{"id":7859,"date":"2024-03-01T09:40:39","date_gmt":"2024-03-01T00:40:39","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=7859"},"modified":"2024-03-10T16:58:54","modified_gmt":"2024-03-10T07:58:54","slug":"sympy-plotting-backends-%e3%81%a7%e6%a5%95%e5%86%86%e3%82%84%e5%9b%9e%e8%bb%a2%e6%a5%95%e5%86%86%e4%bd%93%e3%82%92%e6%8f%8f%e3%81%8f","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/7859\/","title":{"rendered":"SymPy Plotting Backends \u3067\u6955\u5186\u3084\u56de\u8ee2\u6955\u5186\u4f53\u3092\u63cf\u304f"},"content":{"rendered":"<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u7406\u5de5\u7cfb\u306e\u6570\u5b66 B \u306e\u6388\u696d\u3067\uff0c\u6955\u5186\u306e\u5468\u9577\u3084\u9762\u7a4d\uff0c\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\u7a4d\u3084\u4f53\u7a4d\u3092\u6c42\u3081\u3066\u3044\u308b\u306e\u3067\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/%e7%a9%8d%e5%88%86%ef%bc%9a%e3%81%84%e3%81%8f%e3%81%a4%e3%81%8b%e3%81%ae%e5%bf%9c%e7%94%a8\/%e5%8f%82%e8%80%83%ef%bc%9amaxima-%e3%81%a7%e6%a5%95%e5%86%86%e3%81%ae%e9%9d%a2%e7%a9%8d%e3%83%bb%e5%91%a8%ef%bc%8c%e5%9b%9e%e8%bb%a2%e6%a5%95%e5%86%86%e4%bd%93%e3%81%ae%e8%a1%a8%e9%9d%a2%e7%a9%8d\/\">\u53c2\u8003\uff1aMaxima \u3067\u6955\u5186\u306e\u9762\u7a4d\u30fb\u5468\uff0c\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\u7a4d\u30fb\u4f53\u7a4d<\/a><\/li>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/%e7%a9%8d%e5%88%86%ef%bc%9a%e3%81%84%e3%81%8f%e3%81%a4%e3%81%8b%e3%81%ae%e5%bf%9c%e7%94%a8\/%e5%8f%82%e8%80%83%ef%bc%9asympy-%e3%81%a7%e6%a5%95%e5%86%86%e3%81%ae%e9%9d%a2%e7%a9%8d%e3%83%bb%e5%91%a8%ef%bc%8c%e5%9b%9e%e8%bb%a2%e6%a5%95%e5%86%86%e4%bd%93%e3%81%ae%e8%a1%a8%e9%9d%a2%e7%a9%8d\/\">\u53c2\u8003\uff1aSymPy \u3067\u6955\u5186\u306e\u9762\u7a4d\u30fb\u5468\uff0c\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\u7a4d\u30fb\u4f53\u7a4d<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<p><!--more--><\/p>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u5fc5\u8981\u306a\u30e2\u30b8\u30e5\u30fc\u30eb\u306e-import\">\u5fc5\u8981\u306a\u30e2\u30b8\u30e5\u30fc\u30eb\u306e import<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"kn\">from<\/span> <span class=\"nn\">sympy.abc<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">sympy<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n<span class=\"c1\"># SymPy Plotting Backends (SPB) <\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">spb<\/span> <span class=\"kn\">import<\/span> <span class=\"o\">*<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30e9\u30d5\u3092 SVG \u3067 Notebook \u306b\u30a4\u30f3\u30e9\u30a4\u30f3\u8868\u793a<\/span>\r\n<span class=\"o\">%<\/span><span class=\"k\">config<\/span> InlineBackend.figure_formats = ['svg']\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing 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=\"mathtext.fontset-\u306e\u8a2d\u5b9a\"><code>mathtext.fontset<\/code> \u306e\u8a2d\u5b9a<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u30b0\u30e9\u30d5\u3092\u63cf\u304f\u305f\u3081\u3067\u306f\u306a\u304f\u30c7\u30d5\u30a9\u30eb\u30c8\u8a2d\u5b9a\u306e\u305f\u3081<\/span>\r\n<span class=\"kn\">import<\/span> <span class=\"nn\">matplotlib.pyplot<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">plt<\/span>\r\n\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">rcParams<\/span><span class=\"p\">[<\/span><span class=\"s1\">'mathtext.fontset'<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'cm'<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u5857\u308a\u3064\u3076\u3057\u305f\u6955\u5186\">\u5857\u308a\u3064\u3076\u3057\u305f\u6955\u5186<\/h3>\n<p>SymPy Plotting Backends \u3067\u9577\u534a\u5f84 $a$\uff0c\u5358\u534a\u5f84 $b$ \u306e\u6955\u5186\u3092\u63cf\u304f\u4f8b\u3002<code>Ellipse()<\/code> \u3092\u4f7f\u3063\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"n\">a<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2<\/span>\r\n<span class=\"n\">b<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>\r\n<span class=\"n\">alim<\/span> <span class=\"o\">=<\/span> <span class=\"n\">a<\/span><span class=\"o\">+<\/span><span class=\"mf\">0.5<\/span>\r\n<span class=\"n\">blim<\/span> <span class=\"o\">=<\/span> <span class=\"n\">b<\/span><span class=\"o\">+<\/span><span class=\"mf\">0.5<\/span>\r\n\r\n<span class=\"n\">p<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot_geometry<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">Ellipse<\/span><span class=\"p\">(<\/span><span class=\"n\">Point<\/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=\"n\">hradius<\/span><span class=\"o\">=<\/span><span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">vradius<\/span><span class=\"o\">=<\/span><span class=\"n\">b<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"p\">{<\/span><span class=\"s2\">\"facecolor\"<\/span><span class=\"p\">:<\/span> <span class=\"s2\">\"yellow\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"edgecolor\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"darkblue\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">},<\/span> \r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mi\">4<\/span><span class=\"p\">),<\/span> <span class=\"n\">n<\/span><span class=\"o\">=<\/span><span class=\"mi\">400<\/span><span class=\"p\">,<\/span> <span class=\"n\">show<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">);<\/span>\r\n\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">ax<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"o\">.<\/span><span class=\"n\">tight_layout<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># \u8868\u793a\u7bc4\u56f2<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlim<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">alim<\/span><span class=\"p\">,<\/span> <span class=\"n\">alim<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylim<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">blim<\/span><span class=\"p\">,<\/span> <span class=\"n\">blim<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># \u76ee\u76db\u8a2d\u5b9a<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">([<\/span><span class=\"o\">-<\/span><span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">a<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"s2\">\"$-a$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$0$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$a$\"<\/span><span class=\"p\">],<\/span> <span class=\"n\">fontsize<\/span><span class=\"o\">=<\/span><span class=\"mi\">16<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_yticks<\/span><span class=\"p\">([<\/span><span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"s2\">\"$-b$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$0$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$b$\"<\/span><span class=\"p\">],<\/span> <span class=\"n\">fontsize<\/span><span class=\"o\">=<\/span><span class=\"mi\">16<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># x \u8ef8\uff0cy \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\">'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\">0.6<\/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\">'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\">0.6<\/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-7965\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/SPBdaen1.svg\" alt=\"\" width=\"640\" height=\"400\" \/><\/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=\"\u5857\u308a\u3064\u3076\u3057\u7121\u3057\u306e\u6955\u5186\">\u5857\u308a\u3064\u3076\u3057\u7121\u3057\u306e\u6955\u5186<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[4]:<\/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_geometry<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">Ellipse<\/span><span class=\"p\">(<\/span><span class=\"n\">Point<\/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=\"n\">hradius<\/span><span class=\"o\">=<\/span><span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">vradius<\/span><span class=\"o\">=<\/span><span class=\"n\">b<\/span><span class=\"p\">),<\/span>\r\n    <span class=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"darkblue\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">3<\/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\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mi\">4<\/span><span class=\"p\">),<\/span> <span class=\"n\">n<\/span><span class=\"o\">=<\/span><span class=\"mi\">400<\/span><span class=\"p\">,<\/span> <span class=\"n\">show<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">);<\/span>\r\n\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">ax<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"o\">.<\/span><span class=\"n\">tight_layout<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># \u8868\u793a\u7bc4\u56f2<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlim<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">alim<\/span><span class=\"p\">,<\/span> <span class=\"n\">alim<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylim<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">blim<\/span><span class=\"p\">,<\/span> <span class=\"n\">blim<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># \u76ee\u76db\u8a2d\u5b9a<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">([<\/span><span class=\"o\">-<\/span><span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">a<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"s2\">\"$-a$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$0$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$a$\"<\/span><span class=\"p\">],<\/span> <span class=\"n\">fontsize<\/span><span class=\"o\">=<\/span><span class=\"mi\">16<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_yticks<\/span><span class=\"p\">([<\/span><span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"s2\">\"$-b$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$0$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$b$\"<\/span><span class=\"p\">],<\/span> <span class=\"n\">fontsize<\/span><span class=\"o\">=<\/span><span class=\"mi\">16<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># x \u8ef8\uff0cy \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\">'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\">0.6<\/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\">'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\">0.6<\/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-7966\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/SPBdaen2.svg\" alt=\"\" width=\"640\" height=\"400\" \/><\/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=\"\u9577\u8ef8\u306e\u5468\u308a\u306b\u56de\u8ee2\u3057\u305f\u56de\u8ee2\u6955\u5186\u4f53\">\u9577\u8ef8\u306e\u5468\u308a\u306b\u56de\u8ee2\u3057\u305f\u56de\u8ee2\u6955\u5186\u4f53<\/h3>\n<p>\\begin{eqnarray}<br \/>\n\\frac{x^2}{a^2} + \\frac{y^2}{b^2} &amp;=&amp; 1, \\quad b \\equiv a \\sqrt{1-e^2}\\\\<br \/>\n\\therefore\\ \\ y &amp;=&amp; b \\sqrt{1-\\frac{x^2}{a^2}} \\equiv f(x)<br \/>\n\\end{eqnarray}<\/p>\n<p>$y = f(x)$ \u3092 $x$ \u306e\u5468\u308a\u306b\u56de\u8ee2\u3057\u3066\u3067\u304d\u308b\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\u3092\u63cf\u304f\u3002\u307e\u305a\uff0c<\/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=\"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=\"n\">b<\/span><span class=\"o\">*<\/span><span class=\"p\">(<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"o\">-<\/span><span class=\"n\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"o\">\/<\/span><span class=\"n\">a<\/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 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>$-a \\leq x \\leq a$ \u306e\u7bc4\u56f2\u3067 $0 \\leq y \\leq f(x)$ \u306e\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3057\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[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u5857\u308a\u3064\u3076\u3057\u90e8\u5206<\/span>\r\n<span class=\"c1\"># plot_implicit \u306f\u4e0d\u7b49\u5f0f\u3067\u7bc4\u56f2\u6307\u5b9a\u3067\u304d\u308b\u304c\uff0c<\/span>\r\n<span class=\"c1\"># \u5c11\u3057\u6642\u9593\u304c\u304b\u304b\u308b<\/span>\r\n<span class=\"n\">p1<\/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> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">a<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/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=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mi\">4<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"c1\"># \u5857\u308a\u3064\u3076\u3057\u306e\u8272<\/span>\r\n    <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s1\">'lightblue'<\/span><span class=\"p\">,<\/span> <span class=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span>\r\n<span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">p2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"c1\"># y = f(x)<\/span>\r\n    <span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">a<\/span><span class=\"p\">),<\/span> <span class=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"darkblue\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">}),<\/span> \r\n    <span class=\"c1\"># \u9577\u8ef8<\/span>\r\n    <span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">alim<\/span><span class=\"p\">,<\/span> <span class=\"n\">alim<\/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=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">2<\/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=\"p\">(<\/span><span class=\"n\">p1<\/span><span class=\"o\">+<\/span><span class=\"n\">p2<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">ax<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"o\">.<\/span><span class=\"n\">tight_layout<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"c1\"># \u30b0\u30ea\u30c3\u30c9\u3092\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\">linestyle<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># \u8868\u793a\u7bc4\u56f2<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlim<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">alim<\/span><span class=\"p\">,<\/span> <span class=\"n\">alim<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylim<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">blim<\/span><span class=\"p\">,<\/span> <span class=\"n\">blim<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># \u76ee\u76db\u8a2d\u5b9a<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">([<\/span><span class=\"o\">-<\/span><span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">a<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"s2\">\"$-a$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$0$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$a$\"<\/span><span class=\"p\">],<\/span> <span class=\"n\">fontsize<\/span><span class=\"o\">=<\/span><span class=\"mi\">16<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_yticks<\/span><span class=\"p\">([<\/span><span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"s2\">\"$-b$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$0$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$b$\"<\/span><span class=\"p\">],<\/span> <span class=\"n\">fontsize<\/span><span class=\"o\">=<\/span><span class=\"mi\">16<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># x \u8ef8\uff0cy \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\">'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\">0.6<\/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\">'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\">0.6<\/span><span class=\"p\">);<\/span>\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\u975e\u8868\u793a\u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">get_legend<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">set_visible<\/span><span class=\"p\">(<\/span><span class=\"kc\">False<\/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-7967\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/SPBdaen3.svg\" alt=\"\" width=\"640\" height=\"400\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$y = f(x)$ \u3092 $x$ \u8ef8\u306e\u5468\u308a\u306b $\\theta$ \u3060\u3051\u56de\u8ee2\u3055\u305b\u308b\u3068\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\nx &amp;=&amp; x \\\\<br \/>\ny &amp;=&amp; f(x) \\cos\\theta \\\\<br \/>\nz &amp;=&amp; f(x) \\sin\\theta<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3068\u306a\u308b\u3053\u3068\u306b\u7559\u610f\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=\"c1\"># \u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762<\/span>\r\n<span class=\"n\">p1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot3d_parametric_surface<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">x<\/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=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/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=\"o\">*<\/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\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"n\">a<\/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=\"p\">{<\/span><span class=\"s1\">'cmap'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'Blues'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'lw'<\/span><span class=\"p\">:<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'edgecolor'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'lightblue'<\/span><span class=\"p\">},<\/span> \r\n    <span class=\"n\">use_cm<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">,<\/span> <span class=\"n\">color_func<\/span><span class=\"o\">=<\/span><span class=\"n\">f<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">),<\/span> <span class=\"n\">colorbar<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">axis<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">6.4<\/span><span class=\"p\">),<\/span> <span class=\"n\">n<\/span><span class=\"o\">=<\/span><span class=\"mi\">40<\/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=\"n\">alim<\/span><span class=\"p\">,<\/span><span class=\"n\">alim<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">blim<\/span><span class=\"p\">,<\/span> <span class=\"n\">blim<\/span><span class=\"p\">),<\/span> <span class=\"n\">zlim<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">blim<\/span><span class=\"p\">,<\/span> <span class=\"n\">blim<\/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\">show<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span>\r\n<span class=\"p\">);<\/span>\r\n\r\n<span class=\"n\">p2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot3d_parametric_line<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"c1\"># x \u8ef8<\/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\">0<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">alim<\/span><span class=\"p\">,<\/span> <span class=\"n\">a<\/span><span class=\"p\">),<\/span> <span class=\"s2\">\"\"<\/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=\"s2\">\"zorder\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">2<\/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\">0<\/span><span class=\"p\">,<\/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\">alim<\/span><span class=\"p\">),<\/span> <span class=\"s2\">\"\"<\/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=\"s2\">\"zorder\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span><span class=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">2<\/span><span class=\"p\">}),<\/span> \r\n    <span class=\"c1\"># z = z(x)<\/span>\r\n    <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">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=\"o\">-<\/span><span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">a<\/span><span class=\"o\">+<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">),<\/span> <span class=\"s2\">\"\"<\/span><span class=\"p\">,<\/span> <span class=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"darkblue\"<\/span><span class=\"p\">,<\/span><span class=\"s2\">\"zorder\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">}),<\/span>\r\n    <span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">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=\"o\">-<\/span><span class=\"n\">a<\/span><span class=\"o\">+<\/span><span class=\"mf\">0.1<\/span><span class=\"p\">,<\/span>  <span class=\"n\">a<\/span><span class=\"p\">),<\/span> <span class=\"s2\">\"\"<\/span><span class=\"p\">,<\/span> <span class=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"darkblue\"<\/span><span class=\"p\">,<\/span><span class=\"s2\">\"zorder\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span><span class=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">}),<\/span>\r\n    <span class=\"n\">use_cm<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span> <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=\"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-7968\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/SPBdaen4.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=\"\u77ed\u8ef8\u306e\u5468\u308a\u306b\u56de\u8ee2\u3057\u305f\u56de\u8ee2\u6955\u5186\u4f53\">\u77ed\u8ef8\u306e\u5468\u308a\u306b\u56de\u8ee2\u3057\u305f\u56de\u8ee2\u6955\u5186\u4f53<\/h3>\n<p>$\\displaystyle x = a \\sqrt{1-\\frac{y^2}{b^2}} \\equiv g(y)$ \u3092 $y$ \u306e\u5468\u308a\u306b\u56de\u8ee2\u3057\u3066\u3067\u304d\u308b\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\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=\"k\">def<\/span> <span class=\"nf\">g<\/span><span class=\"p\">(<\/span><span class=\"n\">y<\/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=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/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=\"n\">b<\/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 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>$-b \\leq y \\leq b$ \u306e\u7bc4\u56f2\u3067 $0 \\leq x \\leq g(y)$ \u306e\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3057\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[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u5857\u308a\u3064\u3076\u3057\u90e8\u5206<\/span>\r\n<span class=\"n\">p1<\/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\">x<\/span><span class=\"p\">)<\/span> <span class=\"o\">&amp;<\/span> <span class=\"p\">(<\/span><span class=\"n\">x<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"n\">g<\/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=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">a<\/span><span class=\"p\">),<\/span> <span class=\"p\">(<\/span><span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/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=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mi\">4<\/span><span class=\"p\">),<\/span> \r\n    <span class=\"n\">aspect<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'equal'<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"c1\"># \u5857\u308a\u3064\u3076\u3057\u306e\u8272<\/span>\r\n    <span class=\"n\">color<\/span><span class=\"o\">=<\/span><span class=\"s1\">'lightpink'<\/span><span class=\"p\">,<\/span> <span class=\"n\">show<\/span> <span class=\"o\">=<\/span> <span class=\"kc\">False<\/span>\r\n<span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">p2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot_parametric<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"c1\"># x = g(y)<\/span>\r\n    <span class=\"p\">(<\/span><span class=\"n\">g<\/span><span class=\"p\">(<\/span><span class=\"n\">y<\/span><span class=\"p\">),<\/span> <span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"darkred\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">}),<\/span>\r\n    <span class=\"c1\"># \u77ed\u8ef8<\/span>\r\n    <span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"n\">y<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">blim<\/span><span class=\"p\">,<\/span> <span class=\"n\">blim<\/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> <span class=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">2<\/span><span class=\"p\">}),<\/span>\r\n    <span class=\"n\">use_cm<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span> <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=\"p\">(<\/span><span class=\"n\">p1<\/span><span class=\"o\">+<\/span><span class=\"n\">p2<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">ax<\/span> <span class=\"o\">=<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">fig<\/span><span class=\"p\">,<\/span> <span class=\"n\">p<\/span><span class=\"o\">.<\/span><span class=\"n\">ax<\/span>\r\n<span class=\"n\">fig<\/span><span class=\"o\">.<\/span><span class=\"n\">tight_layout<\/span><span class=\"p\">()<\/span>\r\n\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">grid<\/span><span class=\"p\">(<\/span><span class=\"n\">linestyle<\/span> <span class=\"o\">=<\/span> <span class=\"s1\">'dotted'<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># \u8868\u793a\u7bc4\u56f2<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlim<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">alim<\/span><span class=\"p\">,<\/span> <span class=\"n\">alim<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylim<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"n\">blim<\/span><span class=\"p\">,<\/span> <span class=\"n\">blim<\/span><span class=\"p\">)<\/span>\r\n<span class=\"c1\"># \u76ee\u76db\u8a2d\u5b9a<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xticks<\/span><span class=\"p\">([<\/span><span class=\"o\">-<\/span><span class=\"n\">a<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">a<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"s2\">\"$-a$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$0$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$a$\"<\/span><span class=\"p\">],<\/span> <span class=\"n\">fontsize<\/span><span class=\"o\">=<\/span><span class=\"mi\">16<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_yticks<\/span><span class=\"p\">([<\/span><span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">],<\/span> <span class=\"p\">[<\/span><span class=\"s2\">\"$-b$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$0$\"<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"$b$\"<\/span><span class=\"p\">],<\/span> <span class=\"n\">fontsize<\/span><span class=\"o\">=<\/span><span class=\"mi\">16<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">set_ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\"<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"c1\"># x \u8ef8\uff0cy \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\">'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\">0.6<\/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\">'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\">0.6<\/span><span class=\"p\">);<\/span>\r\n<span class=\"c1\"># \u51e1\u4f8b\u3092\u975e\u8868\u793a\u306b<\/span>\r\n<span class=\"n\">ax<\/span><span class=\"o\">.<\/span><span class=\"n\">get_legend<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">set_visible<\/span><span class=\"p\">(<\/span><span class=\"kc\">False<\/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-7969\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/SPBdaen5.svg\" alt=\"\" width=\"640\" height=\"400\" \/><\/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>$x = g(z)$ \u3092 $z$ \u8ef8\u306e\u5468\u308a\u306b $\\theta$ \u3060\u3051\u56de\u8ee2\u3055\u305b\u308b\u3068\uff0c<\/p>\n<p>\\begin{eqnarray}<br \/>\nx &amp;=&amp; g(z) \\cos\\theta \\\\<br \/>\ny &amp;=&amp; g(z) \\sin\\theta \\\\<br \/>\nz &amp;=&amp; z<br \/>\n\\end{eqnarray}<\/p>\n<p>\u3068\u306a\u308b\u3053\u3068\u306b\u7559\u610f\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[10]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-ipython3\">\n<pre><span class=\"c1\"># \u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762<\/span>\r\n<span class=\"n\">p1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot3d_parametric_surface<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">g<\/span><span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"n\">cos<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">),<\/span> <span class=\"n\">g<\/span><span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">),<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"n\">b<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/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=\"p\">{<\/span><span class=\"s1\">'cmap'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'Reds'<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'lw'<\/span><span class=\"p\">:<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span> <span class=\"s1\">'edgecolor'<\/span><span class=\"p\">:<\/span><span class=\"s1\">'pink'<\/span><span class=\"p\">},<\/span> \r\n    <span class=\"n\">use_cm<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">,<\/span> <span class=\"n\">color_func<\/span><span class=\"o\">=<\/span><span class=\"n\">g<\/span><span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"n\">sin<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">),<\/span> <span class=\"n\">colorbar<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span> \r\n    <span class=\"n\">axis<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span> <span class=\"n\">size<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"mf\">6.4<\/span><span class=\"p\">,<\/span> <span class=\"mf\">6.4<\/span><span class=\"p\">),<\/span> <span class=\"n\">n<\/span><span class=\"o\">=<\/span><span class=\"mi\">80<\/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\">2.2<\/span><span class=\"p\">,<\/span><span class=\"mf\">2.2<\/span><span class=\"p\">),<\/span> <span class=\"n\">ylim<\/span><span class=\"o\">=<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mf\">2.2<\/span><span class=\"p\">,<\/span> <span class=\"mf\">2.2<\/span><span class=\"p\">),<\/span> <span class=\"n\">zlim<\/span><span class=\"o\">=<\/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\">show<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span>\r\n    <span class=\"p\">)<\/span>\r\n\r\n<span class=\"n\">p2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">plot3d_parametric_line<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"c1\"># z \u8ef8<\/span>\r\n    <span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"s2\">\"\"<\/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><span class=\"s2\">\"zorder\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">2<\/span><span class=\"p\">}),<\/span> \r\n    <span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"n\">b<\/span><span class=\"p\">,<\/span>  <span class=\"mi\">2<\/span><span class=\"p\">),<\/span> <span class=\"s2\">\"\"<\/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><span class=\"s2\">\"zorder\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span><span class=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">2<\/span><span class=\"p\">}),<\/span> \r\n    <span class=\"c1\"># x = g(z)<\/span>\r\n    <span class=\"p\">(<\/span><span class=\"n\">g<\/span><span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"p\">),<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mi\">2<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">),<\/span> <span class=\"s2\">\"\"<\/span><span class=\"p\">,<\/span> <span class=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"darkred\"<\/span><span class=\"p\">,<\/span><span class=\"s2\">\"zorder\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span><span class=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">}),<\/span> \r\n    <span class=\"p\">(<\/span><span class=\"n\">g<\/span><span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"p\">),<\/span> <span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"p\">(<\/span><span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"o\">-<\/span><span class=\"mf\">0.5<\/span><span class=\"p\">,<\/span>  <span class=\"n\">b<\/span><span class=\"p\">),<\/span> <span class=\"s2\">\"\"<\/span><span class=\"p\">,<\/span> <span class=\"p\">{<\/span><span class=\"s2\">\"color\"<\/span><span class=\"p\">:<\/span><span class=\"s2\">\"darkred\"<\/span><span class=\"p\">,<\/span><span class=\"s2\">\"zorder\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span><span class=\"s2\">\"lw\"<\/span><span class=\"p\">:<\/span><span class=\"mi\">3<\/span><span class=\"p\">}),<\/span> \r\n    <span class=\"n\">use_cm<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span><span class=\"p\">,<\/span> <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=\"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-7970\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/Spbdaen6.svg\" alt=\"\" width=\"640\" height=\"640\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u7406\u5de5\u7cfb\u306e\u6570\u5b66 B \u306e\u6388\u696d\u3067\uff0c\u6955\u5186\u306e\u5468\u9577\u3084\u9762\u7a4d\uff0c\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\u7a4d\u3084\u4f53\u7a4d\u3092\u6c42\u3081\u3066\u3044\u308b\u306e\u3067\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/7859\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n<ul>\n<li>\u53c2\u8003\uff1aMaxima \u3067\u6955\u5186\u306e\u9762\u7a4d\u30fb\u5468\uff0c\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\u7a4d\u30fb\u4f53\u7a4d<\/li>\n<li>\u53c2\u8003\uff1aSymPy \u3067\u6955\u5186\u306e\u9762\u7a4d\u30fb\u5468\uff0c\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\u7a4d\u30fb\u4f53\u7a4d<\/li>\n<\/ul>\n","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[12],"tags":[],"class_list":["post-7859","post","type-post","status-publish","format-standard","hentry","category-sympy","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.0.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u7406\u5de5\u7cfb\u306e\u6570\u5b66 B \u306e\u6388\u696d\u3067\uff0c\u6955\u5186\u306e\u5468\u9577\u3084\u9762\u7a4d\uff0c\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\u7a4d\u3084\u4f53\u7a4d\u3092\u6c42\u3081\u3066\u3044\u308b\u306e\u3067\u3002 \u53c2\u8003\uff1aMaxima\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" 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content=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/7859\/\" \/>\n\t\t<meta property=\"article:published_time\" content=\"2024-03-01T00:40:39+00:00\" \/>\n\t\t<meta property=\"article:modified_time\" content=\"2024-03-10T07:58:54+00:00\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary\" \/>\n\t\t<meta name=\"twitter:title\" content=\"SymPy Plotting Backends \u3067\u6955\u5186\u3084\u56de\u8ee2\u6955\u5186\u4f53\u3092\u63cf\u304f - \u76f8\u5bfe\u8ad6\u306e\u7406\u89e3\u3068\u305d\u306e\u5468\u8fba\" \/>\n\t\t<meta name=\"twitter:description\" content=\"\u7406\u5de5\u7cfb\u306e\u6570\u5b66 B \u306e\u6388\u696d\u3067\uff0c\u6955\u5186\u306e\u5468\u9577\u3084\u9762\u7a4d\uff0c\u56de\u8ee2\u6955\u5186\u4f53\u306e\u8868\u9762\u7a4d\u3084\u4f53\u7a4d\u3092\u6c42\u3081\u3066\u3044\u308b\u306e\u3067\u3002 \u53c2\u8003\uff1aMaxima\" \/>\n\t\t<script type=\"application\/ld+json\" class=\"aioseo-schema\">\n\t\t\t{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"BlogPosting\",\"@id\":\"https:\\\/\\\/home.hirosaki-u.ac.jp\\\/relativity\\\/7859\\\/#blogposting\",\"name\":\"SymPy Plotting Backends \\u3067\\u6955\\u5186\\u3084\\u56de\\u8ee2\\u6955\\u5186\\u4f53\\u3092\\u63cf\\u304f - \\u76f8\\u5bfe\\u8ad6\\u306e\\u7406\\u89e3\\u3068\\u305d\\u306e\\u5468\\u8fba\",\"headline\":\"SymPy Plotting Backends 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