SymPy Plotting Backends \u3067\u30b0\u30e9\u30d5\u4f5c\u6210\uff1aThe Graphic Module \u7de8"},"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>\u3053\u3053\u3067\u306f\uff0c<a href=\"https:\/\/sympy-plot-backends.readthedocs.io\/en\/latest\/index.html\"><strong><span style=\"font-family: helvetica, arial, sans-serif;\">SymPy Plotting Backends (SPB)<\/span><\/strong><\/a> \u306e <span style=\"font-family: helvetica, arial, sans-serif;\"><a href=\"https:\/\/sympy-plot-backends.readthedocs.io\/en\/latest\/modules\/graphics\/index.html#\" target=\"_blank\" rel=\"noopener\"><strong>The Graphic Module<\/strong><\/a><\/span> \u3092\u4f7f\u3063\u305f 2\u6b21\u5143\u30b0\u30e9\u30d5\u4f5c\u6210\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n<p><a href=\"https:\/\/sympy-plot-backends.readthedocs.io\/en\/latest\/index.html\"><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>SymPy Plotting Backends (SPB)<\/strong><\/span><\/a> \u306e <a href=\"https:\/\/sympy-plot-backends.readthedocs.io\/en\/latest\/modules\/plot_functions\/index.html\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>Plot functions<\/strong><\/span><\/a> \u3092\u4f7f\u3063\u305f 2\u6b21\u5143\u30b0\u30e9\u30d5\u4f5c\u6210\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u3067\u8aac\u660e\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/python-%e3%81%a7%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/sympy-plotting-backends-%e3%81%a7%e3%82%b0%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90\/\" target=\"_blank\" rel=\"noopener\">SymPy Plotting Backends \u3067\u30b0\u30e9\u30d5\u4f5c\u6210\uff1aPlot functions \u7de8<\/a><\/li>\n<\/ul>\n<p>Python \u306e SymPy \u81ea\u8eab\u306b\u3082\u30b0\u30e9\u30d5\u4f5c\u6210\u6a5f\u80fd\u306f\u3042\u308a\u307e\u3059\u304c\uff0c<a href=\"https:\/\/sympy-plot-backends.readthedocs.io\/en\/latest\/index.html\"><span style=\"font-family: helvetica, arial, sans-serif;\"><strong>SymPy Plotting Backends (SPB)<\/strong><\/span><\/a> \u306f\uff0c\u8a00\u308f\u3070\u305d\u306e\u6a5f\u80fd\u62e1\u5f35\u7248\u306b\u76f8\u5f53\u3057\u307e\u3059\u3002 <span style=\"font-family: helvetica, arial, sans-serif;\"><strong>SPB \u306b\u3088\u308b\u30b0\u30e9\u30d5\u4f5c\u6210\u306b\u306f\uff0c<a href=\"https:\/\/sympy-plot-backends.readthedocs.io\/en\/latest\/modules\/graphics\/index.html\" target=\"_blank\" rel=\"noopener\">The Graphics Module<\/a> \u306b\u3088\u308b\u65b9\u6cd5\u3068\uff0c<a href=\"https:\/\/sympy-plot-backends.readthedocs.io\/en\/latest\/modules\/plot_functions\/index.html\" target=\"_blank\" rel=\"noopener\">Plot functions<\/a> \u306b\u3088\u308b\u65b9\u6cd5\u306e2\u7a2e\u985e\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002<\/strong><\/span>\u30c9\u30ad\u30e5\u30e1\u30f3\u30c8\u306b\u3088\u308b\u3068\uff0c<strong><a href=\"https:\/\/sympy-plot-backends.readthedocs.io\/en\/latest\/modules\/graphics\/index.html\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: helvetica, arial, sans-serif;\">The Graphics Module<\/span><\/a><\/strong> \u306e\u307b\u3046\u304c\u3088\u308a\u76f4\u611f\u7684\u3067\u7c21\u5358\u3067\u3042\u308a\uff0c\u7570\u306a\u3063\u305f\u30b0\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a\u3055\u305b\u308b\u3053\u3068\u3082\u7c21\u5358\u306b\u3067\u304d\u308b\u306e\u3067\u30aa\u30b9\u30b9\u30e1\u306e\u3088\u3046\u3067\u3059\u3002<strong><a href=\"https:\/\/sympy-plot-backends.readthedocs.io\/en\/latest\/modules\/plot_functions\/index.html\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: helvetica, arial, sans-serif;\">Plot functions<\/span><\/a><\/strong> \u306b\u3088\u308b\u65b9\u6cd5\u306f\u4eca\u5f8c\u306f\u30a2\u30c3\u30d7\u30c7\u30fc\u30c8\u3055\u308c\u306a\u3044\u3088\u3046\u3067\u3059\u3002<\/p>\n<p><!--more--><\/p>\n<p>SPB \u306e <span style=\"font-family: helvetica, arial, sans-serif;\"><strong>The Graphic Module<\/strong><\/span> \u3092\u4f7f\u3063\u3066\u30d7\u30ed\u30c3\u30c8\u3067\u304d\u308b\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/p>\n<ul>\n<li>\u967d\u95a2\u6570 $y = f(x)$:\n<ul>\n<li><code>graphics(line(f(x), (x, xmin, xmax)))<\/code><\/li>\n<\/ul>\n<\/li>\n<li>\u9670\u95a2\u6570 $f(x, y) = 0$:\n<ul>\n<li><code>graphics(implicit_2d(f(x, y), (x, xmin, xmax), (y, ymin, ymax)))<\/code><\/li>\n<\/ul>\n<\/li>\n<li>\u5a92\u4ecb\u5909\u6570\u8868\u793a $x(t), y(t)$:\n<ul>\n<li><code>graphics(line_parametric_2d(x(t), y(t), (t, tmin, tmax)))<\/code><\/li>\n<\/ul>\n<\/li>\n<li>\u70b9\uff0c$x$ \u5ea7\u6a19 $y$ \u5ea7\u6a19\u306e\u6570\u5024\u30c7\u30fc\u30bf:\n<ul>\n<li><code>graphics(list_2d([x1, ..., xn], [y1, ..., yn]))<\/code><\/li>\n<\/ul>\n<\/li>\n<li>\u30d9\u30af\u30c8\u30eb\n<ul>\n<li><code>graphics(arrow_2d((x0, y0), (vx, vy)))<\/code><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>\u307e\u305f\uff0c2\u672c\u306e\u967d\u95a2\u6570\u3067\u631f\u307e\u308c\u305f\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3059\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"SymPy-\u304a\u3088\u3073-SPB-\u306e-import\">SymPy \u304a\u3088\u3073 SPB \u306e import<\/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\r\n<span class=\"c1\"># SymPy Plotting Backends (SPB)<\/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\"># \u65e5\u672c\u8a9e\u304c\u30c8\u30fc\u30d5\u306b\u306a\u308b\u5834\u5408<\/span>\r\n<span class=\"c1\"># import japanize_matplotlib<\/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\r\n<span class=\"c1\"># \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<span class=\"c1\"># mathtext font \u306e\u8a2d\u5b9a<\/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\r\n<span class=\"c1\"># \u30c7\u30d5\u30a9\u30eb\u30c8\u306e figsize \u306e\u8a2d\u5b9a\u5909\u66f4\u306f\uff0c<\/span>\r\n<span class=\"c1\"># \u4e00\u5ea6\u4f55\u304b\u63cf\u3044\u3066\u304b\u3089\u306b\u3059\u308b\u3068\u3088\u3044\u3088\u3046\u3060\u3002<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">rcParams<\/span><span class=\"p\">[<\/span><span class=\"s1\">'figure.figsize'<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">4.8<\/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=\"The-Graphics-Module-graphics()\">The Graphics Module <code>graphics()<\/code><\/h3>\n<p>SymPy Plotting Backends (SPB) \u306e Graphic Module \u3067\u30b0\u30e9\u30d5\u3092\u4f5c\u6210\u3059\u308b\u5834\u5408\u306f <code>graphics()<\/code> \u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u967d\u95a2\u6570\u306e\u30b0\u30e9\u30d5-line()\">\u967d\u95a2\u6570\u306e\u30b0\u30e9\u30d5 <code>line()<\/code><\/h3>\n<p>$x$ \u306e\u967d\u95a2\u6570 $y = f(x)$ \u3092 $x_{\\rm min} \\leq x \\leq x_{\\rm max}$ \u306e\u7bc4\u56f2\u3067\u30b0\u30e9\u30d5\u3092\u4f5c\u6210\u3059\u308b\u306b\u306f <code>line()<\/code> \u3092\u4f7f\u3063\u3066&#8230;<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">xmin<\/span><span class=\"p\">,<\/span> <span class=\"n\">xmax<\/span><span class=\"p\">)))<\/span>\r\n<\/pre>\n<\/div>\n<p><code>(x, xmin, xmax)<\/code> \u3092\u7701\u7565\u3059\u308b\u3068 <code>(x, -10, 10)<\/code> \u3068\u307f\u306a\u3057\u307e\u3059\u3002<\/p>\n<p>\u4f8b\u3068\u3057\u3066\uff0c$f(x) = \\sin x$ \u306e\u30af\u3099\u30e9\u30d5\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">rcParams<\/span><span class=\"p\">[<\/span><span class=\"s1\">'figure.figsize'<\/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_text output_subarea output_execute_result\">\n<pre>[6.4, 4.8]<\/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[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9703\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-01.svg\" alt=\"\" width=\"600\" height=\"400\" \/><\/p>\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[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">rcParams<\/span><span class=\"p\">[<\/span><span class=\"s1\">'figure.figsize'<\/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[4]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>[6.0, 4.0]<\/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=\"figsize-\u306e\u8a2d\u5b9a\u5909\u66f4-plt.rcParams[]\">figsize \u306e\u8a2d\u5b9a\u5909\u66f4 <code>plt.rcParams[]<\/code><\/h4>\n<p>SPB \u3067\u30c7\u30d5\u30a9\u30eb\u30c8\u306e\u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba\u3092\u5909\u66f4\u3059\u308b\u306b\u306f\uff0c\u30d0\u30c3\u30af\u30a8\u30f3\u30c9\u306e Matplotlib \u306e\u8a2d\u5b9a\u5909\u66f4\u65b9\u6cd5\u3092\u4f7f\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3002<\/p>\n<div class=\"highlight\">\n<pre><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\">'figure.figsize'<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">4.8<\/span><span class=\"p\">]<\/span>\r\n<\/pre>\n<\/div>\n<p>\u3057\u304b\u3057\uff0c\u672c\u7a3f\u57f7\u7b46\u6642\u70b9\u306e\u74b0\u5883\u3067\u306f\uff0cSPB \u3067\u6700\u521d\u306b\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3068\u306a\u305c\u304b\uff0c<code>[6.0, 4.0]<\/code> \u306b\u8a2d\u5b9a\u3055\u308c\u3066\u3057\u307e\u3046\u3088\u3046\u306a\u306e\u3067\uff0c\u3042\u3089\u305f\u3081\u3066 <code>[6.4, 4.8]<\/code> \u306b\u8a2d\u5b9a\u3057\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u30c7\u30d5\u30a9\u30eb\u30c8\u306e figsize \u306e\u8a2d\u5b9a\u5909\u66f4\u306f\uff0c<\/span>\r\n<span class=\"c1\"># \u4e00\u5ea6\u4f55\u304b\u63cf\u3044\u3066\u304b\u3089\u306b\u3059\u308b\u3068\u3088\u3044\u3088\u3046\u3060\u3002<\/span>\r\n\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">rcParams<\/span><span class=\"p\">[<\/span><span class=\"s1\">'figure.figsize'<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">4.8<\/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[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9704 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-02.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\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[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">rcParams<\/span><span class=\"p\">[<\/span><span class=\"s1\">'figure.figsize'<\/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[7]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>[6.4, 4.8]<\/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=\"\u30b0\u30e9\u30d5\u5168\u4f53\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u8a2d\u5b9a\u4f8b\">\u30b0\u30e9\u30d5\u5168\u4f53\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u8a2d\u5b9a\u4f8b<\/h4>\n<p>\u30b0\u30e9\u30d5\u5168\u4f53\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u306f <code>graphics()<\/code> \u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u3068\u3057\u3066\u8a2d\u5b9a\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u30bf\u30a4\u30c8\u30eb <code>title=' '<\/code><\/li>\n<li>\u8868\u793a\u7bc4\u56f2 <code>xlim=( , )<\/code> <code>ylim=( , )<\/code><\/li>\n<li>\u30b5\u30a4\u30ba\u3000 <code>size =( , )<\/code> \u30c7\u30d5\u30a9\u30eb\u30c8\u306f <code>(6, 4)<\/code><\/li>\n<li>\u7e26\u6a2a\u6bd4\u3000 <code>aspect = 'equal'<\/code> \u7b49<\/li>\n<li>\u8ef8\u30e9\u30d9\u30eb <code>xlabel=' '<\/code> <code>ylabel=' '<\/code><\/li>\n<li>\u30b0\u30ea\u30c3\u30c9\u306e\u975e\u8868\u793a <code>grid = False<\/code><\/li>\n<\/ul>\n<p>\u306a\u304a\uff0c\u8907\u6570\u306e\u30b0\u30e9\u30d5\u306e\u969b\u306b\u306f\u51e1\u4f8b\u304c\u8868\u793a\u3055\u308c\u307e\u3059\u304c\uff0c1\u672c\u306e\u30b0\u30e9\u30d5\u306e\u969b\u306f\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u306f\u8868\u793a\u3055\u308c\u307e\u305b\u3093\u3002\u3069\u3046\u3057\u3066\u3082\u8868\u793a\u3055\u305b\u305f\u3044\u306a\u3089<\/p>\n<ul>\n<li>\u51e1\u4f8b\u8868\u793a <code>legend = True<\/code> 1\u672c\u306e\u30b0\u30e9\u30d5\u306e\u3068\u304d\u306b\u3082\u51e1\u4f8b\u3092\u8868\u793a\u3055\u305b\u308b<\/li>\n<\/ul>\n<h4 id=\"\u30e9\u30a4\u30f3\u3054\u3068\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b\">\u30e9\u30a4\u30f3\u3054\u3068\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u8a2d\u5b9a\u4f8b<\/h4>\n<p>\u30e9\u30a4\u30f3\u3054\u3068\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u306f <code>line()<\/code> \u5185\u306b <code>rendering_kw={}<\/code> \u3068\u3057\u3066\u8a2d\u5b9a\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u7dda\u306e\u592a\u3055 <code>'lw': ('linewidth':)<\/code><\/li>\n<li>\u7dda\u306e\u8272\u3000 <code>'color':<\/code><\/li>\n<li>\u7dda\u7a2e\u3000\u3000 <code>'ls': ('linestyle':)<\/code> <code>':'<\/code>, <code>'--'<\/code> \u7b49<\/li>\n<\/ul>\n<p>\u30e9\u30a4\u30f3\u3054\u3068\u306e\u51e1\u4f8b\u306f\u81ea\u52d5\u3067\u3064\u304f\u304c\uff0c\u30ab\u30b9\u30bf\u30de\u30a4\u30ba\u3057\u305f\u3044\u3068\u304d\u306f<\/p>\n<ul>\n<li>\u51e1\u4f8b\u30e9\u30d9\u30eb <code>label = ' '<\/code> \u3042\u308b\u3044\u306f <code>' '<\/code> \u306e\u307f\u3067\u3082\u53ef\u306e\u5834\u5408\u3082\u3042\u308a<\/li>\n<\/ul>\n<p>\u3044\u304f\u3064\u304b\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3059\u308b\u4f8b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[8]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'\u6b63\u5f26\u95a2\u6570'<\/span><span class=\"p\">,<\/span>\r\n         <span class=\"n\">rendering_kw<\/span><span class=\"o\">=<\/span><span class=\"p\">{<\/span><span class=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"red\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"ls\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\":\"<\/span><span class=\"p\">}),<\/span>\r\n    <span class=\"n\">legend<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">1.1<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.1<\/span><span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9706 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-03.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u521d\u7b49\u95a2\u6570\u306e\u30b0\u30e9\u30d5\">\u521d\u7b49\u95a2\u6570\u306e\u30b0\u30e9\u30d5<\/h3>\n<p>\u967d\u95a2\u6570 $y = f(x)$ \u306e\u30b0\u30e9\u30d5\u306e\u63cf\u304d\u65b9\u3092\u4f7f\u3063\u3066\uff0c\uff08\u53cc\u66f2\u7dda\u95a2\u6570\u304a\u3088\u3073\u9006\u53cc\u66f2\u7dda\u95a2\u6570\u3092\u542b\u3080\uff09\u521d\u7b49\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u3044\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u967d\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a\">\u967d\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a<\/h4>\n<p>\u8907\u6570\u306e\u967d\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a\u3059\u308b\u306b\u306f\uff0c<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">xmin<\/span><span class=\"p\">,<\/span> <span class=\"n\">xmax<\/span><span class=\"p\">)),<\/span> \r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">g<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">xmin<\/span><span class=\"p\">,<\/span> <span class=\"n\">xmax<\/span><span class=\"p\">)),<\/span> \r\n    <span class=\"o\">...<\/span>\r\n<span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<p>\u306e\u3088\u3046\u306b\u3002<\/p>\n<p>\u307e\u305f\u8907\u6570\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3068\u51e1\u4f8b\u304c\u8868\u793a\u3055\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u3079\u304d\u95a2\u6570\">\u3079\u304d\u95a2\u6570<\/h4>\n<p>\u307e\u305a\uff0c$y = x^{-1}$ \u306e\u30b0\u30e9\u30d5\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-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">line<\/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=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">5<\/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=\"o\">-<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span> <span class=\"mi\">10<\/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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9708 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-04.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$y=x^{-1}$ \u306e\u30b0\u30e9\u30d5\u306e $x\uff1d0$ \u4ed8\u8fd1\uff0c$y \\rightarrow -\\infty$ \u3068 $y \\rightarrow +\\infty$ \u3092\u7e26\u306e\u76f4\u7dda\u3067\u3064\u306a\u3044\u3067\u3057\u307e\u3046\u3002<\/p>\n<h5 id=\"\u4e0d\u9023\u7d9a\u70b9\u3092\u3064\u306a\u3052\u306a\u3044\u5bfe\u7b56\">\u4e0d\u9023\u7d9a\u70b9\u3092\u3064\u306a\u3052\u306a\u3044\u5bfe\u7b56<\/h5>\n<p><code>detect_poles=True<\/code> \u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u3064\u3051\uff0c\u3055\u3089\u306b <code>n<\/code> \u306e\u5024\u3092\u5927\u304d\u3081\u306b\u3059\u308b\u3068\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\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[10]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">line<\/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=\"n\">detect_poles<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">,<\/span> <span class=\"n\">n<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1e4<\/span><span class=\"p\">),<\/span> \r\n         <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">5<\/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=\"o\">-<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span> <span class=\"mi\">10<\/span><span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9709 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-05.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$y = x^{-2}, \\ x^{-1}, \\ x^2, \\ x^3$ \u306e\u30b0\u30e9\u30d5\u4f8b\u3002\uff08\u51e1\u4f8b <code>label<\/code> \u306b $\\LaTeX$ \u8a18\u6cd5\u3092\u4f7f\u3063\u3066\u3044\u307e\u3059\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[11]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">\/<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'$x^{-2}$'<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">line<\/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=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'$x^{-1}$'<\/span><span class=\"p\">,<\/span> <span class=\"n\">detect_poles<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">,<\/span> <span class=\"n\">n<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1e4<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">5<\/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=\"o\">-<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span> <span class=\"mi\">10<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'\u3079\u304d\u95a2\u6570\u306e\u30b0\u30e9\u30d5'<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9710 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-06.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$\\displaystyle y = \\sqrt{x}, \\ \\frac{1}{\\sqrt{x}}$ \u306e\u30b0\u30e9\u30d5\u4f8b\u3002<br \/>\n\uff08<code>\\<\/code> \u3067\u59cb\u307e\u308b $\\LaTeX$ \u30b3\u30de\u30f3\u30c9\u3092\u4f7f\u3046\u969b\u306f\uff0c\u5ff5\u306e\u305f\u3081 <code>r<\/code> \u304b\u3089\u59cb\u3081\u307e\u3059\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[12]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/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=\"mi\">5<\/span><span class=\"p\">),<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$\\sqrt<\/span><span class=\"si\">{x}<\/span><span class=\"s1\">$'<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">line<\/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=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.0001<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$1\/\\sqrt<\/span><span class=\"si\">{x}<\/span><span class=\"s1\">$'<\/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=\"mi\">5<\/span><span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9711 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-07.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u6307\u6570\u95a2\u6570\">\u6307\u6570\u95a2\u6570<\/h4>\n<p>$y = e^{-x}, \\ e^x$ \u306e\u30b0\u30e9\u30d5\u4f8b\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[13]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">exp<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'$e^{-x}$'<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">exp<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'$e^<\/span><span class=\"si\">{x}<\/span><span class=\"s1\">$'<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">5<\/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=\"mi\">5<\/span><span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9712 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-08.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u5bfe\u6570\u95a2\u6570\">\u5bfe\u6570\u95a2\u6570<\/h4>\n<p>$y = \\log x$ \u306e\u30b0\u30e9\u30d5\u4f8b\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[14]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">log<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.0001<\/span><span class=\"p\">,<\/span> <span class=\"mi\">10<\/span><span class=\"p\">),<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$\\log x$'<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">10<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span> <span class=\"n\">legend<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9713 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-09.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u4e09\u89d2\u95a2\u6570\">\u4e09\u89d2\u95a2\u6570<\/h4>\n<p>$ y = \\sin x, \\ \\cos x, \\ \\tan x $ \u306e\u30b0\u30e9\u30d5\u4f8b\u3002<\/p>\n<p>$\\tan x$ \u306e\u4e0d\u9023\u7d9a\u70b9\u306e\u51e6\u7406\u306f <code>detect_poles = True<\/code> \u3067\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[15]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'$\\sin x$'<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'$\\cos x$'<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">tan<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$\\tan x$'<\/span><span class=\"p\">,<\/span> <span class=\"n\">detect_poles<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/span><span class=\"o\">+<\/span><span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9714 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-10.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h5 id=\"\u4e3b\u76ee\u76db\u30fb\u526f\u76ee\u76db\u306e\u30ab\u30b9\u30bf\u30de\u30a4\u30ba\">\u4e3b\u76ee\u76db\u30fb\u526f\u76ee\u76db\u306e\u30ab\u30b9\u30bf\u30de\u30a4\u30ba<\/h5>\n<p>\u30b0\u30e9\u30d5\u306e\u30b9\u30bf\u30a4\u30eb\u306e\u8a73\u7d30\u306a\u8a2d\u5b9a\u5909\u66f4\u306f SPB \u306b\u306f\u5099\u308f\u3063\u3066\u3044\u306a\u3044\u3088\u3046\u3067\u3059\u306e\u3067\uff0c\u30d0\u30c3\u30af\u30a8\u30f3\u30c9\u306e Matplotlib \u306e <code>ax<\/code> \u3067\u8a73\u7d30\u8a2d\u5b9a\u3092\u884c\u3063\u3066\u307f\u307e\u3059\u3002<\/p>\n<p>\u3053\u3053\u3067\u306f\uff0c\u6a2a\u8ef8\u4e3b\u76ee\u76db\u3092 $\\pi$ \u3054\u3068\uff0c\u6a2a\u8ef8\u526f\u76ee\u76db\u3092 $\\frac{\\pi}{2}$ \u3054\u3068\uff0c\u7e26\u8ef8\u526f\u76ee\u76db\u3092 $1$ \u3054\u3068\u306b\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[16]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u304a\u307e\u3058\u306a\u3044\u3002\u3053\u308c\u3067 ax \u304c\u4f7f\u3048\u308b\u3002<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u4e3b\u76ee\u76db<\/span>\r\n<span class=\"n\">Pi<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">float<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">Pi<\/span><span class=\"p\">,<\/span>     <span class=\"o\">-<\/span><span class=\"n\">Pi<\/span><span class=\"p\">,<\/span>      <span class=\"mi\">0<\/span><span class=\"p\">,<\/span>     <span class=\"n\">Pi<\/span><span class=\"p\">,<\/span>      <span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">Pi<\/span><span class=\"p\">],<\/span> \r\n    <span class=\"p\">[<\/span><span class=\"s1\">'$-2\\pi$'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'$-\\pi$'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'$0$'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'$\\pi$'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'$2\\pi$'<\/span><span class=\"p\">])<\/span>\r\n\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">matplotlib.ticker<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">MultipleLocator<\/span>\r\n<span class=\"c1\"># \u6a2a\u8ef8\u526f\u76ee\u76db\u3092 \u03c0\/4 \u3054\u3068\u306b<\/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_minor_locator<\/span><span class=\"p\">(<\/span><span class=\"n\">MultipleLocator<\/span><span class=\"p\">(<\/span><span class=\"n\">Pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span>\r\n<span class=\"c1\"># \u7e26\u8ef8\u526f\u76ee\u76db\u3092 1 \u3054\u3068\u306b<\/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_minor_locator<\/span><span class=\"p\">(<\/span><span class=\"n\">MultipleLocator<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'$\\sin x$'<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'$\\cos x$'<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">tan<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$\\tan x$'<\/span><span class=\"p\">,<\/span> <span class=\"n\">detect_poles<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/span><span class=\"o\">+<\/span><span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ax<\/span> <span class=\"c1\"># ax \u306e\u8a2d\u5b9a\u3092\u53cd\u6620<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9715 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-11.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h5 id=\"\u53c2\u8003\uff1a\u30b0\u30ea\u30c3\u30c9\u306e\u30ab\u30b9\u30bf\u30de\u30a4\u30ba--ax.grid()\">\u53c2\u8003\uff1a\u30b0\u30ea\u30c3\u30c9\u306e\u30ab\u30b9\u30bf\u30de\u30a4\u30ba <code>ax.grid()<\/code><\/h5>\n<p>\u4e0a\u306e\u51fa\u529b\u7d50\u679c\u3092\u307f\u308b\u3068\uff0c\u4e3b\u76ee\u76db\u3068\u526f\u76ee\u76db\u3067\u306f\u30b0\u30ea\u30c3\u30c9\u306e\u30b9\u30bf\u30a4\u30eb\u304c\u7570\u306a\u3063\u3066\u3044\u308b\u3088\u3046\u3067\u3059\u3002\u3053\u306e\u3078\u3093\u306e\u30ab\u30b9\u30bf\u30de\u30a4\u30ba\u306f<\/p>\n<ul>\n<li><code>ax.grid()<\/code><\/li>\n<\/ul>\n<h5 id=\"\u53c2\u8003\uff1a$x$-\u8ef8\u30fb$y$-\u8ef8\u306e\u8868\u793a-ax.axhline(0)-ax.axvline(0)\">\u53c2\u8003\uff1a$x$ \u8ef8\u30fb$y$ \u8ef8\u306e\u8868\u793a <code>ax.axhline(0)<\/code> <code>ax.axvline(0)<\/code><\/h5>\n<p>\u307e\u305f\uff0cPython \u306e\u30b0\u30e9\u30d5\u4f5c\u6210\u754c\u9688\u3067\u306f\uff0c$x$ \u8ef8\uff08$y = 0$\uff09\u3084 $y$ \u8ef8\uff08$x = 0$\uff09\u3092\uff08\u683c\u5b50\u7dda\u3068\u306f\u533a\u5225\u3057\u3066\uff09\u8868\u793a\u3055\u305b\u308b\u7fd2\u6163\u306f\u306a\u3044\u3088\u3046\u3067\u3059\u3002\u3053\u306e\u3042\u305f\u308a\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066\u5bfe\u5fdc\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>$x$ \u8ef8\uff08$y = 0$\uff09\u306e\u8868\u793a <code>ax.axhline(0)<\/code><\/li>\n<li>$y$ \u8ef8\uff08$x = 0$\uff09\u306e\u8868\u793a <code>ax.axvline(0)<\/code><\/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[17]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u304a\u307e\u3058\u306a\u3044\u3002\u3053\u308c\u3067 ax \u304c\u4f7f\u3048\u308b\u3002<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u4e3b\u76ee\u76db<\/span>\r\n<span class=\"n\">Pi<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">float<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">Pi<\/span><span class=\"p\">,<\/span>     <span class=\"o\">-<\/span><span class=\"n\">Pi<\/span><span class=\"p\">,<\/span>      <span class=\"mi\">0<\/span><span class=\"p\">,<\/span>     <span class=\"n\">Pi<\/span><span class=\"p\">,<\/span>      <span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">Pi<\/span><span class=\"p\">],<\/span> \r\n    <span class=\"p\">[<\/span><span class=\"s1\">'$-2\\pi$'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'$-\\pi$'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'$0$'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'$\\pi$'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'$2\\pi$'<\/span><span class=\"p\">])<\/span>\r\n\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">matplotlib.ticker<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">MultipleLocator<\/span>\r\n<span class=\"c1\"># \u6a2a\u8ef8\u526f\u76ee\u76db\u3092 \u03c0\/4 \u3054\u3068\u306b<\/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_minor_locator<\/span><span class=\"p\">(<\/span><span class=\"n\">MultipleLocator<\/span><span class=\"p\">(<\/span><span class=\"n\">Pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span>\r\n<span class=\"c1\"># \u7e26\u8ef8\u526f\u76ee\u76db\u3092 1 \u3054\u3068\u306b<\/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_minor_locator<\/span><span class=\"p\">(<\/span><span class=\"n\">MultipleLocator<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># x\u8ef8 y\u8ef8\u306f dashed \u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">axhline<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'k'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">axvline<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'k'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u306f\u4e3b\u76ee\u76db\u526f\u76ee\u76db\u3068\u3082\u540c\u3058\u30b9\u30bf\u30a4\u30eb\u3067\u76ee\u7acb\u305f\u306a\u304f<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'lightgray'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"n\">which<\/span><span class=\"o\">=<\/span><span class=\"s1\">'both'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'$\\sin x$'<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'$\\cos x$'<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">tan<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$\\tan x$'<\/span><span class=\"p\">,<\/span> <span class=\"n\">detect_poles<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/span><span class=\"o\">+<\/span><span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">grid<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span> <span class=\"c1\"># \u4e00\u65e6 False \u306b\u3057\u3066...<\/span>\r\n    <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ax<\/span>     <span class=\"c1\"># ax \u306e\u8a2d\u5b9a\u3092\u53cd\u6620<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9717 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-12.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u9006\u4e09\u89d2\u95a2\u6570\">\u9006\u4e09\u89d2\u95a2\u6570<\/h4>\n<ul>\n<li>$y = \\sin^{-1} x = \\arcsin x =$ <code>asin(x)<\/code>\n<ul>\n<li>\u5b9a\u7fa9\u57df\u306f $\\displaystyle-1 \\leq x \\leq 1$<\/li>\n<li>\u5024\u57df\u306f $\\displaystyle -\\frac{\\pi}{2} \\leq y \\leq \\frac{\\pi}{2}$<\/li>\n<\/ul>\n<\/li>\n<li>$y = \\cos^{-1} x = \\arccos x =$ <code>acos(x)<\/code>\n<ul>\n<li>\u5b9a\u7fa9\u57df\u306f $\\displaystyle-1 \\leq x \\leq 1$<\/li>\n<li>\u5024\u57df\u306f $\\displaystyle0 \\leq y \\leq \\pi$<\/li>\n<\/ul>\n<\/li>\n<li>$y = \\tan^{-1} x = \\arctan x =$ <code>atan(x)<\/code>\n<ul>\n<li>\u5b9a\u7fa9\u57df\u306f $\\displaystyle-\\infty &lt; x &lt; \\infty$<\/li>\n<li>\u5024\u57df\u306f $\\displaystyle-\\frac{\\pi}{2} \\leq y \\leq \\frac{\\pi}{2}$<\/li>\n<\/ul>\n<\/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[18]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"c1\"># \u7e26\u8ef8\u4e3b\u76ee\u76db<\/span>\r\n<span class=\"n\">Pi<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">float<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_yticks<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"n\">Pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span>      <span class=\"mi\">0<\/span><span class=\"p\">,<\/span>     <span class=\"n\">Pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span>      <span class=\"n\">Pi<\/span><span class=\"p\">],<\/span> \r\n    <span class=\"p\">[<\/span><span class=\"s1\">'$-\\pi\/2$'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'$0$'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'$\\pi\/2$'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'$\\pi$'<\/span><span class=\"p\">])<\/span>\r\n<span class=\"c1\"># \u7e26\u8ef8\u526f\u76ee\u76db<\/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_minor_locator<\/span><span class=\"p\">(<\/span><span class=\"n\">MultipleLocator<\/span><span class=\"p\">(<\/span><span class=\"n\">Pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">4<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u4e3b\u76ee\u76db<\/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_major_locator<\/span><span class=\"p\">(<\/span><span class=\"n\">MultipleLocator<\/span><span class=\"p\">(<\/span><span class=\"mi\">5<\/span><span class=\"p\">))<\/span>\r\n<span class=\"c1\"># \u6a2a\u8ef8\u526f\u76ee\u76db<\/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_minor_locator<\/span><span class=\"p\">(<\/span><span class=\"n\">MultipleLocator<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># x\u8ef8 y\u8ef8\u306f dashed \u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">axhline<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'k'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">axvline<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'k'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u306f\u4e3b\u76ee\u76db\u526f\u76ee\u76db\u3068\u3082\u540c\u3058\u30b9\u30bf\u30a4\u30eb\u3067\u76ee\u7acb\u305f\u306a\u304f<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'lightgray'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"n\">which<\/span><span class=\"o\">=<\/span><span class=\"s1\">'both'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">asin<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$\\arcsin x$'<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">acos<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$\\arccos x$'<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">atan<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span> <span class=\"mi\">10<\/span><span class=\"p\">),<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$\\arctan x$'<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">7<\/span><span class=\"p\">,<\/span> <span class=\"mi\">7<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"n\">pi<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">grid<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span> <span class=\"c1\"># \u4e00\u65e6 False \u306b\u3057\u3066...<\/span>\r\n    <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ax<\/span>     <span class=\"c1\"># ax \u306e\u8a2d\u5b9a\u3092\u53cd\u6620<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9718 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-13.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u53cc\u66f2\u7dda\u95a2\u6570\">\u53cc\u66f2\u7dda\u95a2\u6570<\/h4>\n<p>$y = \\sinh x, \\ \\cosh x, \\ \\tanh x$ \u306e\u30b0\u30e9\u30d5\u4f8b\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[19]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"c1\"># \u7e26\u8ef8\u4e3b\u76ee\u76db<\/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_major_locator<\/span><span class=\"p\">(<\/span><span class=\"n\">MultipleLocator<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span>\r\n<span class=\"c1\"># \u7e26\u8ef8\u526f\u76ee\u76db<\/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_minor_locator<\/span><span class=\"p\">(<\/span><span class=\"n\">MultipleLocator<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u4e3b\u76ee\u76db<\/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_major_locator<\/span><span class=\"p\">(<\/span><span class=\"n\">MultipleLocator<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span>\r\n<span class=\"c1\"># \u6a2a\u8ef8\u526f\u76ee\u76db<\/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_minor_locator<\/span><span class=\"p\">(<\/span><span class=\"n\">MultipleLocator<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># x\u8ef8 y\u8ef8\u306f dashed \u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">axhline<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'k'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">axvline<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'k'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u306f\u4e3b\u76ee\u76db\u526f\u76ee\u76db\u3068\u3082\u540c\u3058\u30b9\u30bf\u30a4\u30eb\u3067\u76ee\u7acb\u305f\u306a\u304f<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'lightgray'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"n\">which<\/span><span class=\"o\">=<\/span><span class=\"s1\">'both'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">sinh<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$\\sinh x$'<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">cosh<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$\\cosh x$'<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">tanh<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$\\tanh x$'<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">5<\/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=\"o\">-<\/span><span class=\"mi\">7<\/span><span class=\"p\">,<\/span> <span class=\"mi\">7<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">grid<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span> <span class=\"c1\"># \u4e00\u65e6 False \u306b\u3057\u3066...<\/span>\r\n    <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ax<\/span>     <span class=\"c1\"># ax \u306e\u8a2d\u5b9a\u3092\u53cd\u6620<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9719 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-14.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u9006\u53cc\u66f2\u7dda\u95a2\u6570\">\u9006\u53cc\u66f2\u7dda\u95a2\u6570<\/h4>\n<ul>\n<li>$ y = \\sinh^{-1} x = \\mbox{arsinh}\\ x = $ <code>asinh(x)<\/code>\n<ul>\n<li>\u5b9a\u7fa9\u57df\u306f $ -\\infty &lt; x &lt; \\infty$<\/li>\n<li>\u5024\u57df\u306f $-\\infty &lt; y &lt; \\infty$<\/li>\n<\/ul>\n<\/li>\n<li>$ y = \\cosh^{-1} x = \\mbox{arcosh}\\ x = $ <code>acosh(x)<\/code>\n<ul>\n<li>\u5b9a\u7fa9\u57df\u306f $ 1 \\leq x &lt; \\infty$<\/li>\n<li>\u5024\u57df\u306f $0 \\leq y &lt; \\infty$<\/li>\n<\/ul>\n<\/li>\n<li>$ y = \\tanh^{-1} x = \\mbox{artanh}\\ x = $ <code>atanh(x)<\/code>\n<ul>\n<li>\u5b9a\u7fa9\u57df\u306f $ -1 &lt; x &lt; 1$<\/li>\n<li>\u5024\u57df\u306f $-\\infty &lt; y &lt; \\infty$<\/li>\n<\/ul>\n<\/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[20]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"c1\"># \u7e26\u8ef8\u4e3b\u76ee\u76db<\/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_major_locator<\/span><span class=\"p\">(<\/span><span class=\"n\">MultipleLocator<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># \u6a2a\u8ef8\u4e3b\u76ee\u76db<\/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_major_locator<\/span><span class=\"p\">(<\/span><span class=\"n\">MultipleLocator<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># x\u8ef8 y\u8ef8\u306f dashed \u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">axhline<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'k'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">axvline<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'k'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u306f\u4e3b\u76ee\u76db\u526f\u76ee\u76db\u3068\u3082\u540c\u3058\u30b9\u30bf\u30a4\u30eb\u3067\u76ee\u7acb\u305f\u306a\u304f<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'lightgray'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"n\">which<\/span><span class=\"o\">=<\/span><span class=\"s1\">'both'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">asinh<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span> <span class=\"mi\">10<\/span><span class=\"p\">),<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$\\sinh^{-1} x$'<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">acosh<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/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=\"sa\">r<\/span><span class=\"s1\">'$\\cosh^{-1} x$'<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">atanh<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mf\">0.99999<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.99999<\/span><span class=\"p\">),<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$\\tanh^{-1} x$'<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">7<\/span><span class=\"p\">,<\/span> <span class=\"mi\">7<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">grid<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span> <span class=\"c1\"># \u4e00\u65e6 False \u306b\u3057\u3066...<\/span>\r\n    <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ax<\/span>     <span class=\"c1\"># ax \u306e\u8a2d\u5b9a\u3092\u53cd\u6620<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9720 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-15.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u9670\u95a2\u6570\u306e\u30b0\u30e9\u30d5-implicit_2d()\">\u9670\u95a2\u6570\u306e\u30b0\u30e9\u30d5 <code>implicit_2d()<\/code><\/h3>\n<p>\u4f8b\u3068\u3057\u3066\uff0c$x^2 + y^2 = 1$ \u306e\u30af\u3099\u30e9\u30d5\u3092\u63cf\u304d\u307e\u3059\u3002$y$ \u306b\u3064\u3044\u3066\u89e3\u3044\u3066\u967d\u95a2\u6570\u306e\u5f62\u306b\u3057\u305f\u308a\uff0c\u4ee5\u4e0b\u3067\u8ff0\u3079\u308b\u3088\u3046\u306a\u5a92\u4ecb\u5909\u6570\u8868\u793a\u306b\u3057\u306a\u304f\u3066\u3082\uff0c\u9670\u95a2\u6570\u306e\u307e\u307e\uff0c\u30b0\u30e9\u30d5\u306b\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u9670\u95a2\u6570 $f(x, y) = 0$ \u3092 <code>(x, xmin, xmax)<\/code>, <code>(y, ymin, ymax)<\/code> \u306e\u7bc4\u56f2\u3067\u63cf\u304f\u66f8\u5f0f\u306f&#8230;<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">implicit_2d<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">xmin<\/span><span class=\"p\">,<\/span> <span class=\"n\">xmax<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"n\">ymin<\/span><span class=\"p\">,<\/span> <span class=\"n\">ymax<\/span><span class=\"p\">)))<\/span>\r\n<\/pre>\n<\/div>\n<p>$f(x, y) \\equiv x^2 + y^2 &#8211; 1 = 0$ \u3068\u3057\u3066\u30d7\u30ed\u30c3\u30c8\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[21]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">implicit_2d<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> \r\n                <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mf\">1.2<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.2<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mf\">1.2<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.2<\/span><span class=\"p\">)<\/span>\r\n               <span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9721 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-16.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u7e26\u6a2a\u6bd4\u30fb\u30b5\u30a4\u30ba\u306e\u8a2d\u5b9a-aspect-size\">\u7e26\u6a2a\u6bd4\u30fb\u30b5\u30a4\u30ba\u306e\u8a2d\u5b9a <code>aspect<\/code> <code>size<\/code><\/h4>\n<p>\u7e26\u6a2a\u306e\u6bd4 <code>aspect<\/code> \u3092\u8a2d\u5b9a\u3057\u3066\u5186\u3089\u3057\u304f\u898b\u3048\u308b\u3088\u3046\u306b\u3057\u307e\u3059\u3002<code>size<\/code> \u3082\u8a2d\u5b9a\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[22]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">implicit_2d<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> \r\n                <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mf\">1.2<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.2<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mf\">1.2<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.2<\/span><span class=\"p\">)<\/span>\r\n               <span class=\"p\">),<\/span> \r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">6.4<\/span><span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9722 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-17.svg\" alt=\"\" width=\"640\" height=\"640\" \/><\/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=\"\u5a92\u4ecb\u5909\u6570\u8868\u793a\u306e\u30b0\u30e9\u30d5-line_parametric_2d()\">\u5a92\u4ecb\u5909\u6570\u8868\u793a\u306e\u30b0\u30e9\u30d5 <code>line_parametric_2d()<\/code><\/h3>\n<p>\u534a\u5f84 $1$ \u306e\u5186\u306e\u65b9\u7a0b\u5f0f\u306f $x^2 +y^2 = 1$ \u3066\u3099\u3059\u3002\u3053\u306e\u5186\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5a92\u4ecb\u5909\u6570\u8868\u793a\u306b\u3057\u3066\u63cf\u304d\u307e\u3059\u3002<\/p>\n<p>$$ x=\\cos t, \\quad y=\\sin t \\quad (0 \\leq t \\leq 2\\pi) $$<\/p>\n<p>\u66f8\u5f0f\u306f&#8230;<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">line_parametric_2d<\/span><span class=\"p\">((<\/span><span class=\"n\">x<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">),<\/span> <span class=\"n\">y<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">,<\/span> <span class=\"n\">tmin<\/span><span class=\"p\">,<\/span> <span class=\"n\">tmax<\/span><span class=\"p\">)))<\/span>\r\n<\/pre>\n<\/div>\n<p>\u30c7\u30d5\u30a9\u30eb\u30c8\u3067 <code>use_cm = True<\/code> \u306b\u306a\u3063\u3066\u3044\u308b\u306e\u3067\uff0c\u30ab\u30e9\u30fc\u30de\u30c3\u30d7\u304c\u4e0d\u8981\u306a\u3089 <code>False<\/code> \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[23]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">line_parametric_2d<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">),<\/span> <span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/span><span class=\"p\">),<\/span> <span class=\"n\">use_cm<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s2\">\"equal\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">6.4<\/span><span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9723 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-18.svg\" alt=\"\" width=\"640\" height=\"640\" \/><\/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=\"\u70b9\u30fb\u6570\u5024\u30c6\u3099\u30fc\u30bf\u306e\u30af\u3099\u30e9\u30d5-list_2d()\">\u70b9\u30fb\u6570\u5024\u30c6\u3099\u30fc\u30bf\u306e\u30af\u3099\u30e9\u30d5 <code>list_2d()<\/code><\/h3>\n<div class=\"highlight\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">list_2d<\/span><span class=\"p\">([<\/span><span class=\"n\">x1<\/span><span class=\"p\">,<\/span> <span class=\"o\">...<\/span><span class=\"p\">,<\/span> <span class=\"n\">xn<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"n\">y1<\/span><span class=\"p\">,<\/span> <span class=\"o\">...<\/span><span class=\"p\">,<\/span> <span class=\"n\">yn<\/span><span class=\"p\">]))<\/span>\r\n<\/pre>\n<\/div>\n<h4 id=\"\u6298\u308c\u7dda\u30b0\u30e9\u30d5\">\u6298\u308c\u7dda\u30b0\u30e9\u30d5<\/h4>\n<p>\u4ee5\u4e0b\u306e\u4f8b\u3067\u306f\uff0c\u914d\u5217 <code>X<\/code> \u306b \u5ea7\u6a19\u306e\u5024\uff0c\u914d\u5217 <code>Y<\/code> \u306b \u5ea7\u6a19\u306e\u5024\u3092\u5165\u308c\u3066\uff0c6\u500b\u306e\u70b9\u3092\u3064\u306a\u3044\u305f\u3099\u6298\u308c\u7dda\u30af\u3099\u30e9\u30d5\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[24]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">X1<\/span> <span class=\"o\">=<\/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\">6<\/span><span class=\"p\">)]<\/span>\r\n<span class=\"n\">Y1<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/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\">6<\/span><span class=\"p\">)]<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">list_2d<\/span><span class=\"p\">(<\/span><span class=\"n\">X1<\/span><span class=\"p\">,<\/span> <span class=\"n\">Y1<\/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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9724 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-19.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u6563\u5e03\u56f3\uff08\u7dda\u3067\u3064\u306a\u304c\u306a\u3044\uff09scatter-=-True\">\u6563\u5e03\u56f3\uff08\u7dda\u3067\u3064\u306a\u304c\u306a\u3044\uff09<code>scatter = True<\/code><\/h4>\n<p>\u30aa\u30d7\u30b7\u30e7\u30f3 <code>scatter = True<\/code> \u3092\u8a2d\u5b9a\u3057\u3066\u5404\u70b9\u3092\u7dda\u3067\u3064\u306a\u304c\u305a\u306b\uff0c\u8d64\u8272 <code>{'color':'red'}<\/code> \u3067\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u4f8b\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[25]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">list_2d<\/span><span class=\"p\">(<\/span><span class=\"n\">X1<\/span><span class=\"p\">,<\/span> <span class=\"n\">Y1<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'\u30c7\u30fc\u30bf'<\/span><span class=\"p\">,<\/span> <span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'red'<\/span><span class=\"p\">},<\/span> <span class=\"n\">scatter<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">legend<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9725 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-20.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u30d5\u30a1\u30a4\u30eb\u304b\u3089\u6570\u5024\u30c7\u30fc\u30bf\u3092\u8aad\u307f\u8fbc\u3093\u3067\u30d7\u30ed\u30c3\u30c8\">\u30d5\u30a1\u30a4\u30eb\u304b\u3089\u6570\u5024\u30c7\u30fc\u30bf\u3092\u8aad\u307f\u8fbc\u3093\u3067\u30d7\u30ed\u30c3\u30c8<\/h4>\n<p>\u3042\u3089\u304b\u3057\u3099\u3081\u4f5c\u6210\u3055\u308c\u305f\u6570\u5024\u30c7\u30fc\u30bf\u30d5\u30a1\u30a4\u30eb\u304b\u3089\u30c7\u30fc\u30bf\u3092\u8aad\u307f\u8fbc\u3093\u3066\u3099\u30af\u3099\u30e9\u30d5\u3092\u63cf\u304f\u3053\u3068\u3082\u3066\u3099\u304d\u307e\u3059\u3002<\/p>\n<p>\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30c6\u30ad\u30b9\u30c8\u30d5\u30a1\u30a4\u30eb <code>mydata2.txt<\/code> \u304c\uff08\u3053\u306e\u30ce\u30fc\u30c8\u30d6\u30c3\u30af\u30d5\u30a1\u30a4\u30eb\u3068\u540c\u3058\u30d5\u30a9\u30eb\u30c0\u306b\uff09\u3042\u308b\u3068\u3057\u307e\u3059\u3002\uff08\u6388\u696d\u3067\u306f\u4e8b\u524d\u306b <code>mydata2.txt<\/code> \u3082\u540c\u3058\u30d5\u30a9\u30eb\u30c0\u306b\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3057\u3066\u304a\u304d\u307e\u3059\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[26]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"o\">!<\/span> cat mydata2.txt\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>0  0\r\n1  1\r\n2  4\r\n3  9\r\n4 16\r\n5 25<\/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<h5 id=\"np.loadtxt()-\u3067\u8aad\u307f\u8fbc\u307f\"><code>np.loadtxt()<\/code> \u3067\u8aad\u307f\u8fbc\u307f<\/h5>\n<p>\u6570\u5024\u30c7\u30fc\u30bf\u306e\u66f8\u304d\u8fbc\u307f\u30fb\u8aad\u307f\u8fbc\u307f\u306b\u306f\uff0cNumPy \u306e <code>savetxt()<\/code> \u3084 <code>loadtxt()<\/code> \u3092\u4f7f\u3046\u3053\u3068\u306b\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[27]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"kn\">import<\/span> <span class=\"nn\">numpy<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">np<\/span>\r\n\r\n<span class=\"c1\"># \u30d5\u30a1\u30a4\u30eb mydata2.txt \u304b\u3089\u8aad\u307f\u8fbc\u307f\uff0cdata \u306b\u4ee3\u5165<\/span>\r\n<span class=\"n\">data<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">loadtxt<\/span><span class=\"p\">(<\/span><span class=\"s1\">'mydata2.txt'<\/span><span class=\"p\">)<\/span> \r\n<span class=\"n\">data<\/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[27]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>array([[ 0.,  0.],\r\n       [ 1.,  1.],\r\n       [ 2.,  4.],\r\n       [ 3.,  9.],\r\n       [ 4., 16.],\r\n       [ 5., 25.]])<\/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>\u8aad\u307f\u8fbc\u3093\u3060 <code>data<\/code> \u306e1\u5217\u76ee <code>data[:,0]<\/code> \u3092 $x$ \u5ea7\u6a19\u306b\uff0c2\u5217\u76ee <code>data[:,1]<\/code> \u3092 $y$ \u5ea7\u6a19\u306b\u3057\u3066\u6563\u5e03\u56f3\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[28]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># numpy.ndarray \u914d\u5217\u3067\u3042\u308c\u3070\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e00\u6319\u306b\u5217\u30c7\u30fc\u30bf\u3092\u6307\u5b9a\u53ef\u80fd<\/span>\r\n<span class=\"c1\"># data \u306e1\u5217\u76ee data[:,0] \u3092 x, 2\u5217\u76ee data[:,1] \u3092 y<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">list_2d<\/span><span class=\"p\">(<\/span><span class=\"n\">data<\/span><span class=\"p\">[:,<\/span><span class=\"mi\">0<\/span><span class=\"p\">],<\/span> <span class=\"n\">data<\/span><span class=\"p\">[:,<\/span><span class=\"mi\">1<\/span><span class=\"p\">],<\/span> <span class=\"s2\">\"\u30c7\u30fc\u30bf\"<\/span><span class=\"p\">,<\/span> \r\n            <span class=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"red\"<\/span><span class=\"p\">},<\/span> <span class=\"n\">scatter<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">legend<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9726 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-21.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304f-arrow_2d()\">\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304f <code>arrow_2d()<\/code><\/h3>\n<p>\u70b9 $(x, y) =$ <code>(x0, y0)<\/code> \u3092\u59cb\u70b9\u3068\u3057\uff0c\u6210\u5206 $\\boldsymbol{v} = (v_x, v_y) = $ <code>(vx, vy)<\/code> \u306e\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304f\u306b\u306f\uff0c<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">arrow_2d<\/span><span class=\"p\">((<\/span><span class=\"n\">x0<\/span><span class=\"p\">,<\/span> <span class=\"n\">y0<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">vx<\/span><span class=\"p\">,<\/span> <span class=\"n\">vy<\/span><span class=\"p\">)))<\/span>\r\n<\/pre>\n<\/div>\n<p>\u539f\u70b9\u3092\u59cb\u70b9\u3068\u3057\uff0c\u6210\u5206\u304c $v_x = 0.5, v_y = 1$ \u306e\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304f\u4f8b\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[29]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">arrow_2d<\/span><span class=\"p\">((<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)),<\/span> \r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">6.4<\/span><span class=\"p\">),<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9727 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-22.svg\" alt=\"\" width=\"640\" height=\"640\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u8907\u6570\u306e\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304f\u4f8b\u3002\u659c\u65b9\u6295\u5c04\u306e\u901f\u5ea6\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u3044\u3066\u307f\u307e\u3059\u3002<\/p>\n<p>\u9069\u5b9c\u7121\u6b21\u5143\u5316\u3092\u884c\u3063\u3066\uff0c\u659c\u65b9\u6295\u5c04\u306e\u4f4d\u7f6e $(x(t), y(t))$ \u3068\u901f\u5ea6 $(v_x(t), v_y(t))$ \u306f<\/p>\n<p>\\begin{eqnarray}<br \/>\nx &amp;=&amp; t \\\\<br \/>\ny &amp;=&amp; t &#8211; \\frac{1}{4} t^2 \\\\<br \/>\nv_x &amp;=&amp; 1 \\\\<br \/>\nv_y &amp;=&amp; 1 &#8211; \\frac{1}{2} t<br \/>\n\\end{eqnarray}<\/p>\n<p>\u306e\u3088\u3046\u306b\u66f8\u3051\u308b\u3068\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[30]:<\/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\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">t<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">t<\/span> <span class=\"o\">-<\/span> <span class=\"n\">t<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"o\">\/<\/span><span class=\"mi\">4<\/span>\r\n\r\n<span class=\"k\">def<\/span> <span class=\"nf\">Vx<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"mi\">1<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">Vy<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"mi\">1<\/span> <span class=\"o\">-<\/span> <span class=\"n\">t<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/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[31]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">arrow_2d<\/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\">Y<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">)),<\/span> <span class=\"p\">(<\/span><span class=\"n\">Vx<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">),<\/span> <span class=\"n\">Vy<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">)),<\/span> \r\n             <span class=\"n\">rendering_kw<\/span><span class=\"o\">=<\/span><span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'b'<\/span><span class=\"p\">}),<\/span> \r\n    <span class=\"n\">arrow_2d<\/span><span class=\"p\">((<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">)),<\/span> <span class=\"p\">(<\/span><span class=\"n\">Vx<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"n\">Vy<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">)),<\/span> \r\n             <span class=\"n\">rendering_kw<\/span><span class=\"o\">=<\/span><span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'b'<\/span><span class=\"p\">}),<\/span>\r\n    <span class=\"n\">arrow_2d<\/span><span class=\"p\">((<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">)),<\/span> <span class=\"p\">(<\/span><span class=\"n\">Vx<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">),<\/span> <span class=\"n\">Vy<\/span><span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">)),<\/span> \r\n             <span class=\"n\">rendering_kw<\/span><span class=\"o\">=<\/span><span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'b'<\/span><span class=\"p\">}),<\/span>\r\n    <span class=\"n\">arrow_2d<\/span><span class=\"p\">((<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"p\">)),<\/span> <span class=\"p\">(<\/span><span class=\"n\">Vx<\/span><span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"n\">Vy<\/span><span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"p\">)),<\/span> \r\n             <span class=\"n\">rendering_kw<\/span><span class=\"o\">=<\/span><span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'b'<\/span><span class=\"p\">}),<\/span>\r\n    <span class=\"n\">arrow_2d<\/span><span class=\"p\">((<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"mi\">4<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"mi\">4<\/span><span class=\"p\">)),<\/span> <span class=\"p\">(<\/span><span class=\"n\">Vx<\/span><span class=\"p\">(<\/span><span class=\"mi\">4<\/span><span class=\"p\">),<\/span> <span class=\"n\">Vy<\/span><span class=\"p\">(<\/span><span class=\"mi\">4<\/span><span class=\"p\">)),<\/span> \r\n             <span class=\"n\">rendering_kw<\/span><span class=\"o\">=<\/span><span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'b'<\/span><span class=\"p\">}),<\/span>\r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.4<\/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=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span> <span class=\"n\">legend<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9728 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-23.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e\u3088\u3046\u306b\uff0c<code>arrow_2d()<\/code> \u3067\u306f\u8907\u6570\u306e\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304f\u969b\u306b\u5c11\u3057\u624b\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002\u307e\u305f\uff0c\u597d\u307f\u306e\u554f\u984c\u3067\u306f\u3042\u308a\u307e\u3059\u304c\uff0c\u30d9\u30af\u30c8\u30eb\u3092\u592a\u304f\u3059\u308b\u3068\u4f55\u3068\u306a\u304f\u4e38\u307f\u3092\u5e2f\u3073\u305f\u77e2\u5370\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u30c7\u30d5\u30a9\u30eb\u30c8\u306e\u51e1\u4f8b\u3082\u30c7\u30d0\u30c3\u30b0\u7528\u4ee5\u5916\u306b\u306f\u7279\u306b\u5fc5\u8981\u3068\u3055\u308c\u308b\u6a5f\u4f1a\u306f\u5c11\u306a\u3044\u304b\u3068\u601d\u308f\u308c\u308b\u3057\uff0c\u672c\u7a3f\u57f7\u7b46\u6642\u70b9\u3067\u306f\uff0c\u30d5\u30a9\u30f3\u30c8\u306e\u554f\u984c\u3067\u65e5\u672c\u8a9e\u306e\u51e1\u4f8b\u3092\u8a2d\u5b9a\u3067\u304d\u307e\u305b\u3093\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[32]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">arrow_2d<\/span><span class=\"p\">((<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)),<\/span> \r\n    <span class=\"n\">arrow_2d<\/span><span class=\"p\">((<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"n\">rendering_kw<\/span><span class=\"o\">=<\/span><span class=\"p\">{<\/span><span class=\"s1\">'lw'<\/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=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9729 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-24.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u53c2\u8003\uff1aMatplotlib-\u6d41\u306b\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304f-ax.quiver()\">\u53c2\u8003\uff1aMatplotlib \u6d41\u306b\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304f <code>ax.quiver()<\/code><\/h4>\n<p>\u4ee5\u4e0b\u306e\u3088\u3046\u306b Matplotlib \u306e <code>ax.quiver()<\/code> \u3092\u4f7f\u3063\u3066\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304f\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[33]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># ax.quiver() \u7528\u306b\u30ea\u30b9\u30c8\u4f5c\u6210<\/span>\r\n<span class=\"c1\"># \u59cb\u70b9\u306e x, y \u5ea7\u6a19<\/span>\r\n<span class=\"n\">Xlist<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/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\">5<\/span><span class=\"p\">)]<\/span>\r\n<span class=\"n\">Ylist<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">Y<\/span><span class=\"p\">(<\/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\">5<\/span><span class=\"p\">)]<\/span>\r\n<span class=\"c1\"># \u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206<\/span>\r\n<span class=\"n\">Vxlist<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">Vx<\/span><span class=\"p\">(<\/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\">5<\/span><span class=\"p\">)]<\/span>\r\n<span class=\"n\">Vylist<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">Vy<\/span><span class=\"p\">(<\/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\">5<\/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[34]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u304a\u307e\u3058\u306a\u3044\u3002\u3053\u308c\u3067 ax \u304c\u4f7f\u3048\u308b\u3002<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"c1\"># Matplotlib \u3067\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304f<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">quiver<\/span><span class=\"p\">(<\/span><span class=\"n\">Xlist<\/span><span class=\"p\">,<\/span> <span class=\"n\">Ylist<\/span><span class=\"p\">,<\/span> <span class=\"n\">Vxlist<\/span><span class=\"p\">,<\/span> <span class=\"n\">Vylist<\/span><span class=\"p\">,<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"sa\">r<\/span><span class=\"s1\">'$\\vec<\/span><span class=\"si\">{v}<\/span><span class=\"s1\">$'<\/span><span class=\"p\">,<\/span>\r\n          <span class=\"c1\"># \u5168\u30d9\u30af\u30c8\u30eb\u306b\u8272\u3092\u4e00\u62ec\u6307\u5b9a<\/span>\r\n          <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"blue\"<\/span><span class=\"p\">,<\/span> \r\n          <span class=\"c1\"># \u30d9\u30af\u30c8\u30eb\u306e\u5f62\u72b6\u3082\u305d\u306e\u6c17\u306b\u306a\u308c\u3070\u7d30\u304b\u304f\u8a2d\u5b9a\u53ef\u80fd<\/span>\r\n          <span class=\"c1\"># width=0.02, <\/span>\r\n          <span class=\"c1\"># headaxislength=2.5, headlength=2.8,<\/span>\r\n          <span class=\"c1\"># \u4ee5\u4e0b\u306e3\u70b9\u30bb\u30c3\u30c8\u3092\u66f8\u304b\u306a\u3044\u3068\u81ea\u52d5\u30b9\u30b1\u30fc\u30ea\u30f3\u30b0\u3055\u308c\u308b<\/span>\r\n          <span class=\"n\">angles<\/span><span class=\"o\">=<\/span><span class=\"s1\">'xy'<\/span><span class=\"p\">,<\/span> <span class=\"n\">scale_units<\/span><span class=\"o\">=<\/span><span class=\"s1\">'xy'<\/span><span class=\"p\">,<\/span> <span class=\"n\">scale<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ax<\/span><span class=\"p\">,<\/span> <span class=\"c1\"># ax \u3092\u53cd\u6620<\/span>\r\n         <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mf\">5.5<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">1.5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> \r\n         <span class=\"n\">aspect<\/span><span class=\"o\">=<\/span><span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span> <span class=\"n\">legend<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9730 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-25.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u8907\u6570\u306e\u30af\u3099\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a\">\u8907\u6570\u306e\u30af\u3099\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a<\/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<p>\u8907\u6570\u306e\u30af\u3099\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a\u3059\u308b\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<h4 id=\"\u8907\u6570\u306e\u967d\u95a2\u6570\u3092\u91cd\u306d\u3066\u8868\u793a\">\u8907\u6570\u306e\u967d\u95a2\u6570\u3092\u91cd\u306d\u3066\u8868\u793a<\/h4>\n<p>\u967d\u95a2\u6570 $y = x^2 &#8211; 1$ \u3068 $y = 4 x &#8211; 5$ \u306e 2 \u3064\u306e\u30af\u3099\u30e9\u30d5\u3092\u91cd\u306d\u3066\u63cf\u304d\u307e\u3059\u3002<\/p>\n<p>$x$ \u306e\u7bc4\u56f2\u306f\u72ec\u7acb\u306b\u6307\u5b9a\u53ef\u80fd\u3066\u3099\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[35]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">)),<\/span> \r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"mi\">4<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">5<\/span><span class=\"p\">,<\/span>  <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">3<\/span><span class=\"p\">)),<\/span> \r\n    <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">10<\/span><span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9731 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-26.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u6570\u5024\u30c7\u30fc\u30bf\u3068\u7406\u8ad6\u66f2\u7dda\u3092\u91cd\u306d\u3066\u8868\u793a\">\u6570\u5024\u30c7\u30fc\u30bf\u3068\u7406\u8ad6\u66f2\u7dda\u3092\u91cd\u306d\u3066\u8868\u793a<\/h4>\n<p>\u524d\u7bc0\u306e\u6570\u5024\u30c6\u3099\u30fc\u30bf\u30d5\u30a1\u30a4\u30eb <code>mydata2.txt<\/code> \u3068\u7406\u8ad6\u66f2\u7dda $y = x^2$ \u306e 2 \u3064\u306e\u30af\u3099\u30e9\u30d5<\/p>\n<ul>\n<li>\u6570\u5024\u30c7\u30fc\u30bf <code>list_2d()<\/code><\/li>\n<li>\u967d\u95a2\u6570 <code>line()<\/code><\/li>\n<\/ul>\n<p>\u3092\u91cd\u306d\u3066\u8868\u793a\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<h5 id=\"\u63cf\u304f\u9806\u756a\u3092\u6307\u5b9a-'zorder'\">\u63cf\u304f\u9806\u756a\u3092\u6307\u5b9a <code>'zorder'<\/code><\/h5>\n<p>\u8907\u6570\u306e\u30b0\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a\u3059\u308b\u969b\uff0c\u30aa\u30d7\u30b7\u30e7\u30f3 <code>'zorder'<\/code> \u3092\u4f7f\u3063\u3066\u63cf\u304b\u308c\u308b\u9806\u756a\u3092\u8abf\u6574\u3067\u304d\u307e\u3059\u3002<code>{'zorder':0}<\/code> \u3060\u3068\u6700\u521d\uff08\u3064\u307e\u308a\u6700\u80cc\u9762\uff09\u306b\u63cf\u304b\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[36]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">list_2d<\/span><span class=\"p\">(<\/span><span class=\"n\">data<\/span><span class=\"p\">[:,<\/span><span class=\"mi\">0<\/span><span class=\"p\">],<\/span> <span class=\"n\">data<\/span><span class=\"p\">[:,<\/span><span class=\"mi\">1<\/span><span class=\"p\">],<\/span> <span class=\"s2\">\"\u30c7\u30fc\u30bf\"<\/span><span class=\"p\">,<\/span> \r\n            <span class=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"blue\"<\/span><span class=\"p\">},<\/span> <span class=\"n\">scatter<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/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=\"mi\">5<\/span><span class=\"p\">),<\/span> <span class=\"s2\">\"\u7406\u8ad6\u66f2\u7dda\"<\/span><span class=\"p\">,<\/span> <span class=\"p\">{<\/span><span class=\"s1\">'zorder'<\/span><span class=\"p\">:<\/span><span class=\"mi\">0<\/span><span class=\"p\">})<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9732 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-27.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u3055\u307e\u3056\u307e\u306a\u30b0\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a\">\u3055\u307e\u3056\u307e\u306a\u30b0\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a<\/h4>\n<p><code>graphics()<\/code> \u306e\u5f37\u529b\u306a\u3068\u3053\u308d\u306f\uff0c\u967d\u95a2\u6570 <code>line()<\/code> \u3060\u3051\u3067\u306a\u304f\uff0c\u5a92\u4ecb\u5909\u6570\u8868\u793a <code>line_parametric_2d()<\/code>\uff0c\u6570\u5024\u30c7\u30fc\u30bf <code>list_2d()<\/code>\uff0c\u30d9\u30af\u30c8\u30eb <code>arrow_2d()<\/code> \u306a\u3069\u3082\u5168\u3066\u91cd\u306d\u3066\u8868\u793a\u3067\u304d\u308b\u3068\u3053\u308d\u3067\u3059\u3002<\/p>\n<p>\u4f8b\u3048\u3070\uff0c\u524d\u63b2\u306e\u659c\u65b9\u6295\u5c04<\/p>\n<p>\\begin{eqnarray}<br \/>\nx &amp;=&amp; t \\\\<br \/>\ny &amp;=&amp; t &#8211; \\frac{1}{4} t^2 \\\\<br \/>\n\\therefore\\ \\ y &amp;=&amp; x &#8211; \\frac{1}{4} x^2<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3092\u4f7f\u3063\u3066\uff0c<\/p>\n<ul>\n<li>\u967d\u95a2\u6570 <code>line()<\/code><\/li>\n<li>\u5a92\u4ecb\u5909\u6570\u8868\u793a <code>line_parametric_2d()<\/code><\/li>\n<li>\u6570\u5024\u30c7\u30fc\u30bf <code>list_2d()<\/code><\/li>\n<li>\u30d9\u30af\u30c8\u30eb <code>arrow_2d()<\/code><\/li>\n<\/ul>\n<p>\u3092\u91cd\u306d\u3066\u8868\u793a\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<p><code>arrow_2d()<\/code> \u306e\u51e1\u4f8b\u306b\u306f\u65e5\u672c\u8a9e\u304c\u4f7f\u3048\u306a\u3044\u3088\u3046\u3067\u3059\u3002\u307e\u305f\uff0c<code>label=''<\/code> \u3067\u3082\u51e1\u4f8b\u306f\u975e\u8868\u793a\u306b\u306a\u3089\u305a\uff0c<code>show_in_legend=False<\/code> \u3068\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[37]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"c1\"># \u967d\u95a2\u6570\u3092\u5c11\u3057\u4e0a\u306b\u305a\u3089\u3057\u3066<\/span>\r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span> <span class=\"o\">-<\/span> <span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"o\">\/<\/span><span class=\"mi\">4<\/span> <span class=\"o\">+<\/span> <span class=\"mf\">0.5<\/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=\"mi\">4<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'\u967d\u95a2\u6570'<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"c1\"># \u5a92\u4ecb\u5909\u6570\u8868\u793a<\/span>\r\n    <span class=\"n\">line_parametric_2d<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">4<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'\u5a92\u4ecb\u5909\u6570\u8868\u793a'<\/span><span class=\"p\">,<\/span> <span class=\"n\">use_cm<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"c1\"># \u6570\u5024\u30c7\u30fc\u30bf<\/span>\r\n    <span class=\"n\">list_2d<\/span><span class=\"p\">([<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/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\">5<\/span><span class=\"p\">)],<\/span> \r\n            <span class=\"p\">[<\/span><span class=\"n\">Y<\/span><span class=\"p\">(<\/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\">5<\/span><span class=\"p\">)],<\/span> <span class=\"s1\">'\u6570\u5024\u30c7\u30fc\u30bf'<\/span><span class=\"p\">,<\/span> <span class=\"n\">scatter<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"c1\"># \u30d9\u30af\u30c8\u30eb<\/span>\r\n    <span class=\"n\">arrow_2d<\/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\">Y<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">)),<\/span> <span class=\"p\">(<\/span><span class=\"n\">Vx<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">),<\/span> <span class=\"n\">Vy<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">)),<\/span> <span class=\"s1\">'vector'<\/span><span class=\"p\">,<\/span>\r\n             <span class=\"n\">rendering_kw<\/span><span class=\"o\">=<\/span><span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'b'<\/span><span class=\"p\">}),<\/span> \r\n    <span class=\"n\">arrow_2d<\/span><span class=\"p\">((<\/span><span class=\"n\">X<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"n\">Y<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">)),<\/span> <span class=\"p\">(<\/span><span class=\"n\">Vx<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"n\">Vy<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">)),<\/span> <span class=\"n\">show_in_legend<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span>\r\n             <span class=\"n\">rendering_kw<\/span><span class=\"o\">=<\/span><span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'b'<\/span><span class=\"p\">}),<\/span>\r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.4<\/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=\"o\">-<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9733 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-28.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u6975\u5ea7\u6a19\u8868\u793a\u306e\u30b0\u30e9\u30d5-line_polar()\">\u6975\u5ea7\u6a19\u8868\u793a\u306e\u30b0\u30e9\u30d5 <code>line_polar()<\/code><\/h3>\n<p>\u6975\u5ea7\u6a19\u8868\u793a $r = r(\\varphi)$ \u306e\u30b0\u30e9\u30d5\u306f<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">line_polar<\/span><span class=\"p\">(<\/span><span class=\"n\">r<\/span><span class=\"p\">(<\/span><span class=\"n\">phi<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">phi<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/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<h4 id=\"\u7126\u70b9\u3092\u539f\u70b9\u3068\u3057\u305f\u6955\u5186\u306e\u30af\u3099\u30e9\u30d5\">\u7126\u70b9\u3092\u539f\u70b9\u3068\u3057\u305f\u6955\u5186\u306e\u30af\u3099\u30e9\u30d5<\/h4>\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>\u592a\u967d\u304b\u3089\u306e\u4e07\u6709\u5f15\u529b\u3092\u53d7\u3051\u3066\u904b\u52d5\u3059\u308b\u60d1\u661f\u306f\uff0c\u592a\u967d\uff08\u4e8c\u4f53\u554f\u984c\u3066\u3099\u306f\u8cea\u91cf\u4e2d\u5fc3\uff09\u3092\u7126\u70b9\u306e\u4e00\u3064\u3068\u3057\u305f\u6955\u5186\u904b\u52d5\u3092\u63cf\u3044\u3066\u904b\u52d5\u3057\u307e\u3059\u3002<br \/>\n\u7126\u70b9\u306e\u4e00\u3064\u3092\u539f\u70b9\u3068\u3057\uff0c\u9577\u534a\u5f84 $a$\uff0c\u96e2\u5fc3\u7387 $e$ \u306e\u6955\u5186\u306e\u65b9\u7a0b\u5f0f\u306f\uff0c\u6975\u5ea7\u6a19 $r$\uff0c$\\varphi$ \u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304b\u3099\u3066\u3099\u304d\u307e\u3059\u3002<\/p>\n<p>$$ r= \\frac{a (1\u2212e^2)}{ 1 + e\\cos\\phi}$$<\/p>\n<h4 id=\"\u51a5\u738b\u661f\uff0c\u6d77\u738b\u661f\u306e\u8ecc\u9053\">\u51a5\u738b\u661f\uff0c\u6d77\u738b\u661f\u306e\u8ecc\u9053<\/h4>\n<p>\u3055\u3066\uff0c\u304b\u3064\u3066\u306f\u7b2c9\u60d1\u661f\uff0c\u73fe\u5728\u3067\u306f\u6e96\u60d1\u661f\u306e\u4e00\u3064\u3067\u3042\u308b\u51a5\u738b\u661f\u3082\u6955\u5186\u8ecc\u9053\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n<p>\u307e\u305a\uff0c\u7126\u70b9\u3092\u539f\u70b9\u3068\u3057\u305f\u6975\u5ea7\u6a19\u8868\u793a\u306e\u6955\u5186\u306e\u5f0f\u3092\u95a2\u6570\u3068\u3057\u3066\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[38]:<\/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\">'a e phi'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># elliptical\uff08\u6955\u5186\uff09\u306e e \u3092\u3064\u3051\u3066...<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">re<\/span><span class=\"p\">(<\/span><span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">e<\/span><span class=\"p\">,<\/span> <span class=\"n\">phi<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">a<\/span><span class=\"o\">*<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">e<\/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\">1<\/span><span class=\"o\">+<\/span><span class=\"n\">e<\/span><span class=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">phi<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"n\">re<\/span><span class=\"p\">(<\/span><span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">e<\/span><span class=\"p\">,<\/span> <span class=\"n\">phi<\/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[38]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle \\frac{a \\left(1 &#8211; e^{2}\\right)}{e \\cos{\\left(\\phi \\right)} + 1}$<\/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>\u51a5\u738b\u661f\u306e\u8ecc\u9053\u9577\u534a\u5f84 $\ud835\udc4e_P=39.445 \\mbox{au}$\uff0c\u96e2\u5fc3\u7387 $\ud835\udc52_P=0.250$<br \/>\n\u3092\u4f7f\u3063\u3066\u51a5\u738b\u661f\u306e\u8ecc\u9053\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u53c2\u8003\uff1a<a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E5%86%A5%E7%8E%8B%E6%98%9F\">\u51a5\u738b\u661f &#8211; Wikipedia<\/a><\/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[39]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u51a5\u738b\u661f\u306e\u8ecc\u9053\u9577\u534a\u5f84\u3068\u96e2\u5fc3\u7387<\/span>\r\n<span class=\"n\">aP<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">39.445<\/span>\r\n<span class=\"n\">eP<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.250<\/span>\r\n\r\n<span class=\"n\">Pluto<\/span> <span class=\"o\">=<\/span> <span class=\"n\">line_polar<\/span><span class=\"p\">(<\/span><span class=\"n\">re<\/span><span class=\"p\">(<\/span><span class=\"n\">aP<\/span><span class=\"p\">,<\/span> <span class=\"n\">eP<\/span><span class=\"p\">,<\/span> <span class=\"n\">phi<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">phi<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/span><span class=\"p\">),<\/span> \r\n               <span class=\"s1\">'\u51a5\u738b\u661f'<\/span><span class=\"p\">,<\/span> <span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'green'<\/span><span class=\"p\">})<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">Pluto<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">6.4<\/span><span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9734 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-29.svg\" alt=\"\" width=\"640\" height=\"640\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3067\u306f\uff0c\u3053\u306e\u51a5\u738b\u661f\u306e\u8ecc\u9053\u3068\uff0c\u305d\u306e\u5185\u5074\u3092\u307e\u308f\u308b\u6d77\u738b\u661f\u306e\u8ecc\u9053\u3092\u91cd\u306d\u3066\u63cf\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u6d77\u738b\u661f\u306e\u8ecc\u9053\u9577\u534a\u5f84\u306f $a_N=30.181 \\mbox{au}$\uff0c\u96e2\u5fc3\u7387\u306f $e_N=0.0097$ \u3068\u5c0f\u3055\u3044\u306e\u3067\u7c21\u5358\u306e\u305f\u3081\u306b $e_N=0$ \u3068\u3057\u3066\u6271\u3044\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u53c2\u8003\uff1a<a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E6%B5%B7%E7%8E%8B%E6%98%9F\">\u6d77\u738b\u661f &#8211; Wikipedia<\/a><\/li>\n<\/ul>\n<p>\u5b9f\u969b\u306e2\u3064\u306e\u5929\u4f53\u306e\u8ecc\u9053\u306f\u540c\u3058\u5e73\u9762\u4e0a\u306b\u3042\u308a\u307e\u305b\u3093\u304c\uff0c\u592a\u967d\u304b\u3089\u306e\u8ddd\u96e2\u306e\u307f\u3092\u307f\u308b\u305f\u3081\u306b\uff0c\u3053\u3053\u3067\u306f\u540c\u4e00\u5e73\u9762\u4e0a\u306b\u63cf\u304d\u307e\u3059\u3002<\/p>\n<h5 id=\"\u30b0\u30ea\u30c3\u30c9\u306e\u975e\u8868\u793a-grid-=-False\">\u30b0\u30ea\u30c3\u30c9\u306e\u975e\u8868\u793a <code>grid = False<\/code><\/h5>\n<p>\u539f\u70b9\u306b\u3042\u308b\u592a\u967d\u306e\u4f4d\u7f6e\u3092\u8868\u3059\u305f\u3081\u306b\uff0c$x$ \u8ef8\u3068 $y$ \u8ef8\u306e\u7dda\u3092\u5f15\u304d\uff0c\u30b0\u30ea\u30c3\u30c9\u3092\u975e\u8868\u793a\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[40]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u6d77\u738b\u661f\u306e\u8ecc\u9053\u9577\u534a\u5f84\u3068\u96e2\u5fc3\u7387<\/span>\r\n<span class=\"n\">aN<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">30.181<\/span>\r\n<span class=\"n\">eN<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n<span class=\"n\">Neptune<\/span> <span class=\"o\">=<\/span> <span class=\"n\">line_polar<\/span><span class=\"p\">(<\/span><span class=\"n\">re<\/span><span class=\"p\">(<\/span><span class=\"n\">aN<\/span><span class=\"p\">,<\/span> <span class=\"n\">eN<\/span><span class=\"p\">,<\/span> <span class=\"n\">phi<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">phi<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"o\">*<\/span><span class=\"n\">pi<\/span><span class=\"p\">),<\/span> \r\n               <span class=\"s1\">'\u6d77\u738b\u661f'<\/span><span class=\"p\">,<\/span> <span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'blue'<\/span><span class=\"p\">})<\/span>\r\n\r\n<span class=\"n\">Sun<\/span> <span class=\"o\">=<\/span> <span class=\"n\">list_2d<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">],[<\/span><span class=\"mi\">0<\/span><span class=\"p\">],<\/span> <span class=\"s1\">'\u592a\u967d'<\/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\">'zorder'<\/span><span class=\"p\">:<\/span><span class=\"mi\">10<\/span><span class=\"p\">},<\/span> <span class=\"n\">scatter<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u304a\u307e\u3058\u306a\u3044\u3002\u3053\u308c\u3067 ax \u304c\u4f7f\u3048\u308b\u3002<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">(<\/span><span class=\"n\">figsize<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">6.4<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># x\u8ef8 y\u8ef8\u306f dashed \u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">axhline<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'k'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">axvline<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'k'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">Pluto<\/span><span class=\"p\">,<\/span> <span class=\"n\">Neptune<\/span><span class=\"p\">,<\/span> <span class=\"n\">Sun<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ax<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span> <span class=\"n\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9735 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-30.svg\" alt=\"\" width=\"640\" height=\"640\" \/><\/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=\"\u53c2\u8003\uff1a\u5404\u7a2e\u56f3\u5f62\u306e\u8868\u793a\u3068\u5857\u308a\u3064\u3076\u3057-geometry()\">\u53c2\u8003\uff1a\u5404\u7a2e\u56f3\u5f62\u306e\u8868\u793a\u3068\u5857\u308a\u3064\u3076\u3057 <code>geometry()<\/code><\/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=\"\u70b9-geometry(Point2D(x0,-y0))\">\u70b9 <code>geometry(Point2D(x0, y0))<\/code><\/h4>\n<p>\u5ea7\u6a19 $(x, y) = $ <code>(x0, y0)<\/code> \u306b\u70b9\u3092\u63cf\u304f\u3002<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Point2D<\/span><span class=\"p\">(<\/span><span class=\"n\">x0<\/span><span class=\"p\">,<\/span> <span class=\"n\">y0<\/span><span class=\"p\">)))<\/span>\r\n<\/pre>\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[41]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Point2D<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span><span class=\"mi\">0<\/span><span class=\"p\">),<\/span> \r\n             <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s1\">'\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u306f\u5857\u308a\u3064\u3076\u3057'<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Point2D<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span><span class=\"mi\">0<\/span><span class=\"p\">),<\/span>\r\n             <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s1\">'fill=False \u3067\u5857\u308a\u3064\u3076\u3057\u306a\u3057'<\/span><span class=\"p\">,<\/span> <span class=\"n\">fill<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9736 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-31.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u7dda\u5206-geometry(Segment())\">\u7dda\u5206 <code>geometry(Segment())<\/code><\/h4>\n<p>\u70b9 <code>(x0, y0)<\/code> \u304b\u3089 <code>(x1, y1)<\/code> \u307e\u3067\u306e\u7dda\u5206\u3092\u63cf\u304f\u3002<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Segment<\/span><span class=\"p\">((<\/span><span class=\"n\">x0<\/span><span class=\"p\">,<\/span> <span class=\"n\">y0<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x1<\/span><span class=\"p\">,<\/span> <span class=\"n\">y1<\/span><span class=\"p\">))))<\/span>\r\n<\/pre>\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[42]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Segment<\/span><span class=\"p\">((<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">)),<\/span> <span class=\"s1\">''<\/span><span class=\"p\">),<\/span>  \r\n    <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Segment<\/span><span class=\"p\">((<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)),<\/span> <span class=\"s1\">''<\/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\">'lw'<\/span><span class=\"p\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'zorder'<\/span><span class=\"p\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">})<\/span> <span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3088\u308a\u4e0a\u306b<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9737 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-32.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u591a\u89d2\u5f62-geometry(Polygon())\">\u591a\u89d2\u5f62 <code>geometry(Polygon())<\/code><\/h4>\n<p><code>(x0, y0)<\/code> \u3092\u4e2d\u5fc3\u3068\u3057\uff0c\u300c\u534a\u5f84\u300d<code>R<\/code> \u306e\u6b63 <code>N<\/code> \u89d2\u5f62<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Polygon<\/span><span class=\"p\">((<\/span><span class=\"n\">x0<\/span><span class=\"p\">,<\/span> <span class=\"n\">y0<\/span><span class=\"p\">),<\/span> <span class=\"n\">R<\/span><span class=\"p\">,<\/span> <span class=\"n\">n<\/span> <span class=\"o\">=<\/span> <span class=\"n\">N<\/span><span class=\"p\">)))<\/span>\r\n<\/pre>\n<\/div>\n<p><code>p1 = (x1, y1), p2, ...<\/code> \u3092\u9802\u70b9\u3068\u3057\u305f\u591a\u89d2\u5f62<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Polygon<\/span><span class=\"p\">(<\/span><span class=\"n\">p1<\/span><span class=\"p\">,<\/span> <span class=\"n\">p2<\/span><span class=\"p\">,<\/span> <span class=\"o\">...<\/span><span class=\"p\">)))<\/span>\r\n<\/pre>\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[43]:<\/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=\"p\">,<\/span> <span class=\"n\">p2<\/span><span class=\"p\">,<\/span> <span class=\"n\">p3<\/span><span class=\"p\">,<\/span> <span class=\"n\">p4<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"mi\">3<\/span><span class=\"p\">,<\/span> <span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Polygon<\/span><span class=\"p\">((<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span><span class=\"mi\">0<\/span><span class=\"p\">),<\/span> <span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"n\">n<\/span><span class=\"o\">=<\/span><span class=\"mi\">8<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'\u6b638\u89d2\u5f62'<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Polygon<\/span><span class=\"p\">(<\/span><span class=\"n\">p1<\/span><span class=\"p\">,<\/span> <span class=\"n\">p2<\/span><span class=\"p\">,<\/span> <span class=\"n\">p3<\/span><span class=\"p\">,<\/span> <span class=\"n\">p4<\/span><span class=\"p\">),<\/span> \r\n             <span class=\"s1\">'\u9802\u70b9\u306e\u5ea7\u6a19\u3092\u6307\u5b9a'<\/span><span class=\"p\">,<\/span> <span class=\"n\">fill<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Point2D<\/span><span class=\"p\">(<\/span><span class=\"n\">p1<\/span><span class=\"p\">)),<\/span>\r\n    <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Point2D<\/span><span class=\"p\">(<\/span><span class=\"n\">p2<\/span><span class=\"p\">)),<\/span>\r\n    <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Point2D<\/span><span class=\"p\">(<\/span><span class=\"n\">p3<\/span><span class=\"p\">)),<\/span>\r\n    <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Point2D<\/span><span class=\"p\">(<\/span><span class=\"n\">p4<\/span><span class=\"p\">)),<\/span>\r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span> <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">3.5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9738 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-33.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u6955\u5186-geometry(Ellipse())\">\u6955\u5186 <code>geometry(Ellipse())<\/code><\/h4>\n<p>\u70b9 <code>(x0, y0)<\/code> \u3092\u4e2d\u5fc3\u3068\u3057\uff0c\u9577\u534a\u5f84\uff08\u6a2a\u534a\u5f84\uff09<code>a<\/code>\uff0c\u5358\u534a\u5f84\uff08\u7e26\u534a\u5f84\uff09<code>b<\/code> \u306e\u6955\u5186<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Ellipse<\/span><span class=\"p\">((<\/span><span class=\"n\">x0<\/span><span class=\"p\">,<\/span> <span class=\"n\">y0<\/span><span class=\"p\">),<\/span> <span class=\"n\">hradius<\/span> <span class=\"o\">=<\/span> <span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">vradius<\/span> <span class=\"o\">=<\/span> <span class=\"n\">b<\/span><span class=\"p\">)))<\/span>\r\n<\/pre>\n<\/div>\n<p>\u70b9 <code>(x0, y0)<\/code> \u3092\u4e2d\u5fc3\u3068\u3057\uff0c\u9577\u534a\u5f84\uff08\u6a2a\u534a\u5f84\uff09<code>a<\/code>\uff0c\u96e2\u5fc3\u7387 <code>e<\/code> \u306e\u6955\u5186<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Ellipse<\/span><span class=\"p\">((<\/span><span class=\"n\">x0<\/span><span class=\"p\">,<\/span> <span class=\"n\">y0<\/span><span class=\"p\">),<\/span> <span class=\"n\">hradius<\/span> <span class=\"o\">=<\/span> <span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">eccentricity<\/span> <span class=\"o\">=<\/span> <span class=\"n\">e<\/span><span class=\"p\">)))<\/span>\r\n<\/pre>\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[44]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Ellipse<\/span><span class=\"p\">((<\/span><span class=\"o\">-<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">2<\/span><span class=\"p\">),<\/span> <span class=\"n\">hradius<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"n\">vradius<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span><span class=\"p\">),<\/span> \r\n             <span class=\"s1\">'$a=2, b=1$'<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Ellipse<\/span><span class=\"p\">((<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">),<\/span> <span class=\"n\">hradius<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">3<\/span><span class=\"p\">,<\/span> <span class=\"n\">eccentricity<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.8<\/span><span class=\"p\">),<\/span> \r\n             <span class=\"s1\">'$a = 3, e = 0.8$'<\/span><span class=\"p\">,<\/span> <span class=\"n\">fill<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9739 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-34.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u5186-geometry(Circle())\">\u5186 <code>geometry(Circle())<\/code><\/h4>\n<p>\u70b9 <code>(x0, y0)<\/code> \u3092\u4e2d\u5fc3\u3068\u3057\uff0c\u534a\u5f84 <code>r<\/code> \u306e\u5186<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span><span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Circle<\/span><span class=\"p\">((<\/span><span class=\"n\">x0<\/span><span class=\"p\">,<\/span> <span class=\"n\">y0<\/span><span class=\"p\">),<\/span> <span class=\"n\">r<\/span><span class=\"p\">)))<\/span>\r\n<\/pre>\n<\/div>\n<h5 id=\"\u67a0\u7dda\u8272-'edgecolor'-\u3068\u80cc\u666f\u8272-'facecolor'\">\u67a0\u7dda\u8272 <code>'edgecolor'<\/code> \u3068\u80cc\u666f\u8272 <code>'facecolor'<\/code><\/h5>\n<p><code>Circle()<\/code> \u306b\u9650\u3089\u305a\uff0c\u5168\u3066\u306e\u56f3\u5f62\u306e\u67a0\u7dda\u306e\u8272\u3092 <code>'edgecolor'<\/code> \u3067\uff0c\u5857\u308a\u6f70\u3057\uff08\u80cc\u666f\uff09\u306e\u8272\u3092 <code>'facecolor'<\/code> \u3067\u305d\u308c\u305e\u308c\u72ec\u7acb\u306b\u8a2d\u5b9a\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[45]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Circle<\/span><span class=\"p\">((<\/span><span class=\"mi\">1<\/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\">rendering_kw<\/span><span class=\"o\">=<\/span><span class=\"p\">{<\/span><span class=\"s1\">'lw'<\/span><span class=\"p\">:<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> \r\n                           <span class=\"s1\">'edgecolor'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'black'<\/span><span class=\"p\">,<\/span> \r\n                           <span class=\"s1\">'facecolor'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'yellow'<\/span><span class=\"p\">}),<\/span> \r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9740 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-35.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u9818\u57df\u306e\u5857\u308a\u3064\u3076\u3057-implicit_2d()\">\u9818\u57df\u306e\u5857\u308a\u3064\u3076\u3057 <code>implicit_2d()<\/code><\/h3>\n<h4 id=\"2\u672c\u306e\u967d\u95a2\u6570\u3067\u631f\u307e\u308c\u305f\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3059\">2\u672c\u306e\u967d\u95a2\u6570\u3067\u631f\u307e\u308c\u305f\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3059<\/h4>\n<p>\u3053\u3053\u3067\u306f\uff0c<code>implicit_2d()<\/code> \u3092\u4f7f\u3063\u3066\uff0c$x$ \u8ef8\uff08$y = 0$\uff09\u3068 $y = f(x)$ \u3067\u631f\u307e\u308c\u305f\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<p>$0.5 \\leq x \\leq 2$ \u3067 $0 \\leq y \\leq f(x)$ \u306e\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3059\u4f8b\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[46]:<\/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>\r\n    <span class=\"k\">return<\/span> <span class=\"mf\">0.6<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span> <span class=\"o\">+<\/span> <span class=\"mf\">0.4<\/span><span class=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/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[47]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">implicit_2d<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"c1\"># \u9818\u57df\u3092\u793a\u3059\u4e0d\u7b49\u5f0f<\/span>\r\n        <span class=\"p\">(<\/span><span class=\"mi\">0<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span> <span class=\"o\">&amp;<\/span> <span class=\"p\">(<\/span><span class=\"n\">y<\/span> <span class=\"o\">&lt;=<\/span><span class=\"n\">f<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)),<\/span> \r\n        <span class=\"c1\"># \u5857\u308a\u3064\u3076\u3059 x \u306e\u7bc4\u56f2<\/span>\r\n        <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> \r\n        <span class=\"c1\"># \u4e0d\u7b49\u5f0f\u304c\u6e80\u305f\u3055\u308c\u3066\u3044\u308b\u304b\u3092\u63a2\u3059 y \u306e\u7bc4\u56f2<\/span>\r\n        <span class=\"p\">(<\/span><span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.2<\/span><span class=\"p\">),<\/span> \r\n        <span class=\"n\">adaptive<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">,<\/span> <span class=\"c1\"># \u3053\u308c\u3092\u3064\u3051\u306a\u3044\u3068\u8b66\u544a\u304c\u51fa\u308b<\/span>\r\n        <span class=\"c1\"># \u5857\u308a\u3064\u3076\u3057\u306e\u8272<\/span>\r\n        <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s1\">'yellow'<\/span>\r\n    <span class=\"p\">),<\/span>\r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.2<\/span><span class=\"p\">,<\/span> <span class=\"mf\">2.5<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.2<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.5<\/span><span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9741 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-36.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u6247\u5f62\u3092\u63cf\u3044\u3066\u5857\u308a\u3064\u3076\u3059\">\u6247\u5f62\u3092\u63cf\u3044\u3066\u5857\u308a\u3064\u3076\u3059<\/h4>\n<p>\u307e\u305a\uff0c\u6247\u5f62\u3092\uff0c\u5186\u5468\u306e\u4e00\u90e8\u3068\u539f\u70b9\u304b\u3089\u306e2\u672c\u306e\u76f4\u7dda\u3067\u56f2\u307e\u308c\u305f\u9818\u57df\u3068\u8003\u3048\u3066\u7e01\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\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[48]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u5916\u67a0<\/span>\r\n<span class=\"n\">Arc1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">line_parametric_2d<\/span><span class=\"p\">(<\/span>\r\n            <span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">),<\/span> <span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">,<\/span> <span class=\"n\">pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">6<\/span><span class=\"p\">,<\/span> <span class=\"n\">pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"s1\">''<\/span><span class=\"p\">,<\/span>\r\n            <span class=\"n\">use_cm<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">,<\/span> \r\n            <span class=\"n\">rendering_kw<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'black'<\/span><span class=\"p\">})<\/span>\r\n<span class=\"n\">Line1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Segment<\/span><span class=\"p\">((<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">6<\/span><span class=\"p\">),<\/span> <span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">6<\/span><span class=\"p\">))),<\/span> \r\n            <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">''<\/span><span class=\"p\">,<\/span>\r\n            <span class=\"n\">rendering_kw<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'black'<\/span><span class=\"p\">})<\/span>\r\n<span class=\"n\">Line2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Segment<\/span><span class=\"p\">((<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">3<\/span><span class=\"p\">))),<\/span> \r\n            <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">''<\/span><span class=\"p\">,<\/span>\r\n            <span class=\"n\">rendering_kw<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'black'<\/span><span class=\"p\">})<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">Arc1<\/span><span class=\"p\">,<\/span> <span class=\"n\">Line1<\/span><span class=\"p\">,<\/span> <span class=\"n\">Line2<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9742 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-37.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u6247\u5f62\u306e\u5185\u90e8\u3092\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\nx^2 + y^2 &amp;\\leq&amp; 1 \\\\<br \/>\ny &amp;\\geq&amp; \\tan\\frac{\\pi}{6} \\ x \\\\<br \/>\ny &amp;\\leq&amp; \\tan\\frac{\\pi}{3} \\ x<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3092\u6e80\u305f\u3059\u9818\u57df\u3068\u3057\u3066\uff0c<code>implicit_2d()<\/code> \u3067\u5857\u308a\u3064\u3076\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[49]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">FilledArea1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">implicit_2d<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"p\">((<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"o\">+<\/span><span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span> \r\n          <span class=\"o\">&amp;<\/span> <span class=\"p\">(<\/span><span class=\"n\">tan<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">6<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span>\r\n          <span class=\"o\">&amp;<\/span> <span class=\"p\">(<\/span><span class=\"n\">y<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"n\">tan<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">3<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span><span class=\"p\">)),<\/span> \r\n        <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">),<\/span> \r\n        <span class=\"n\">adaptive<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">,<\/span> \r\n        <span class=\"n\">color<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'yellow'<\/span><span class=\"p\">)<\/span> \r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">FilledArea1<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"n\">legend<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9743 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-38.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u67a0\u7dda\u3082\u91cd\u306d\u3066\u8868\u793a\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[50]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"c1\"># \u6247\u5f62\u5857\u308a\u3064\u3076\u3057\u90e8\u5206<\/span>\r\n    <span class=\"n\">FilledArea1<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"c1\"># \u67a0\u7dda\u90e8\u5206<\/span>\r\n    <span class=\"n\">Arc1<\/span><span class=\"p\">,<\/span> <span class=\"n\">Line1<\/span><span class=\"p\">,<\/span> <span class=\"n\">Line2<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span> <span class=\"p\">,<\/span> <span class=\"n\">legend<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9744 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-39.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u25cb\u7df4\u7fd2\uff1a\u30c9\u30c3\u30c6\u30f3\u30e1\u30a4\u30ab\u30a4\u3092\u5857\u308a\u3064\u3076\u3057\">\u25cb\u7df4\u7fd2\uff1a\u30c9\u30c3\u30c6\u30f3\u30e1\u30a4\u30ab\u30a4\u3092\u5857\u308a\u3064\u3076\u3057<\/h4>\n<p>\u51a5\u738b\u661f\u3068\u6d77\u738b\u661f\u306e\u8ecc\u9053\u306e\u30b0\u30e9\u30d5\u3092\u307f\u308b\u3068\uff0c\u8ecc\u9053\u304c\u4ea4\u5dee\u3057\u3066\u3044\u308b\u3002\u3053\u308c\u306f\uff0c\u3042\u308b\u671f\u9593\u51a5\u738b\u661f\u306e\u307b\u3046\u304c\u6d77\u738b\u661f\u3088\u308a\u592a\u967d\u306b\u8fd1\u3044\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u305d\u3053\u3067\uff0c\u4ee5\u4e0b\u306e\u6307\u793a\u306b\u5f93\u3063\u3066\u30b0\u30e9\u30d5\u3092\u4f5c\u6210\u305b\u3088\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<h5 id=\"1.-\u6d77\u738b\u661f\u3068\u51a5\u738b\u661f\u306e\u8ecc\u9053\u304c\u4ea4\u5dee\u3059\u308b\u70b9\u3092\u6c42\u3081\u308b\">1. \u6d77\u738b\u661f\u3068\u51a5\u738b\u661f\u306e\u8ecc\u9053\u304c\u4ea4\u5dee\u3059\u308b\u70b9\u3092\u6c42\u3081\u308b<\/h5>\n<p>\u7c21\u5358\u306e\u305f\u3081\uff0c\u6d77\u738b\u661f\u306f\u534a\u5f84 $a_N$ \u306e\u5186\u8ecc\u9053\u3068\u3057\uff0c\u5b9f\u969b\u306e2\u3064\u306e\u5929\u4f53\u306e\u8ecc\u9053\u306f\u540c\u3058\u5e73\u9762\u4e0a\u306b\u306a\u3044\u304c\uff0c\u592a\u967d\u304b\u3089\u306e\u8ddd\u96e2\u306e\u307f\u3092\u307f\u308b\u305f\u3081\u306b\uff0c\u3053\u3053\u3067\u306f\u540c\u4e00\u5e73\u9762\u4e0a\u306b\u63cf\u304f\u3053\u3068\u306b\u3059\u308b\u3002<\/p>\n<p>$$r(a, e, \\phi) = \\frac{a (1-e^2)}{1 + e \\cos\\phi}$$<\/p>\n<p>\u3068\u3057\uff0c<\/p>\n<p>$$ r(a_P, e_P, \\phi) = a_N$$<\/p>\n<p>\u3068\u306a\u308b $\\phi$ \u306e\u5024 $\\phi_{\\rm eq}$ (<code>phieq<\/code>) \u3092<code>nsolve()<\/code> \u3067\u6570\u5024\u7684\u306b\u6c42\u3081\u308b\u3002SymPy \u306b\u3088\u308b\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u306e\u6c42\u3081\u65b9\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u3092\u53c2\u7167\uff1a<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/python-%e3%81%a7%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/sympy-%e3%81%a7%e5%be%ae%e5%88%86%e7%a9%8d%e5%88%86%e3%83%bb%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%ae%e8%a7%a3\/#i-15\">\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3<\/a><\/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[51]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u6955\u5186\u306e\u6975\u5ea7\u6a19\u8868\u793a<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">re<\/span><span class=\"p\">(<\/span><span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">e<\/span><span class=\"p\">,<\/span> <span class=\"n\">phi<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">a<\/span><span class=\"o\">*<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">e<\/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\">1<\/span><span class=\"o\">+<\/span><span class=\"n\">e<\/span><span class=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">phi<\/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[52]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u51a5\u738b\u661f Pluto \u306e\u8ecc\u9053\u9577\u534a\u5f84\uff0c\u96e2\u5fc3\u7387<\/span>\r\n<span class=\"n\">aP<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">39.445<\/span>\r\n<span class=\"n\">eP<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.250<\/span>\r\n<span class=\"c1\"># \u6d77\u738b\u661f Neptune \u306e\u8ecc\u9053\u534a\u5f84<\/span>\r\n<span class=\"n\">aN<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">30.181<\/span>\r\n<span class=\"n\">eN<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/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[53]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># nsolve() \u3092\u4f7f\u3063\u3066\u6570\u5024\u7684\u306b\u89e3\u3092\u6c42\u3081\u308b<\/span>\r\n<span class=\"n\">phi_eq<\/span> <span class=\"o\">=<\/span> <span class=\"n\">nsolve<\/span><span class=\"p\">(<\/span><span class=\"n\">Eq<\/span><span class=\"p\">(<\/span><span class=\"n\">re<\/span><span class=\"p\">(<\/span><span class=\"n\">aP<\/span><span class=\"p\">,<\/span> <span class=\"n\">eP<\/span><span class=\"p\">,<\/span> <span class=\"n\">phi<\/span><span class=\"p\">),<\/span> <span class=\"n\">aN<\/span><span class=\"p\">),<\/span> <span class=\"n\">phi<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"nb\">float<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span>\r\n<span class=\"n\">phi_eq<\/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[53]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle 0.448599704341525$<\/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[54]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u3082\u3046\u4e00\u3064\u306e\u89e3\u306f...<\/span>\r\n<span class=\"n\">nsolve<\/span><span class=\"p\">(<\/span><span class=\"n\">Eq<\/span><span class=\"p\">(<\/span><span class=\"n\">re<\/span><span class=\"p\">(<\/span><span class=\"n\">aP<\/span><span class=\"p\">,<\/span> <span class=\"n\">eP<\/span><span class=\"p\">,<\/span> <span class=\"n\">phi<\/span><span class=\"p\">),<\/span> <span class=\"n\">aN<\/span><span class=\"p\">),<\/span> <span class=\"n\">phi<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"nb\">float<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/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[54]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle -0.448599704341525$<\/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>\u8ecc\u9053\u306e\u5bfe\u79f0\u6027\u304b\u3089\uff0c$- \\phi_{\\rm eq} &lt; \\phi &lt; + \\phi_{\\rm eq}$ \u306e\u9593\u306f\u51a5\u738b\u661f\u306e\u307b\u3046\u304c\u6d77\u738b\u661f\u3088\u308a\u592a\u967d\u306b\u8fd1\u3044\u3053\u3068\u306b\u306a\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<h5 id=\"2.-\u539f\u70b9\u30682\u3064\u306e\u8ecc\u9053\u306e\u4ea4\u70b9\u3092\u7d50\u3076\u76f4\u7dda\u30922\u672c\u5b9a\u7fa9\">2. \u539f\u70b9\u30682\u3064\u306e\u8ecc\u9053\u306e\u4ea4\u70b9\u3092\u7d50\u3076\u76f4\u7dda\u30922\u672c\u5b9a\u7fa9<\/h5>\n<p>\u4ea4\u70b9\u306e1\u3064\u306f<\/p>\n<ul>\n<li>$(a_N \\cos\\phi_{\\rm eq}, a_N \\sin \\phi_{\\rm eq})$\uff0c<\/li>\n<\/ul>\n<p>\u3082\u3046\u4e00\u3064\u306e\u4ea4\u70b9\u306f<\/p>\n<ul>\n<li>$(a_N \\cos\\phi_{\\rm eq}, -a_N \\sin \\phi_{\\rm eq})$<\/li>\n<\/ul>\n<p>\u3067\u3042\u308b\u304b\u3089\uff0c\u539f\u70b9\u3068\u4ea4\u70b9\u3092\u7d50\u3076\u76f4\u7dda\uff08\u7dda\u5206\uff09\u30921\u672c\u305a\u3064\uff0c\u8a082\u672c\u5b9a\u7fa9\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[55]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">LineA<\/span> <span class=\"o\">=<\/span> <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Segment<\/span><span class=\"p\">((<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">),<\/span> \r\n                         <span class=\"p\">(<\/span><span class=\"n\">aN<\/span><span class=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">phi_eq<\/span><span class=\"p\">),<\/span> <span class=\"n\">aN<\/span><span class=\"o\">*<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">phi_eq<\/span><span class=\"p\">))),<\/span> <span class=\"s1\">''<\/span><span class=\"p\">,<\/span>\r\n                 <span class=\"n\">rendering_kw<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'black'<\/span><span class=\"p\">})<\/span>\r\n<span class=\"n\">LineB<\/span> <span class=\"o\">=<\/span> <span class=\"n\">geometry<\/span><span class=\"p\">(<\/span><span class=\"n\">Segment<\/span><span class=\"p\">((<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">),<\/span> \r\n                         <span class=\"p\">(<\/span><span class=\"n\">aN<\/span><span class=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">phi_eq<\/span><span class=\"p\">),<\/span> <span class=\"o\">-<\/span><span class=\"n\">aN<\/span><span class=\"o\">*<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">phi_eq<\/span><span class=\"p\">))),<\/span> <span class=\"s1\">''<\/span><span class=\"p\">,<\/span>\r\n                 <span class=\"n\">rendering_kw<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'black'<\/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<h5 id=\"3.-\u5857\u308a\u3064\u3076\u3059\u6247\u5f62\u306e\u90e8\u5206\u3092\u5b9a\u7fa9\">3. \u5857\u308a\u3064\u3076\u3059\u6247\u5f62\u306e\u90e8\u5206\u3092\u5b9a\u7fa9<\/h5>\n<p>\u6700\u5f8c\u306b\uff0c\u6d77\u738b\u661f\u306e\u307b\u3046\u304c\u51a5\u738b\u661f\u3088\u308a\u592a\u967d\u304b\u3089\u9060\u3044\u671f\u9593\u306e\u6247\u5f62\u306e\u90e8\u5206\u3092\uff0c\u5857\u308a\u3064\u3076\u3059\u9818\u57df\u3068\u3057\u3066\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[56]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">FilledArea<\/span> <span class=\"o\">=<\/span> <span class=\"n\">implicit_2d<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"p\">((<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"o\">+<\/span><span class=\"n\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"n\">aN<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span> \r\n         <span class=\"o\">&amp;<\/span> <span class=\"p\">(<\/span><span class=\"n\">tan<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">phi_eq<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"n\">y<\/span><span class=\"p\">)<\/span> \r\n         <span class=\"o\">&amp;<\/span> <span class=\"p\">(<\/span><span class=\"n\">y<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"n\">tan<\/span><span class=\"p\">(<\/span><span class=\"n\">phi_eq<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span><span class=\"p\">)),<\/span> \r\n        <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\">aN<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">aN<\/span><span class=\"p\">,<\/span> <span class=\"n\">aN<\/span><span class=\"p\">),<\/span> \r\n        <span class=\"n\">adaptive<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">,<\/span> \r\n        <span class=\"n\">color<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'yellow'<\/span><span class=\"p\">,<\/span> <span class=\"n\">label<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'\u6d77\u738b\u661f\u304c\u9060\u3044\u671f\u9593'<\/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[57]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u304a\u307e\u3058\u306a\u3044\u3002\u3053\u308c\u3067 ax \u304c\u4f7f\u3048\u308b\u3002<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">(<\/span><span class=\"n\">figsize<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">6.4<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># x\u8ef8 y\u8ef8\u306f dashed \u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">axhline<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'k'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">axvline<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"o\">=<\/span><span class=\"s1\">'k'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ls<\/span><span class=\"o\">=<\/span><span class=\"s1\">'--'<\/span><span class=\"p\">,<\/span> <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">FilledArea<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">Pluto<\/span><span class=\"p\">,<\/span> <span class=\"n\">Neptune<\/span><span class=\"p\">,<\/span> <span class=\"n\">Sun<\/span><span class=\"p\">,<\/span> <span class=\"n\">LineA<\/span><span class=\"p\">,<\/span> <span class=\"n\">LineB<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ax<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span> <span class=\"n\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9745 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-40.svg\" alt=\"\" width=\"640\" height=\"640\" \/><\/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<h5 id=\"4.-\u6d77\u738b\u661f\u304c\u51a5\u738b\u661f\u3088\u308a\u592a\u967d\u304b\u3089\u9060\u3044\u671f\u9593\u3092\u6c42\u3081\u308b\">4. \u6d77\u738b\u661f\u304c\u51a5\u738b\u661f\u3088\u308a\u592a\u967d\u304b\u3089\u9060\u3044\u671f\u9593\u3092\u6c42\u3081\u308b<\/h5>\n<p>\u6d77\u738b\u661f\u306e\u516c\u8ee2\u5468\u671f\uff081\u5468 $2\\pi$ \u30e9\u30b8\u30a2\u30f3\u3067\uff09$T_N$ \u306e\u3046\u3061\uff0c$\\displaystyle \\frac{2\\phi_{\\rm eq}}{2 \\pi}$ \u306e\u9593\u306f\u6d77\u738b\u661f\u304c\u51a5\u738b\u661f\u3088\u308a\u9060\u3044\u304b\u3089<\/p>\n<p>$$t_1 = T_N \\times \\frac{\\phi_{\\rm eq}}{\\pi}$$<\/p>\n<p>\u3067\u4e0e\u3048\u3089\u308c\u308b\u6642\u9593 $t_1$ \u306e\u9593\u3060\u3051\uff0c\u6d77\u738b\u661f\u304c\u51a5\u738b\u661f\u3088\u308a\u592a\u967d\u304b\u3089\u9060\u3044\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n<p>\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066 $t_1$ (<code>t1<\/code>) \u3092\u6c42\u3081\u308b\u3002<\/p>\n<div class=\"highlight\">\n<pre><span class=\"c1\"># \u6d77\u738b\u661f\u306e\u516c\u8ee2\u5468\u671f\u306f\u4f55\u5e74\uff1f<\/span>\r\n<span class=\"n\">TN<\/span> <span class=\"o\">=<\/span> <span class=\"o\">...<\/span>\r\n\r\n<span class=\"c1\"># round() \u3067\u6570\u5024\u3092\u4e38\u3081\u308b<\/span>\r\n<span class=\"n\">t1<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">round<\/span><span class=\"p\">(<\/span><span class=\"n\">TN<\/span> <span class=\"o\">*<\/span> <span class=\"n\">phi_eq<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30e9\u30d5\u306b\u8868\u793a\u3055\u305b\u308b\u6e96\u5099<\/span>\r\n<span class=\"n\">mytext<\/span> <span class=\"o\">=<\/span> <span class=\"s2\">\"\u3053\u306e\u671f\u9593\u306f\"<\/span><span class=\"o\">+<\/span><span class=\"nb\">str<\/span><span class=\"p\">(<\/span><span class=\"n\">t1<\/span><span class=\"p\">)<\/span><span class=\"o\">+<\/span><span class=\"s2\">\"\u5e74\"<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30e9\u30d5\u306e x=10, y=0.5 \u304b\u3089\u306f\u3058\u307e\u308b\u30c6\u30ad\u30b9\u30c8\u3092\u66f8\u304f<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">text<\/span><span class=\"p\">(<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span> <span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"n\">mytext<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<p>\u3042\u308b\u3044\u306f\u30b0\u30e9\u30d5\u306e\u30bf\u30a4\u30c8\u30eb\u306b\u66f8\u3044\u3066\u3082\u3088\u3044\u3060\u308d\u3046\u3002<\/p>\n<p><code>title = '\u6d77\u738b\u661f\u304c\u51a5\u738b\u661f\u3088\u308a\u3082\u592a\u967d\u304b\u3089\u9060\u3044\u671f\u9593\u306f??\u5e74'<\/code><\/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[58]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><\/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[59]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><\/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>&nbsp;<\/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<h5 id=\"\u5b8c\u6210\u30a4\u30e1\u30fc\u30b8\">\u5b8c\u6210\u30a4\u30e1\u30fc\u30b8<\/h5>\n<p>\u3060\u3044\u305f\u3044\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u30b0\u30e9\u30d5\u304c\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9746 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Kansei-Image-1.svg\" alt=\"\" width=\"640\" height=\"640\" \/><\/p>\n<p><img decoding=\"async\" src=\"Kansei-Image.svg\" alt=\"\" width=\"100%\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u6708\u5225\u5e73\u5e74\u6c17\u6e29\u306e\u30ab\u30fc\u30d6\u30d5\u30a3\u30c3\u30c8\">\u6708\u5225\u5e73\u5e74\u6c17\u6e29\u306e\u30ab\u30fc\u30d6\u30d5\u30a3\u30c3\u30c8<\/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<p>\u5f18\u524d\u5e02\u306e\u6708\u5225\u5e73\u5e74\u6c17\u6e29\u306e\u30c6\u3099\u30fc\u30bf\u3092\u4f7f\u3063\u3066\u914d\u5217 <code>HiroT<\/code> \u3092\u4f5c\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u53c2\u8003\uff1a<a href=\"https:\/\/www.data.jma.go.jp\/obd\/stats\/etrn\/view\/nml_amd_ym.php?prec_no=31&amp;block_no=0166&amp;year=&amp;month=&amp;day=&amp;view=\">\u5f18\u524d\u3000\u5e73\u5e74\u5024\uff08\u5e74\u30fb\u6708\u3054\u3068\u306e\u5024\uff09\u3000\u4e3b\u306a\u8981\u7d20<\/a><\/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[60]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">Month<\/span> <span class=\"o\">=<\/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\">13<\/span><span class=\"p\">)]<\/span> <span class=\"c1\"># 12 \u307e\u3067\u306e\u3068\u304d\u306f 13 \u3068\u66f8\u304f<\/span>\r\n<span class=\"n\">HiroT<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mf\">1.5<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mf\">1.0<\/span><span class=\"p\">,<\/span>  <span class=\"mf\">2.3<\/span><span class=\"p\">,<\/span>  <span class=\"mf\">8.6<\/span><span class=\"p\">,<\/span> <span class=\"mf\">14.3<\/span><span class=\"p\">,<\/span> <span class=\"mf\">18.3<\/span><span class=\"p\">,<\/span>\r\n         <span class=\"mf\">22.3<\/span><span class=\"p\">,<\/span> <span class=\"mf\">23.5<\/span><span class=\"p\">,<\/span> <span class=\"mf\">19.4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">12.9<\/span><span class=\"p\">,<\/span>  <span class=\"mf\">6.5<\/span><span class=\"p\">,<\/span>  <span class=\"mf\">0.8<\/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[61]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">list_2d<\/span><span class=\"p\">(<\/span><span class=\"n\">Month<\/span><span class=\"p\">,<\/span> <span class=\"n\">HiroT<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'\u6708\u5225\u5e73\u5e74\u6c17\u6e29'<\/span><span class=\"p\">,<\/span> <span class=\"n\">scatter<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">legend<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9747 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-41.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306b\u3088\u308b\u30ab\u30fc\u30d6\u30d5\u30a3\u30c3\u30c8-scipy.optimize.curve_fit()\">\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306b\u3088\u308b\u30ab\u30fc\u30d6\u30d5\u30a3\u30c3\u30c8 <code>scipy.optimize.curve_fit()<\/code><\/h4>\n<p>\u30b0\u30e9\u30d5\u3092\u307f\u308b\u3068\uff0c\u6708\u5225\u5e73\u5e74\u57fa\u672c\u306f 12\u30f6\u6708\u5468\u671f\u306e\u6b63\u5f26\u95a2\u6570\u3042\u308b\u3044\u306f\u4f59\u5f26\u95a2\u6570\u306e\u3088\u3046\u306b\u307f\u3048\u307e\u3059\u3002\u3067\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u95a2\u6570\u3067\u30d5\u30a3\u30c3\u30c8\u3057\u3066\u307f\u307e\u3059\u3002$a, b, c$ \u304c\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3067\u6c7a\u5b9a\u3059\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u3059\u3002<\/p>\n<p>$$f(x, a, b, c) = a + b \\sin\\left(\\frac{2\\pi x}{12}\\right)<br \/>\n+ c \\cos\\left(\\frac{2\\pi x}{12}\\right)$$<\/p>\n<p><code>scipy.optimize.curve_fit()<\/code> \u3067\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><code>help(curve_fit)<\/code> \u304b\u3089\u4e00\u90e8\u3092\u5f15\u7528\uff1a<\/p>\n<pre><code>curve_fit(f, xdata, ydata, ...)     \r\nUse non-linear least squares to fit a function, f, to data.    \r\nReturns\r\n-------\r\npopt : array\r\n    Optimal values for the parameters\r\npcov : 2-D array\r\n    The estimated covariance of popt.<\/code><\/pre>\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[62]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># fit \u3055\u308c\u308b\u95a2\u6570\u3092 SymPy \u306e symbolic \u306a\u95a2\u6570\u3068\u3057\u3066\u5b9a\u7fa9<\/span>\r\n<span class=\"n\">var<\/span><span class=\"p\">(<\/span><span class=\"s1\">'x a b c'<\/span><span class=\"p\">)<\/span>\r\n<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\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">a<\/span> <span class=\"o\">+<\/span> <span class=\"n\">b<\/span><span class=\"o\">*<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"mi\">6<\/span><span class=\"p\">)<\/span> <span class=\"o\">+<\/span> <span class=\"n\">c<\/span><span class=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"mi\">6<\/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[63]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># scipy.optimize.curve_fit \u7528\u306b NumPy \u306e \u95a2\u6570\u306b\u5909\u63db<\/span>\r\n<span class=\"n\">args<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">func<\/span> <span class=\"o\">=<\/span> <span class=\"n\">lambdify<\/span><span class=\"p\">(<\/span><span class=\"n\">args<\/span><span class=\"p\">,<\/span> <span class=\"n\">f<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'numpy'<\/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[64]:<\/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.optimize<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">curve_fit<\/span>\r\n\r\n<span class=\"n\">popt<\/span><span class=\"p\">,<\/span> <span class=\"n\">pcov<\/span> <span class=\"o\">=<\/span> <span class=\"n\">curve_fit<\/span><span class=\"p\">(<\/span><span class=\"n\">func<\/span><span class=\"p\">,<\/span> <span class=\"n\">Month<\/span><span class=\"p\">,<\/span> <span class=\"n\">HiroT<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">popt<\/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[64]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>array([10.53333333, -8.34025527, -9.16106713])<\/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>\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306b\u3088\u3063\u3066\u6c42\u3081\u305f\u5024\u3092 $a, b, c$ \u306b\u4ee3\u5165\u3057\u3066 $f(x, a, b, c)$ \u306e\u30b0\u30e9\u30d5\u3092\u91cd\u306d\u3066\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[65]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u6700\u5c0f\u4e8c\u4e57\u6cd5\u306b\u3088\u3063\u3066\u6c42\u3081\u305f\u5024\u3092 a, b, c \u306b\u4ee3\u5165<\/span>\r\n<span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span> <span class=\"o\">=<\/span> <span class=\"n\">popt<\/span>\r\n\r\n<span class=\"c1\"># \u305b\u3063\u304b\u304f\u3060\u304b\u3089\u6a2a\u8ef8\u76ee\u76db\u3092\u8abf\u6574<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">subplots<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">matplotlib.ticker<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">MultipleLocator<\/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_major_locator<\/span><span class=\"p\">(<\/span><span class=\"n\">MultipleLocator<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">))<\/span>\r\n\r\n<span class=\"n\">graphics<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">list_2d<\/span><span class=\"p\">(<\/span><span class=\"n\">Month<\/span><span class=\"p\">,<\/span> <span class=\"n\">HiroT<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'\u6708\u5225\u5e73\u5e74\u6c17\u6e29'<\/span><span class=\"p\">,<\/span> <span class=\"n\">scatter<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">line<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">12<\/span><span class=\"p\">),<\/span> <span class=\"s1\">'\u95a2\u6570\u30d5\u30a3\u30c3\u30c8'<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">ax<\/span><span class=\"p\">,<\/span> <span class=\"c1\"># ax \u306e\u8a2d\u5b9a\u3092\u53cd\u6620<\/span>\r\n    <span class=\"n\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'\u5f18\u524d\u5e02\u306e\u6708\u5225\u5e73\u5e74\u6c17\u6e29'<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'\u6708'<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'\u00b0C'<\/span>\r\n<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_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-9748 size-large\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbgm-42.svg\" alt=\"\" width=\"640\" height=\"481\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u25cb\u7df4\u7fd2\uff1a\u30ab\u30fc\u30d6\u30d5\u30a3\u30c3\u30c8\">\u25cb\u7df4\u7fd2\uff1a\u30ab\u30fc\u30d6\u30d5\u30a3\u30c3\u30c8<\/h4>\n<p>\u5f18\u524d\u5e02\u306e\u6708\u5225\u5e73\u5e74\u6c17\u6e29\u306e\u30c6\u3099\u30fc\u30bf\u3092\u4f7f\u3063\u3066<\/p>\n<ol>\n<li>\u30d5\u30a3\u30c3\u30c8\u3055\u305b\u308b\u95a2\u6570\u3092\uff08\u5468\u671f12\u30f6\u6708\u306e\u5468\u671f\u95a2\u6570\u3092\u30d5\u30fc\u30ea\u30a8\u7d1a\u6570\u306b\u5c55\u958b\u3059\u308b\u8981\u9818\u3067\uff09\u4ee5\u4e0b\u306e\u3088\u3046\u306a <code>g(x)<\/code> \u306b\u3057\uff0c\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3067\u6c42\u3081\u3066\u307f\u3088\u3002<br \/>\n\\begin{eqnarray}<br \/>\ng(x) = A_0 &amp;+&amp; a_1 \\cos \\frac{2\\pi x}{12} + a_2 \\cos \\frac{4\\pi x}{12} \\\\<br \/>\n&amp;+&amp; b_1 \\sin \\frac{2\\pi x}{12} + b_2 \\sin \\frac{4\\pi x}{12}<br \/>\n\\end{eqnarray}<\/li>\n<li>\u6708\u5225\u5e73\u5e74\u6c17\u6e29\u306e\u6570\u5024\u30c6\u3099\u30fc\u30bf\u3068\u30d5\u30a3\u30c3\u30c8\u66f2\u7dda $f(x)$ \u304a\u3088\u3073 $g(x)$ \u306e\u30b0\u30e9\u30d5\u3092\u91cd\u306d\u3066\u63cf\u3051\u3002<\/li>\n<li>\u6708\u5e73\u5e74\u6c17\u6e29\u306e\u5e73\u5747\u5024\u3092\u6c42\u3081\u3066\u307f\u3088\u3002\uff08$g(x)$ \u306e\u5b9a\u6570\u90e8\u5206 $A_0$ \u304c\u5e73\u5747\u5024\u3002\uff09<\/li>\n<\/ol>\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[66]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u5909\u6570\u306e\u5ba3\u8a00<\/span>\r\n<span class=\"n\">var<\/span><span class=\"p\">(<\/span><span class=\"s1\">'x A0 a1 a2 b1 b2'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># SymPy \u306e symbolic \u306a\u95a2\u6570\u3068\u3057\u3066\u5b9a\u7fa9<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">g<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">A0<\/span><span class=\"p\">,<\/span> <span class=\"n\">a1<\/span><span class=\"p\">,<\/span> <span class=\"n\">a2<\/span><span class=\"p\">,<\/span> <span class=\"n\">b1<\/span><span class=\"p\">,<\/span> <span class=\"n\">b2<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">A0<\/span><span class=\"o\">+<\/span><span class=\"n\">a1<\/span><span class=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"mi\">6<\/span><span class=\"p\">)<\/span><span class=\"o\">+<\/span><span class=\"n\">a2<\/span><span class=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"mi\">3<\/span><span class=\"p\">)<\/span><span class=\"o\">+<\/span><span class=\"n\">b1<\/span><span class=\"o\">*<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"mi\">6<\/span><span class=\"p\">)<\/span><span class=\"o\">+<\/span><span class=\"n\">b2<\/span><span class=\"o\">*<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">pi<\/span><span class=\"o\">*<\/span><span class=\"n\">x<\/span><span class=\"o\">\/<\/span><span class=\"mi\">3<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">g<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">A0<\/span><span class=\"p\">,<\/span> <span class=\"n\">a1<\/span><span class=\"p\">,<\/span> <span class=\"n\">a2<\/span><span class=\"p\">,<\/span> <span class=\"n\">b1<\/span><span class=\"p\">,<\/span> <span class=\"n\">b2<\/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[66]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">$\\displaystyle A_{0} + a_{1} \\cos{\\left(\\frac{\\pi x}{6} \\right)} + a_{2} \\cos{\\left(\\frac{\\pi x}{3} \\right)} + b_{1} \\sin{\\left(\\frac{\\pi x}{6} \\right)} + b_{2} \\sin{\\left(\\frac{\\pi x}{3} \\right)}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><\/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[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><\/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[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u306a\u304a\uff0c3. \u306e\u5225\u89e3\u3068\u3057\u3066\uff0c\u30ea\u30b9\u30c8\u306e\u7dcf\u548c <code>sum()<\/code> \u3068\u8981\u7d20\u6570 <code>len()<\/code> \u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5e73\u5747\u5024\u3092\u6c42\u3081\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3057\u305f\u306d\u3002<\/p>\n<ul>\n<li>\u53c2\u8003\uff1a<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e3%81%af%e3%81%97%e3%82%99%e3%82%81%e3%81%a6%e3%81%ae-python-%e3%83%95%e3%82%9a%e3%83%ad%e3%82%af%e3%82%99%e3%83%a9%e3%83%9f%e3%83%b3%e3%82%af%e3%82%99\/#_sum_len_max_min\">\u306f\u3057\u3099\u3081\u3066\u306e Python \u30d5\u309a\u30ed\u30af\u3099\u30e9\u30df\u30f3\u30af\u3099<\/a><\/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[67]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"nb\">sum<\/span><span class=\"p\">(<\/span><span class=\"n\">HiroT<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">HiroT<\/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[67]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>10.533333333333333<\/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>\u307e\u305f\uff0c\u6708\u5e73\u5e74\u6c17\u6e29\u306e\u6700\u5927\u5024\u3084\u6700\u5c0f\u5024\u3082\u7c21\u5358\u306b\u6c42\u3081\u3089\u308c\u307e\u3059\u306d\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre> \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u3053\u3067\u306f\uff0cSymPy Plotting Backends (SPB) \u306e The Graphic Module \u3092\u4f7f\u3063\u305f 2\u6b21\u5143\u30b0\u30e9\u30d5\u4f5c\u6210\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n<p>SymPy Plotting Backends (SPB) \u306e Plot functions \u3092\u4f7f\u3063\u305f 2\u6b21\u5143\u30b0\u30e9\u30d5\u4f5c\u6210\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u3067\u8aac\u660e\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<ul>\n<li>SymPy Plotting Backends \u3067\u30b0\u30e9\u30d5\u4f5c\u6210\uff1aPlot functions \u7de8<\/li>\n<\/ul>\n<p>Python \u306e SymPy \u81ea\u8eab\u306b\u3082\u30b0\u30e9\u30d5\u4f5c\u6210\u6a5f\u80fd\u306f\u3042\u308a\u307e\u3059\u304c\uff0cSymPy Plotting Backends (SPB) \u306f\uff0c\u8a00\u308f\u3070\u305d\u306e\u6a5f\u80fd\u62e1\u5f35\u7248\u306b\u76f8\u5f53\u3057\u307e\u3059\u3002 SPB \u306b\u3088\u308b\u30b0\u30e9\u30d5\u4f5c\u6210\u306b\u306f\uff0cThe Graphics Module \u306b\u3088\u308b\u65b9\u6cd5\u3068\uff0cPlot functions \u306b\u3088\u308b\u65b9\u6cd5\u306e2\u7a2e\u985e\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u30c9\u30ad\u30e5\u30e1\u30f3\u30c8\u306b\u3088\u308b\u3068\uff0cThe Graphics Module \u306e\u307b\u3046\u304c\u3088\u308a\u76f4\u611f\u7684\u3067\u7c21\u5358\u3067\u3042\u308a\uff0c\u7570\u306a\u3063\u305f\u30b0\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a\u3055\u305b\u308b\u3053\u3068\u3082\u7c21\u5358\u306b\u3067\u304d\u308b\u306e\u3067\u30aa\u30b9\u30b9\u30e1\u306e\u3088\u3046\u3067\u3059\u3002Plot functions \u306b\u3088\u308b\u65b9\u6cd5\u306f\u4eca\u5f8c\u306f\u30a2\u30c3\u30d7\u30c7\u30fc\u30c8\u3055\u308c\u306a\u3044\u3088\u3046\u3067\u3059\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/python-%e3%81%a7%e3%82%b0%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90\/sympy-plotting-backends-%e3%81%a7%e3%82%b0%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90%ef%bc%9athe-graphic-module-%e7%b7%a8\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":9699,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-9701","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\/9701","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=9701"}],"version-history":[{"count":15,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/9701\/revisions"}],"predecessor-version":[{"id":9845,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/9701\/revisions\/9845"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/9699"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=9701"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}