{"id":6738,"date":"2024-11-24T20:00:04","date_gmt":"2024-11-24T11:00:04","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=6738"},"modified":"2024-11-26T10:59:48","modified_gmt":"2024-11-26T01:59:48","slug":"sympy-plotting-backends-%e3%81%a7%e3%82%b0%e3%83%a9%e3%83%95%e4%bd%9c%e6%88%90","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%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\/","title":{"rendered":"SymPy Plotting Backends \u3067\u30b0\u30e9\u30d5\u4f5c\u6210\uff1aPlot functions \u7de8"},"content":{"rendered":"<p>\u3053\u3053\u3067\u306f\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> \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\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n<p><span style=\"font-family: helvetica, arial, sans-serif;\"><a href=\"https:\/\/sympy-plot-backends.readthedocs.io\/en\/latest\/index.html\"><strong>SymPy Plotting Backends (SPB)<\/strong><\/a><\/span> \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\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%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\/\" target=\"_blank\" rel=\"noopener\">SymPy Plotting Backends \u3067\u30b0\u30e9\u30d5\u4f5c\u6210\uff1aThe Graphic Module \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\">SymPy Plotting Backends (SPB)<\/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<!--more--><\/p>\n<p>&nbsp;<\/p>\n<p>\u4ee5\u4e0b\u306e\u30da\u30fc\u30b8\u306e\u5185\u5bb9\u3068\u307b\u307c\u540c\u7b49\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/5875\/\" target=\"_blank\" rel=\"noopener\">Python \u306b\u3088\u308b\u30b0\u30e9\u30d5\u4f5c\u6210 SymPy Plotting Backends \u7de8<\/a><\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Python \u3092\u4f7f\u3063\u3066\uff0c\u95a2\u6570\u306e\u30af\u3099\u30e9\u30d5\u3092\u63cf\u304f\u3053\u3068\u304b\u3099\u3066\u3099\u304d\u307e\u3059\u3002\u307e\u305f\uff0c\u6570\u5024\u30c6\u3099\u30fc\u30bf\u3082\u30af\u3099\u30e9\u30d5\u306b\u3059\u308b\u3053\u3068\u304b\u3099\u3066\u3099\u304d\u307e\u3059\u3002<\/p>\n<p>\u3053\u3053\u3067\u306f\uff0c<a href=\"https:\/\/sympy-plot-backends.readthedocs.io\/en\/latest\/index.html\">SymPy Plotting Backends (SPB)<\/a> \u306e <a href=\"https:\/\/sympy-plot-backends.readthedocs.io\/en\/latest\/modules\/plot_functions\/index.html\" target=\"_blank\" rel=\"noopener\">Plot functions<\/a> \u3092\u4f7f\u3063\u305f 2\u6b21\u5143\u30b0\u30e9\u30d5\u4f5c\u6210\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<br \/>\nSPB \u3067\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>plot(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>plot_implicit(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>plot_parametric(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>plot_list([x1, ..., xn], [y1, ..., yn])<\/code><\/li>\n<\/ul>\n<\/li>\n<li>\u30d9\u30af\u30c8\u30eb\n<ul>\n<li><code>ax.quiver(X, Y, 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 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=\"c1\"><span class=\"kn\">from<\/span> <span class=\"nn\">sympy<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span> \r\n# 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\"># \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<span class=\"c1\">#<\/span>\r\n<span class=\"c1\"># init_printing()<\/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=\"\u967d\u95a2\u6570\u306e\u30b0\u30e9\u30d5\">\u967d\u95a2\u6570\u306e\u30b0\u30e9\u30d5<\/h3>\n<p>\u4f8b\u3068\u3057\u3066\uff0c$y = \\sin x$ \u306e\u30af\u3099\u30e9\u30d5\u3092 $\u22122\\pi \\leq x \\leq 2\\pi$ \u306e\u7bc4\u56f2\u3066\u3099\u63cf\u304d\u307e\u3059\u3002\u57fa\u672c\u7684\u306a\u5b9a\u6570\u306e\u4e00\u3064\u3066\u3099\u3042\u308b\u5186\u5468\u7387 $\\pi$ \u306f SPB \u3066\u3099\u306f <code>pi<\/code> \u3068\u66f8\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\">plot<\/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=\"p\">;<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6782\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig01.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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>\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[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">plot<\/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> \r\n     <span class=\"c1\"># \u51e1\u4f8b,     \u7dda\u306e\u592a\u3055\u3068\u8272<\/span>\r\n     <span class=\"s2\">\"\u6b63\u5f26\u95a2\u6570\"<\/span><span class=\"p\">,<\/span> <span class=\"p\">{<\/span><span class=\"s2\">\"linewidth\"<\/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>      \r\n     <span class=\"c1\"># \u8868\u793a\u7bc4\u56f2<\/span>\r\n     <span class=\"n\">xlim<\/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=\"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> <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 size-large wp-image-6783\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig02.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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\">\u9670\u95a2\u6570\u306e\u30b0\u30e9\u30d5<\/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\">plot_implicit<\/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>$f(x, y) \\equiv x^2 + y^2 &#8211; 1$ \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[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">plot_implicit<\/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><span class=\"p\">;<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6784\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig03.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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\">\u7e26\u6a2a\u6bd4\u30fb\u30b5\u30a4\u30ba\u306e\u8a2d\u5b9a<\/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[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">plot_implicit<\/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> <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=\"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=\"mi\">6<\/span><span class=\"p\">,<\/span> <span class=\"mi\">6<\/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 size-large wp-image-6785\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig04.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\">\u5a92\u4ecb\u5909\u6570\u8868\u793a\u306e\u30b0\u30e9\u30d5<\/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\">plot_parametric<\/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[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">plot_parametric<\/span><span class=\"p\">(<\/span><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> \r\n                <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s2\">\"equal\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">use_cm<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/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 size-large wp-image-6786\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig05.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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\">\u70b9\u30fb\u6570\u5024\u30c6\u3099\u30fc\u30bf\u306e\u30af\u3099\u30e9\u30d5<\/h3>\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[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">X<\/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\">Y<\/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\">plot_list<\/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>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6787\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig06.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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>\u30aa\u30d7\u30b7\u30e7\u30f3 <code>is_point = True<\/code> \u3092\u8a2d\u5b9a\u3057\u3066\uff0c\u5404\u70b9\u3092\u7dda\u3067\u3064\u306a\u304c\u305a\u306b\u8d64\u8272\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[8]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">plot_list<\/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=\"s2\">\"\u30c7\u30fc\u30bf\"<\/span><span class=\"p\">,<\/span> <span class=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"red\"<\/span><span class=\"p\">},<\/span> \r\n          <span class=\"n\">is_point<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/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 size-large wp-image-6788\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig07.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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\">\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u304f<\/h3>\n<p>SPB \u306b\u306f <code>plot_vector()<\/code> \u304c\u3042\u308a\u307e\u3059\u304c\uff0c\u3053\u308c\u306f\u30d9\u30af\u30c8\u30eb\u5834\u3092\u63cf\u304f\u95a2\u6570\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e00\u65e6 <code>plot()<\/code> \u3059\u308c\u3070 <code>matplotlib.pyplot.quiver()<\/code> \u304c\u4f7f\u3048\u308b\u306e\u3067\uff0cMatplotlib \u6d41\u306b\u30d9\u30af\u30c8\u30eb\u3092\u63cf\u3044\u3066\u307f\u307e\u3059\u3002<\/p>\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[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u59cb\u70b9\u306e x \u5ea7\u6a19<\/span>\r\n<span class=\"n\">X<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span>\r\n<span class=\"c1\"># \u59cb\u70b9\u306e y \u5ea7\u6a19<\/span>\r\n<span class=\"n\">Y<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span>\r\n<span class=\"c1\"># \u30d9\u30af\u30c8\u30eb\u306e x \u6210\u5206<\/span>\r\n<span class=\"n\">Vx<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">]<\/span>\r\n<span class=\"c1\"># \u30d9\u30af\u30c8\u30eb\u306e y \u6210\u5206<\/span>\r\n<span class=\"n\">Vy<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span>\r\n\r\n<span class=\"n\">p<\/span><span class=\"o\">=<\/span><span class=\"n\">plot<\/span><span class=\"p\">(<\/span><span class=\"n\">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=\"s2\">\"equal\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">),<\/span> <span class=\"n\">show<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">=<\/span><span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">ax<\/span>\r\n<span class=\"c1\"># ax \u3092\u5b9a\u7fa9\u3057\u305f\u3089\uff0c\u3042\u3068\u306f Matplotlib \u6d41\u306b<\/span>\r\n<span class=\"c1\"># x \u306e\u76ee\u76db\u3092 0.5 \u523b\u307f\u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">([<\/span><span class=\"mf\">0.5<\/span><span class=\"o\">*<\/span><span class=\"n\">i<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">4<\/span><span class=\"p\">,<\/span><span class=\"mi\">5<\/span><span class=\"p\">)])<\/span>\r\n<span class=\"c1\"># y \u306e\u76ee\u76db\u3092 0.5 \u523b\u307f\u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_yticks<\/span><span class=\"p\">([<\/span><span class=\"mf\">0.5<\/span><span class=\"o\">*<\/span><span class=\"n\">i<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">4<\/span><span class=\"p\">,<\/span><span class=\"mi\">5<\/span><span class=\"p\">)])<\/span>\r\n<span class=\"c1\"># x\u8ef8 y\u8ef8<\/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\">color<\/span><span class=\"o\">=<\/span><span class=\"s1\">'black'<\/span><span class=\"p\">,<\/span> <span class=\"n\">dashes<\/span><span class=\"o\">=<\/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=\"n\">linewidth<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.7<\/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\">color<\/span><span class=\"o\">=<\/span><span class=\"s1\">'black'<\/span><span class=\"p\">,<\/span> <span class=\"n\">dashes<\/span><span class=\"o\">=<\/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=\"n\">linewidth<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.7<\/span><span class=\"p\">);<\/span>\r\n\r\n<span class=\"c1\"># \u30d9\u30af\u30c8\u30eb<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">quiver<\/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=\"n\">Vx<\/span><span class=\"p\">,<\/span> <span class=\"n\">Vy<\/span><span class=\"p\">,<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"blue\"<\/span><span class=\"p\">,<\/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<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6789\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig08.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<\/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\">X<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"n\">t<\/span> <span class=\"k\">for<\/span> <span class=\"n\">t<\/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\">Y<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[(<\/span><span class=\"n\">t<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.25<\/span><span class=\"o\">*<\/span><span class=\"n\">t<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span> <span class=\"k\">for<\/span> <span class=\"n\">t<\/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\">Vx<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mf\">0.5<\/span> <span class=\"k\">for<\/span> <span class=\"n\">t<\/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\">Vy<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[(<\/span><span class=\"mf\">0.5<\/span><span class=\"o\">-<\/span><span class=\"mf\">0.25<\/span><span class=\"o\">*<\/span><span class=\"n\">t<\/span><span class=\"p\">)<\/span> <span class=\"k\">for<\/span> <span class=\"n\">t<\/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\r\n<span class=\"n\">X<\/span><span class=\"p\">,<\/span> <span class=\"n\">Y<\/span><span class=\"p\">,<\/span> <span class=\"n\">Vx<\/span><span class=\"p\">,<\/span> <span class=\"n\">Vy<\/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[10]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>([0, 1, 2, 3, 4],\r\n [0.0, 0.75, 1.0, 0.75, 0.0],\r\n [0.5, 0.5, 0.5, 0.5, 0.5],\r\n [0.5, 0.25, 0.0, -0.25, -0.5])<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[11]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot<\/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\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"mf\">4.5<\/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\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"mi\">6<\/span><span class=\"p\">,<\/span><span class=\"mi\">3<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s2\">\"$y$\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">show<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">ax<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">quiver<\/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=\"n\">Vx<\/span><span class=\"p\">,<\/span> <span class=\"n\">Vy<\/span><span class=\"p\">,<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"blue\"<\/span><span class=\"p\">,<\/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<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6790\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig09.svg\" alt=\"\" width=\"640\" height=\"320\" \/><\/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<p>$y = x^2 &#8211; 1$ \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 $-5 \\leq x \\leq 5$ \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[12]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># var('x')<\/span>\r\n\r\n<span class=\"n\">plot<\/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=\"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=\"o\">-<\/span><span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/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 size-large wp-image-6791\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig10.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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>\u305d\u308c\u305e\u308c\u306e\u66f2\u7dda\u3054\u3068\u306b\uff0c\u3044\u304f\u3064\u304b\u30aa\u30d5\u309a\u30b7\u30e7\u30f3\u3092\u8a2d\u5b9a\u3057\u3066\u63cf\u304f\u4f8b\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[13]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">plot<\/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=\"s2\">\"linewidth\"<\/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> \r\n     <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=\"s2\">\"linewidth\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"black\"<\/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=\"c1\"># \u8868\u793a\u7bc4\u56f2<\/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><span class=\"p\">;<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6792\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig11.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u6570\u5024\u30c6\u3099\u30fc\u30bf\u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u8fbc\u3080\">\u6570\u5024\u30c6\u3099\u30fc\u30bf\u30d5\u30a1\u30a4\u30eb\u3092\u8aad\u307f\u8fbc\u3080<\/h3>\n<p>SPB \u3066\u3099\u306f\uff0c\u3042\u3089\u304b\u3057\u3099\u3081\u4f5c\u6210\u3055\u308c\u305f\u6570\u5024\u30c6\u3099\u30fc\u30bf\u30d5\u30a1\u30a4\u30eb\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>\u307e\u305a\uff0c\u6570\u5024\u30c7\u30fc\u30bf\u30d5\u30a1\u30a4\u30eb <code>data.txt<\/code> \u3092\u3042\u3089\u304b\u3057\u3099\u3081\u4f5c\u6210\u3057\u3066\u304a\u304d\u307e\u3059\u3002\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[14]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u30d5\u30a1\u30a4\u30eb\u306b\u66f8\u304d\u8fbc\u3080\u30c7\u30fc\u30bf\u3092\u4f5c\u6210<\/span>\r\n\r\n<span class=\"n\">dat<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<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\">dat<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">([<\/span><span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">i<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">])<\/span>\r\n<span class=\"n\">dat<\/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[14]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>[[0, 0], [1, 1], [2, 4], [3, 9], [4, 16], [5, 25]]<\/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[15]:<\/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 data.txt \u306b dat \u3092\u66f8\u304d\u8fbc\u3080<\/span>\r\n\r\n<span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">savetxt<\/span><span class=\"p\">(<\/span><span class=\"s1\">'data.txt'<\/span><span class=\"p\">,<\/span> <span class=\"n\">dat<\/span><span class=\"p\">,<\/span> <span class=\"n\">fmt<\/span><span class=\"o\">=<\/span><span class=\"s1\">'<\/span><span class=\"si\">%i<\/span><span class=\"s1\">'<\/span><span class=\"p\">)<\/span> <span class=\"c1\"># \u6574\u6570\u3068\u3057\u3066\u66f8\u304d\u51fa\u3057<\/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[16]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u30d5\u30a1\u30a4\u30eb\u306e\u5185\u5bb9\u8868\u793a<\/span>\r\n<span class=\"o\">!<\/span>cat data.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\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[17]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u30d5\u30a1\u30a4\u30eb data.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\">'data.txt'<\/span><span class=\"p\">,<\/span> <span class=\"n\">dtype<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'int'<\/span><span class=\"p\">)<\/span> <span class=\"c1\"># \u6574\u6570\u3068\u3057\u3066\u8aad\u307f\u8fbc\u307f<\/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[18]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># Python \u3067\u4f5c\u6210\u3057\u305f dat \u306f\u30ea\u30b9\u30c8<\/span>\r\n<span class=\"nb\">type<\/span><span class=\"p\">(<\/span><span class=\"n\">dat<\/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[18]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>list<\/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[19]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># NumPy \u306e loadtxt() \u3067\u8aad\u307f\u8fbc\u3093\u3060 data \u306f\u914d\u5217\u306b\u306a\u308b<\/span>\r\n<span class=\"nb\">type<\/span><span class=\"p\">(<\/span><span class=\"n\">data<\/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[19]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>numpy.ndarray<\/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[20]:<\/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<span class=\"n\">plot_list<\/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> <span class=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"red\"<\/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> <span class=\"n\">is_point<\/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 size-large wp-image-6793\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig12.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u6570\u5024\u30c6\u3099\u30fc\u30bf\u3068\u7406\u8ad6\u66f2\u7dda\u3092\u91cd\u306d\u3066\u8868\u793a\">\u6570\u5024\u30c6\u3099\u30fc\u30bf\u3068\u7406\u8ad6\u66f2\u7dda\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>\u524d\u7bc0\u306e\u6570\u5024\u30c6\u3099\u30fc\u30bf\u30d5\u30a1\u30a4\u30eb <code>data.txt<\/code> \u3068\u7406\u8ad6\u66f2\u7dda $y = x^2$ \u306e 2 \u3064\u306e\u30af\u3099\u30e9\u30d5\u3092\u91cd\u306d\u3066\u8868\u793a\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[21]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">p1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot_list<\/span><span class=\"p\">(<\/span><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> <span class=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"red\"<\/span><span class=\"p\">},<\/span> \r\n               <span class=\"n\">is_point<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/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=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">p2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot<\/span><span class=\"p\">(<\/span><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\">6<\/span><span class=\"p\">),<\/span> <span class=\"s2\">\"\u7406\u8ad6\u66f2\u7dda $y=x^2$\"<\/span><span class=\"p\">,<\/span> <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\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"p\">(<\/span><span class=\"n\">p1<\/span> <span class=\"o\">+<\/span> <span class=\"n\">p2<\/span><span class=\"p\">)<\/span><span class=\"o\">.<\/span><span class=\"n\">show<\/span><span class=\"p\">();<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"output_svg output_subarea \">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6794\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig13.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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=\"\u6d77\u738b\u661f\u3068\u51a5\u738b\u661f\u306e\u8ecc\u9053\">\u6d77\u738b\u661f\u3068\u51a5\u738b\u661f\u306e\u8ecc\u9053<\/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=\"\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>$$ r= \\frac{a (1\u2212e^2)}{ 1 + e\\cos\\varphi}$$<\/p>\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\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<p>\u307e\u305a\uff0c\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[22]:<\/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\">r<\/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<span class=\"k\">def<\/span> <span class=\"nf\">x<\/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\">r<\/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><span class=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">phi<\/span><span class=\"p\">)<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">y<\/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\">r<\/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><span class=\"o\">*<\/span><span class=\"n\">sin<\/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[23]:<\/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<\/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[24]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">plot_parametric<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">x<\/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\">y<\/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> <span class=\"s2\">\"\u51a5\u738b\u661f\"<\/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\">legend<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">,<\/span> <span class=\"n\">use_cm<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/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 size-large wp-image-6795\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig14.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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<\/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=\"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<\/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[26]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">plot_parametric<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"p\">(<\/span><span class=\"n\">x<\/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\">y<\/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=\"s2\">\"\u51a5\u738b\u661f\"<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"p\">(<\/span><span class=\"n\">x<\/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=\"n\">y<\/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=\"s2\">\"\u6d77\u738b\u661f\"<\/span><span class=\"p\">),<\/span> \r\n    <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=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s2\">\"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=\"n\">use_cm<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/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 size-large wp-image-6796\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig15.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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\uff1a\u6975\u5ea7\u6a19\u8868\u793a\u3067\u30d7\u30ed\u30c3\u30c8\">\u53c2\u8003\uff1a\u6975\u5ea7\u6a19\u8868\u793a\u3067\u30d7\u30ed\u30c3\u30c8<\/h4>\n<p>\u6975\u5ea7\u6a19\u8868\u793a\u3067\u30d7\u30ed\u30c3\u30c8\u3059\u308b\u5834\u5408\u306f\uff0c<code>plot_polar()<\/code> \u3092\u4f7f\u3044\u307e\u3059\u3002\uff08<code>plot_polar()<\/code> \u306e\u5834\u5408\u306f\u30c7\u30d5\u30a9\u30eb\u30c8\u3067 <code>aspect = \"equal\"<\/code> \u306b\u306a\u3063\u3066\u3044\u308b\u3088\u3046\u3067\u3059\u3002\uff09<\/p>\n<h5 id=\"x-\u8ef8-y-\u8ef8\u3092\u5f15\u304f\">x \u8ef8 y \u8ef8\u3092\u5f15\u304f<\/h5>\n<p>\u307e\u305f\uff0cMatplotlib \u696d\u754c\u3067\u306f $x$ \u8ef8\u3084 $y$ \u8ef8\u3092\u5f15\u304f\u3068\u3044\u3046\u6163\u7fd2\u304c\u306a\u3044\u306e\u304b\uff0c\u305d\u306e\u3088\u3046\u306a\u30aa\u30d7\u30b7\u30e7\u30f3\u304c\u898b\u5f53\u305f\u308a\u307e\u305b\u3093\u3002\u4ed5\u65b9\u304c\u306a\u3044\u306e\u3067\uff0c<code>axhline()<\/code> \u3068 <code>axvline()<\/code> \u3092\u4f7f\u3063\u3066\u305d\u308c\u3089\u3057\u3044\u7dda\u3092\u5f15\u3044\u3066\u307f\u307e\u3059\u3002<\/p>\n<h5 id=\"\u30b0\u30ea\u30c3\u30c9\u306e\u975e\u8868\u793a\">\u30b0\u30ea\u30c3\u30c9\u306e\u975e\u8868\u793a<\/h5>\n<p><code>grid = False<\/code> \u3067\u30b0\u30ea\u30c3\u30c9\u3092\u975e\u8868\u793a\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[27]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot_polar<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">r<\/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=\"s2\">\"\u51a5\u738b\u661f\"<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">r<\/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=\"s2\">\"\u6d77\u738b\u661f\"<\/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=\"n\">xlim<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">60<\/span><span class=\"p\">,<\/span> <span class=\"mi\">40<\/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\">50<\/span><span class=\"p\">,<\/span> <span class=\"mi\">50<\/span><span class=\"p\">),<\/span> <span class=\"n\">size<\/span> <span class=\"o\">=<\/span> <span class=\"p\">(<\/span><span class=\"mi\">6<\/span><span class=\"p\">,<\/span> <span class=\"mi\">6<\/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=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">);<\/span>\r\n<span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">ax<\/span>\r\n<span class=\"c1\"># x\u8ef8 y\u8ef8<\/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\">color<\/span><span class=\"o\">=<\/span><span class=\"s1\">'black'<\/span><span class=\"p\">,<\/span> <span class=\"n\">dashes<\/span><span class=\"o\">=<\/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=\"n\">linewidth<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.6<\/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\">color<\/span><span class=\"o\">=<\/span><span class=\"s1\">'black'<\/span><span class=\"p\">,<\/span> <span class=\"n\">dashes<\/span><span class=\"o\">=<\/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=\"n\">linewidth<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.6<\/span><span class=\"p\">);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6797\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig16.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=\"\u6708\u5225\u5e73\u5e74\u6c17\u6e29\u306e\u95a2\u6570\u30d5\u30a3\u30c3\u30c8\">\u6708\u5225\u5e73\u5e74\u6c17\u6e29\u306e\u95a2\u6570\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[28]:<\/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\">Month<\/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[28]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]<\/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[29]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><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[30]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot_list<\/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=\"s2\">\"\u6708\u5225\u5e73\u5e74\u6c17\u6e29\"<\/span><span class=\"p\">,<\/span> \r\n              <span class=\"n\">is_point<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/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 size-large wp-image-6798\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig17.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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>\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[31]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># 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[32]:<\/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[33]:<\/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[33]:<\/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 $a, b, c$ \u306e\u5024\u3092\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[34]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">p1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot_list<\/span><span class=\"p\">(<\/span><span class=\"n\">Month<\/span><span class=\"p\">,<\/span> <span class=\"n\">HiroT<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"\u6708\u5225\u5e73\u5e74\u6c17\u6e29\"<\/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\">25<\/span><span class=\"p\">),<\/span> \r\n               <span class=\"n\">xlabel<\/span> <span class=\"o\">=<\/span> <span class=\"s2\">\"\u6708\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">ylabel<\/span> <span class=\"o\">=<\/span> <span class=\"s2\">\"\u00b0C\"<\/span><span class=\"p\">,<\/span> \r\n               <span class=\"n\">is_point<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">True<\/span><span class=\"p\">,<\/span> <span class=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">);<\/span>\r\n\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<span class=\"n\">p2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot<\/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=\"s2\">\"\u95a2\u6570\u30d5\u30a3\u30c3\u30c8\"<\/span><span class=\"p\">,<\/span> \r\n          <span class=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p1<\/span> <span class=\"o\">+<\/span> <span class=\"n\">p2<\/span>\r\n<span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">ax<\/span>\r\n<span class=\"c1\"># x \u306e\u4e3b\u76ee\u76db\u3092 1 \u523b\u307f\u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">([<\/span><span class=\"n\">i<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">13<\/span><span class=\"p\">)]);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6799\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig18.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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=\"\u7df4\u7fd2-3-1\">\u7df4\u7fd2 3-1<\/h3>\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[35]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># 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 A0 a1 a2 b1 b2'<\/span><span class=\"p\">)<\/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<\/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> \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[\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<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<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\">\u9818\u57df\u306e\u5857\u308a\u3064\u3076\u3057<\/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>plot_implicit()<\/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[36]:<\/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[37]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># 0 &lt;= y &lt;= f(x) \u306e\u9818\u57df\u3092 0.5 &lt;= x &lt;= 2 \u306e\u7bc4\u56f2\u3067\u5857\u308a\u3064\u3076\u3059<\/span>\r\n<span class=\"c1\"># plot_implicit() \u306e\u5834\u5408\u306f x \u306e\u7bc4\u56f2\u3068 y \u306e\u7bc4\u56f2\u304c\u5fc5\u8981<\/span>\r\n<span class=\"n\">var<\/span><span class=\"p\">(<\/span><span class=\"s1\">'x y'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">plot_implicit<\/span><span class=\"p\">(<\/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\"># \u30b0\u30e9\u30d5\u306e\u8868\u793a\u7bc4\u56f2<\/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=\"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><span class=\"p\">;<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6936\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbnuri01-1.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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>\u3044\u304f\u3064\u304b\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u6307\u5b9a\u3057\u3066\u63cf\u304f\u4f8b\u3002<\/p>\n<p>$x$ \u8ef8 $y$ \u8ef8\u3092\u8868\u793a\u3057\u307e\u3059\u3002<br \/>\n\u30c7\u30d5\u30a9\u30eb\u30c8\u306e\u30b0\u30ea\u30c3\u30c9\u7dda\u304c\u5c11\u3057\u76ee\u969c\u308a\u306a\u5834\u5408\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u7d30\u3081\u306e\u7070\u8272\u70b9\u7dda\u306b\u3057\u3066\u76ee\u7acb\u305f\u306a\u3044\u3088\u3046\u306b\u3059\u308b\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[38]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># y = f(x) \u3092 0.25 &lt;= x &lt;= 2.25 \u306e\u7bc4\u56f2\u3067\u63cf\u304f<\/span>\r\n<span class=\"n\">p1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot<\/span><span class=\"p\">(<\/span>\r\n    <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=\"mf\">0.25<\/span><span class=\"p\">,<\/span> <span class=\"mf\">2.25<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"c1\"># \u51e1\u4f8b\u3002$ \u3067\u56f2\u307e\u308c\u305f\u90e8\u5206\u306f latex \u8a18\u6cd5<\/span>\r\n    <span class=\"s2\">\"$f(x)$\"<\/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\">0.2<\/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=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span> <span class=\"c1\"># \u5f8c\u3067\u307e\u3068\u3081\u3066\u8868\u793a<\/span>\r\n<span class=\"p\">)<\/span> \r\n\r\n<span class=\"c1\"># 0 &lt;= y &lt;= f(x) \u306e\u9818\u57df\u3092 0.5 &lt;= x &lt;= 2 \u306e\u7bc4\u56f2\u3067\u5857\u308a\u3064\u3076\u3059<\/span>\r\n<span class=\"c1\"># plot_implicit() \u306e\u5834\u5408\u306f x \u306e\u7bc4\u56f2\u3068 y \u306e\u7bc4\u56f2\u304c\u5fc5\u8981<\/span>\r\n<span class=\"n\">p2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot_implicit<\/span><span class=\"p\">(<\/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=\"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> <span class=\"p\">(<\/span><span class=\"n\">y<\/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=\"c1\"># \u51e1\u4f8b\u3002$ \u3067\u56f2\u307e\u308c\u305f\u90e8\u5206\u306f latex \u8a18\u6cd5<\/span>\r\n    <span class=\"s2\">\"$0 \\leq y \\leq f(x)$\"<\/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=\"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> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s1\">'yellow'<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span> <span class=\"c1\"># \u5f8c\u3067\u307e\u3068\u3081\u3066\u8868\u793a<\/span>\r\n<span class=\"p\">)<\/span> \r\n\r\n<span class=\"c1\"># 2\u3064\u306e\u30b0\u30e9\u30d5\u3092\u91cd\u306d\u3066<\/span>\r\n<span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p1<\/span> <span class=\"o\">+<\/span> <span class=\"n\">p2<\/span>\r\n<span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">ax<\/span>\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\u7d30\u3081\u306e\u7070\u8272\u70b9\u7dda\u3067<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">which<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"major\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"lightgray\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">dashes<\/span><span class=\"o\">=<\/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=\"n\">linewidth<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># x\u8ef8 y\u8ef8<\/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\">color<\/span><span class=\"o\">=<\/span><span class=\"s1\">'black'<\/span><span class=\"p\">,<\/span> <span class=\"n\">dashes<\/span><span class=\"o\">=<\/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=\"n\">linewidth<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.6<\/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\">color<\/span><span class=\"o\">=<\/span><span class=\"s1\">'black'<\/span><span class=\"p\">,<\/span> <span class=\"n\">dashes<\/span><span class=\"o\">=<\/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=\"n\">linewidth<\/span><span class=\"o\">=<\/span><span class=\"mf\">0.6<\/span><span class=\"p\">);<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6937\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbnuri02-1.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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\u306e\u5185\u90e8\u3092\u5857\u308a\u3064\u3076\u3059\">\u591a\u89d2\u5f62\u306e\u5185\u90e8\u3092\u5857\u308a\u3064\u3076\u3059<\/h4>\n<p><code>plot_geometry(Polygon())<\/code> \u3092\u4f7f\u3063\u3066\uff0c$(0, 0)$ \u3092\u4e2d\u5fc3\u3068\u3057\uff0c\u300c\u534a\u5f84\u300d\uff08\u4e2d\u5fc3\u304b\u3089\u9802\u70b9\u307e\u3067\u306e\u8ddd\u96e2\uff09\u304c $2$ \u306e\u6b63\u56db\u89d2\u5f62 $n=4$\uff08\u6b63\u65b9\u5f62\uff09\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[39]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">plot_geometry<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"c1\">#       \u4e2d\u5fc3\uff0c \u534a\u5f84\uff0c\u9802\u70b9\u306e\u6570<\/span>\r\n    <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\">4<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u306f\u7121\u3057\u306b<\/span>\r\n    <span class=\"n\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"c1\"># \u5857\u308a\u3064\u3076\u3055\u306a\u3044<\/span>\r\n    <span class=\"n\">is_filled<\/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 size-large wp-image-6938\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbnuri03-1.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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[40]:<\/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\u3067\u306f\u5185\u90e8\u3092\u5857\u308a\u3064\u3076\u3059<\/span>\r\n<span class=\"n\">plot_geometry<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"c1\">#       \u4e2d\u5fc3\uff0c \u534a\u5f84\uff0c\u9802\u70b9\u306e\u6570<\/span>\r\n    <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\">4<\/span><span class=\"p\">),<\/span> \r\n    <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 size-large wp-image-6939\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbnuri04-1.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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[41]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u9802\u70b9\u306e x, y \u5ea7\u6a19\u3092\u6307\u5b9a\u3057\u3066\u63cf\u304f\u4f8b<\/span>\r\n<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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">),<\/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=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">),<\/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\r\n<span class=\"n\">plot_geometry<\/span><span class=\"p\">(<\/span>\r\n    <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=\"c1\"># \u5857\u308a\u3064\u3076\u3057\u306e\u8272<\/span>\r\n    <span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'yellow'<\/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 size-large wp-image-6940\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbnuri05-1.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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\u306e\u5185\u90e8\u3092\u5857\u308a\u3064\u3076\u3059\">\u5186\u306e\u5185\u90e8\u3092\u5857\u308a\u3064\u3076\u3059<\/h4>\n<p><code>plot_geometry(Circle())<\/code> \u3092\u4f7f\u3063\u3066\uff0c$(0, 0)$ \u3092\u4e2d\u5fc3\u3068\u3057\uff0c\u534a\u5f84\u304c $1$ \u306e\u5186\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[42]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u539f\u70b9 (0, 0) \u3092\u4e2d\u5fc3\u3068\u3057\u305f\u534a\u5f84 1 \u306e\u5186<\/span>\r\n<span class=\"n\">plot_geometry<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">Circle<\/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\">1<\/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> \r\n    <span class=\"c1\"># \u5857\u308a\u3064\u3076\u3055\u306a\u3044<\/span>\r\n    <span class=\"n\">is_filled<\/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 size-large wp-image-6941\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbnuri06-1.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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[43]:<\/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\u3067\u306f\u5185\u90e8\u3092\u63fa\u308a\u3064\u3076\u3059<\/span>\r\n<span class=\"n\">plot_geometry<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">Circle<\/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\">1<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"c1\"># \u7e01\u306e\u8272\u3092\u8d64\u306b<\/span>\r\n    <span class=\"p\">{<\/span><span class=\"s1\">'edgecolor'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'red'<\/span><span class=\"p\">},<\/span> \r\n    <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 size-large wp-image-6942\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbnuri07-1.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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=\"color-\u3068-edgecolor-\u306e\u540c\u6642\u8a2d\u5b9a\"><code>color<\/code> \u3068 <code>edgecolor<\/code> \u306e\u540c\u6642\u8a2d\u5b9a<\/h4>\n<p>\u672c\u7a3f\u57f7\u7b46\u6642\u70b9\u3067\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b <code>edgecolor<\/code> \u3068 <code>color<\/code> \u3092\u4e21\u65b9\u8a2d\u5b9a\u3057\u3088\u3046\u3068\u3057\u3066\u3082\u3046\u307e\u304f\u3044\u304b\u306a\u3044\u3088\u3046\u3060\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[44]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">plot_geometry<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">Circle<\/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\">1<\/span><span class=\"p\">),<\/span> <span class=\"p\">{<\/span><span class=\"s1\">'edgecolor'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'red'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'yellow'<\/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 size-large wp-image-6943\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbnuri08.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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>\u3069\u3046\u3057\u3066\u3082\u3068\u3044\u3046\u306e\u3067\u3042\u308c\u3070\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5225\u3005\u306b\u4f5c\u6210\u3057\u3066\u91cd\u306d\u3066\u8868\u793a\u3055\u305b\u308b\u3068\u3044\u3046\u65b9\u6cd5\u304c\u3042\u308b\u3060\u308d\u3046\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=\"c1\"># \u5186\u306e\u307f\u3092\u8d64\u8272\u306e\u7dda\u3067<\/span>\r\n<span class=\"n\">en1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot_geometry<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">Circle<\/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\">1<\/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> \r\n    <span class=\"n\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">,<\/span> <span class=\"n\">legend<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">,<\/span> <span class=\"n\">is_filled<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">show<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span>\r\n<span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u5186\u306e\u5185\u90e8\u3092\u9ec4\u8272\u3067\u5857\u308a\u3064\u3076\u3059<\/span>\r\n<span class=\"n\">en2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot_geometry<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">Circle<\/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\">1<\/span><span class=\"p\">),<\/span> <span class=\"p\">{<\/span><span class=\"s1\">'color'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'yellow'<\/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=\"n\">legend<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">show<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span>\r\n<span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u91cd\u306d\u3066\u8868\u793a<\/span>\r\n<span class=\"p\">(<\/span><span class=\"n\">en1<\/span> <span class=\"o\">+<\/span> <span class=\"n\">en2<\/span><span class=\"p\">)<\/span><span class=\"o\">.<\/span><span class=\"n\">show<\/span><span class=\"p\">()<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"output_svg output_subarea \">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6944\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbnuri09.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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>\u5186\u306e\u5185\u90e8\u304c $ x^2 + y^2 \\leq 1$ \u3067\u3042\u308b\u3053\u3068\u304b\u3089\uff0c<code>plot_implicit()<\/code> \u3092\u4f7f\u3063\u3066\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 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=\"n\">plot_implicit<\/span><span class=\"p\">(<\/span>\r\n    <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> <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=\"p\">(<\/span><span class=\"n\">y<\/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=\"c1\"># color \u306f\u5857\u308a\u3064\u3076\u3059\u8272\uff0cborder_color \u306f\u7e01\u306e\u7dda\u306e\u8272<\/span>\r\n    <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"yellow\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">border_color<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"red\"<\/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\">1.1<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.1<\/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\">1.1<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.1<\/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\">grid<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/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 size-large wp-image-6945\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbnuri10.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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\u306e\u5185\u90e8\u3092\u5857\u308a\u3064\u3076\u3059\">\u6247\u5f62\u306e\u5185\u90e8\u3092\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[47]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u5186\u306e\u4e00\u90e8\u3092\u5a92\u4ecb\u5909\u6570\u8868\u793a\u3067<\/span>\r\n<span class=\"n\">p1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot_parametric<\/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=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"black\"<\/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\">1.1<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.1<\/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\">1.1<\/span><span class=\"p\">,<\/span> <span class=\"mf\">1.1<\/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=\"n\">legend<\/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\">use_cm<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">,<\/span> <span class=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># 2\u672c\u306e\u76f4\u7dda<\/span>\r\n<span class=\"n\">p2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot_list<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"p\">([<\/span><span class=\"mi\">0<\/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=\"p\">[<\/span><span class=\"mi\">0<\/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> <span class=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"black\"<\/span><span class=\"p\">}),<\/span> \r\n    <span class=\"p\">([<\/span><span class=\"mi\">0<\/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=\"p\">[<\/span><span class=\"mi\">0<\/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> <span class=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"black\"<\/span><span class=\"p\">}),<\/span> <span class=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u91cd\u306d\u3066\u8868\u793a<\/span>\r\n<span class=\"p\">(<\/span><span class=\"n\">p1<\/span><span class=\"o\">+<\/span><span class=\"n\">p2<\/span><span class=\"p\">)<\/span><span class=\"o\">.<\/span><span class=\"n\">show<\/span><span class=\"p\">();<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6946\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbnuri11.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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>plot_implicit()<\/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[48]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">p3<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot_implicit<\/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> <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> <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> <span class=\"n\">legend<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">color<\/span> <span class=\"o\">=<\/span> <span class=\"s2\">\"yellow\"<\/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\"># \u30b0\u30e9\u30d5\u306e\u8868\u793a\u7bc4\u56f2<\/span>\r\n    <span class=\"n\">xlim<\/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> <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=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s2\">\"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>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6948\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbnuri12A.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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>\u7e01\u306e\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[49]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"p\">(<\/span><span class=\"n\">p1<\/span><span class=\"o\">+<\/span><span class=\"n\">p2<\/span><span class=\"o\">+<\/span><span class=\"n\">p3<\/span><span class=\"p\">)<\/span><span class=\"o\">.<\/span><span class=\"n\">show<\/span><span class=\"p\">();<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6949\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbnuri13.svg\" alt=\"\" width=\"640\" height=\"427\" \/><\/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=\"\u7df4\u7fd2-3-2\">\u7df4\u7fd2 3-2<\/h3>\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<h4 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<\/h4>\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\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[50]:<\/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\">r<\/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<span class=\"c1\"># x \u5ea7\u6a19<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">x<\/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\">r<\/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><span class=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">phi<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># y \u5ea7\u6a19<\/span>\r\n<span class=\"k\">def<\/span> <span class=\"nf\">y<\/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\">r<\/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><span class=\"o\">*<\/span><span class=\"n\">sin<\/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[51]:<\/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\">39.767<\/span>\r\n<span class=\"n\">eP<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.254<\/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\">30.1104<\/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[52]:<\/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\">phieq<\/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\">r<\/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<\/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\"># \u3082\u3046\u4e00\u3064\u306e\u89e3\u306f...<\/span>\r\n<span class=\"c1\"># nsolve(Eq(r(aP, eP, phi), aN), phi, (-float(pi)\/2, 0))<\/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<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<h4 id=\"2.-\u6d77\u738b\u661f\u3068\u51a5\u738b\u661f\u306e\u8ecc\u9053\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\">2. \u6d77\u738b\u661f\u3068\u51a5\u738b\u661f\u306e\u8ecc\u9053\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-large wp-image-6797\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/spbfig16.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<h4 id=\"3.-\u539f\u70b9\u30682\u3064\u306e\u8ecc\u9053\u306e\u4ea4\u70b9\u3092\u7d50\u3076\u76f4\u7dda\u30922\u672c\u63cf\u304f\">3. \u539f\u70b9\u30682\u3064\u306e\u8ecc\u9053\u306e\u4ea4\u70b9\u3092\u7d50\u3076\u76f4\u7dda\u30922\u672c\u63cf\u304f<\/h4>\n<p>\u539f\u70b9 $(0, 0)$ \u3068 $(x1, y1)$ \u3092\u7d50\u3076\u76f4\u7dda\u3092\u63cf\u304f\u306e\u306f<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">plot_list<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">x1<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">y1<\/span><span class=\"p\">])<\/span>\r\n<\/pre>\n<\/div>\n<p>\u3067\u3042\u3063\u305f\u3002<\/p>\n<p>\u4ea4\u70b9\u306e1\u3064\u306f<\/p>\n<ul>\n<li>$(x(a_N, e_N, \\phi_{\\rm eq}), y(a_N, e_N, \\phi_{\\rm eq}))$\uff0c<\/li>\n<\/ul>\n<p>\u3082\u3046\u4e00\u3064\u306f<\/p>\n<ul>\n<li>$(x(a_N, e_N, -\\phi_{\\rm eq}), y(a_N, e_N, -\\phi_{\\rm eq}))$<\/li>\n<\/ul>\n<p>\u3067\u3042\u308b\u304b\u3089\uff0c1\u672c\u305a\u3064\u76f4\u7dda\u3092\u5f15\u304f\u3002\u539f\u70b9 $(0, 0)$ \u3068 $(x2, y2)$ \u3092\u7d50\u3076\u76f4\u7dda\u3082\u4e00\u7dd2\u306b\u540c\u3058\u8272\u3067\u63cf\u304f\u306b\u306f\uff0c<\/p>\n<div class=\"highlight\">\n<pre><span class=\"n\">plot_list<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">x1<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">y1<\/span><span class=\"p\">],<\/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=\"p\">([<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">x2<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">y2<\/span><span class=\"p\">],<\/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=\"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=\"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<\/h4>\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\">phieq<\/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=7, y=0 \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\">7<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">mytext<\/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=\"5.-\u6247\u5f62\u306e\u90e8\u5206\u3092\u5857\u308a\u3064\u3076\u3059\">5. \u6247\u5f62\u306e\u90e8\u5206\u3092\u5857\u308a\u3064\u3076\u3059<\/h4>\n<p>\u6700\u5f8c\u306b\uff0c\u51a5\u738b\u661f\u306e\u307b\u3046\u304c\u6d77\u738b\u661f\u3088\u308a\u592a\u967d\u306b\u8fd1\u3044\u671f\u9593\u306e\u6247\u5f62\u306e\u90e8\u5206\u3092\u5857\u308a\u3064\u3076\u3057\uff0c\u30b0\u30e9\u30d5\u3092\u5b8c\u6210\u3055\u305b\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<h4 id=\"\u5b8c\u6210\u30a4\u30e1\u30fc\u30b8\">\u5b8c\u6210\u30a4\u30e1\u30fc\u30b8<\/h4>\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 size-large wp-image-6951\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/kadai4answer.svg\" alt=\"\" width=\"640\" height=\"640\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u3053\u3053\u3067\u306f\uff0cSymPy Plotting Backends (SPB) \u306e Plot functions \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 The Graphic Module \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\uff1aThe Graphic Module \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%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\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":6721,"menu_order":30,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-6738","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\/6738","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=6738"}],"version-history":[{"count":13,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/6738\/revisions"}],"predecessor-version":[{"id":9810,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/6738\/revisions\/9810"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/6721"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=6738"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}