{"id":3934,"date":"2022-09-22T15:42:40","date_gmt":"2022-09-22T06:42:40","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=3934"},"modified":"2023-03-28T09:58:26","modified_gmt":"2023-03-28T00:58:26","slug":"maxima-%e3%81%a7%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e5%a0%b4%ef%bc%88%e9%9b%bb%e5%a0%b4%e3%83%bb%e7%a3%81%e5%a0%b4%ef%bc%89%e3%82%92%e6%8f%8f%e3%81%8f","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3934\/","title":{"rendered":"Maxima \u3067\u30d9\u30af\u30c8\u30eb\u5834\uff08\u96fb\u5834\u30fb\u78c1\u5834\uff09\u3092\u63cf\u304f"},"content":{"rendered":"<p>\u96fb\u78c1\u6c17\u5b66\u306e\u6388\u696d\u306e\u6e96\u5099\u300c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3595\/\">gnuplot \u3067\u30d9\u30af\u30c8\u30eb\u5834\uff08\u96fb\u5834\u30fb\u78c1\u5834\uff09\u3092\u63cf\u304f<\/a>\u300d\u306e Maxima \u7248\u3002<br \/>\n<!--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=\"\u70b9\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834-$\\boldsymbol{E}$\">\u70b9\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834 $\\boldsymbol{E}$<\/h3>\n<p>\\begin{eqnarray}<br \/>\n\\boldsymbol{E}<br \/>\n&amp;=&amp; \\frac{q_1}{4\\pi \\varepsilon_0} \\frac{\\boldsymbol{r} &#8211; \\boldsymbol{r}_1}{|\\boldsymbol{r} &#8211; \\boldsymbol{r}_1|^3}\\end{eqnarray}<\/p>\n<p>$z=0$ \u306e $xy$ \u5e73\u9762\u30672\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u5834\u3092\u63cf\u304f\u3002<\/p>\n<p>$$\\boldsymbol{r} = (x, y, 0), \\quad \\boldsymbol{r}_1 = (x_1, y_1, 0)$$$$E_x = s \\frac{x-x_1}{\\left((x-x_1)^2 + (y-y_1)^2\\right)^{3\/2}}$$$$E_y = s \\frac{y-y_1}{\\left((x-x_1)^2 + (y-y_1)^2\\right)^{3\/2}}$$<\/p>\n<p>$s$ \u306f $\\mbox{scaling}$ \u4fc2\u6570\u3002\u5b9f\u969b\u306e\u63cf\u753b\u306e\u969b\u306b\u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055\u3092\u5fae\u8abf\u6574\u3059\u308b\u4fc2\u6570\u3002<\/p>\n<ul>\n<li>\u53c2\u8003\uff1a<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e9%9d%99%e9%9b%bb%e5%a0%b4%ef%bc%9a%e9%9b%bb%e8%8d%b7%e5%af%86%e5%ba%a6%e3%81%8b%e3%82%89%e7%9b%b4%e6%8e%a5%e9%9b%bb%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b\/#i-2\">\u300c\u70b9\u96fb\u8377\u306e\u96fb\u8377\u5bc6\u5ea6\u3068\u96fb\u5834\u300d<\/a><\/li>\n<\/ul>\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=\"\u6b63\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\">\u6b63\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u96fb\u5834 E *\/<\/span>\r\n<span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">x<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span>3$\r\n<span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">y<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span>3$\r\n\r\n<span class=\"cm\">\/* 2\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306f vector([\u59cb\u70b9\u306ex, \u59cb\u70b9\u306ey], [x\u6210\u5206, y\u6210\u5206]) *\/<\/span>\r\n<span class=\"nf\">vecE<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">vector<\/span><span class=\"p\">([<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">-<\/span><span class=\"nv\">x1<\/span>, <span class=\"nv\">y<\/span><span class=\"o\">-<\/span><span class=\"nv\">y1<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">-<\/span><span class=\"nv\">x1<\/span>, <span class=\"nv\">y<\/span><span class=\"o\">-<\/span><span class=\"nv\">y1<\/span><span class=\"p\">)])<\/span>$\r\n\r\n<span class=\"cm\">\/* (x1, y1) \u306f\u6b63\u96fb\u8377\u306e\u4f4d\u7f6e *\/<\/span>\r\n<span class=\"p\">[<\/span><span class=\"nv\">x1<\/span>, <span class=\"nv\">y1<\/span><span class=\"p\">]<\/span><span class=\"o\">:<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 1<span class=\"p\">]<\/span>$\r\n\r\n<span class=\"cm\">\/* -3 &lt;= x &lt;= 3, -3 &lt;= y &lt;= 3 \u3067 1\/2 \u523b\u307f\u306e\u683c\u5b50\u70b9\u3092\u59cb\u70b9\u306b *\/<\/span>\r\n<span class=\"cm\">\/* makelist \u3067\u306f1\u6b21\u5143\u306e\u30ea\u30b9\u30c8\u3057\u304b\u4f5c\u308c\u306a\u3044\u3088\u3046\u306a\u306e\u3067\uff0c\u5c11\u3057\u5de5\u592b *\/<\/span>\r\n<span class=\"nv\">coordx<\/span><span class=\"o\">:<\/span> <span class=\"nf\">setify<\/span><span class=\"p\">(<\/span><span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span><span class=\"o\">-<\/span>3<span class=\"o\">+<\/span><span class=\"nv\">i<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span>, <span class=\"nv\">i<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">12<\/span><span class=\"p\">))<\/span>$\r\n<span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">listify<\/span><span class=\"p\">(<\/span><span class=\"nf\">cartesian_product<\/span><span class=\"p\">(<\/span><span class=\"nv\">coordx<\/span>,<span class=\"nv\">coordx<\/span><span class=\"p\">))<\/span>$\r\n\r\n<span class=\"cm\">\/* \u6b63\u96fb\u8377\u306e\u4f4d\u7f6e\u3067\u306f\u96fb\u5834\u306e\u5206\u6bcd\u304c\u30bc\u30ed\u306b\u306a\u308b\u306e\u3067\u9664\u304f *\/<\/span>\r\n<span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nf\">delete<\/span><span class=\"p\">([<\/span><span class=\"nv\">x1<\/span>, <span class=\"nv\">y1<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">coordxy<\/span><span class=\"p\">))<\/span>$\r\n\r\n<span class=\"nv\">scaling<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>2$\r\n<span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u5834\u306e\u30c7\u30fc\u30bf *\/<\/span>\r\n<span class=\"nv\">vecfE<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span><span class=\"nf\">vecE<\/span><span class=\"p\">(<\/span><span class=\"nv\">k<\/span><span class=\"p\">[<\/span>1<span class=\"p\">]<\/span>, <span class=\"nv\">k<\/span><span class=\"p\">[<\/span>2<span class=\"p\">])<\/span>, <span class=\"nv\">k<\/span>, <span class=\"nv\">coordxy<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* draw the vector field *\/<\/span>\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* title \u306e\u30d5\u30a9\u30f3\u30c8\u30b5\u30a4\u30ba\u306e\u5909\u66f4\u4f8b\u3002gnuplot \u306e\u6d41\u5100\u3002 *\/<\/span>\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/=16 \u6b63\u96fb\u8377\u306b\u3088\u308b\u96fb\u5834}\"<\/span>, \r\n  <span class=\"nv\">xtics<\/span><span class=\"o\">=<\/span><span class=\"no\">false<\/span>, <span class=\"nv\">ytics<\/span><span class=\"o\">=<\/span><span class=\"no\">false<\/span>,\r\n\r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span>, 3<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span>, 3<span class=\"p\">]<\/span>,\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span><span class=\"o\">=<\/span><span class=\"nv\">xy<\/span>,\r\n\r\n  <span class=\"cm\">\/* \u6b63\u96fb\u8377\u306e\u4f4d\u7f6e *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">black<\/span>,\r\n  <span class=\"nv\">point_size<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.5<\/span>, \r\n  <span class=\"nv\">point_type<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">6<\/span>, \r\n  <span class=\"nf\">points<\/span><span class=\"p\">([[<\/span><span class=\"nv\">x1<\/span>, <span class=\"nv\">y1<\/span><span class=\"p\">]])<\/span>,\r\n  <span class=\"nf\">label<\/span><span class=\"p\">([<\/span><span class=\"s\">\"\uff0b\"<\/span>, <span class=\"nv\">x1<\/span>, <span class=\"nv\">y1<\/span><span class=\"p\">])<\/span>, \r\n\r\n  <span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u5834\u306e\u8868\u793a *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">blue<\/span>,\r\n  <span class=\"nv\">head_length<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.2<\/span>,\r\n  <span class=\"nv\">head_angle<\/span>  <span class=\"o\">=<\/span> <span class=\"mi\">20<\/span>, \r\n  <span class=\"nv\">vecfE<\/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-full wp-image-3948\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxvec-fig01.svg\" alt=\"\" width=\"600\" height=\"500\" \/><\/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[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5f18\u5927 JupyterHub \u3067\u306f <\/span>\r\n<span class=\"cm\">   set_draw_defaults(file_name=\"~\/.maxplot\",terminal='svg)$<\/span>\r\n<span class=\"cm\">   \u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3002*\/<\/span>\r\n<span class=\"nf\">system<\/span><span class=\"p\">(<\/span><span class=\"s\">\"cp ~\/.maxplot.svg .\/maxvec-fig01.svg\"<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"$\\boldsymbol{E}$-\u306e\u5411\u304d\u3092\u8868\u3059\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u5834\">$\\boldsymbol{E}$ \u306e\u5411\u304d\u3092\u8868\u3059\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u5834<\/h3>\n<p>\u96fb\u5834 $\\boldsymbol{E}$ \u306e\u5927\u304d\u3055\u306f\u96fb\u8377\u304b\u3089\u306e\u8ddd\u96e2\u306e2\u4e57\u306b\u53cd\u6bd4\u4f8b\u3059\u308b\u306e\u3067\uff0c\u4e0a\u56f3\u306e\u3088\u3046\u306b\u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055\u304c\u5927\u304d\u304f\u5909\u5316\u3059\u308b\u3002\u3053\u308c\u306f\u3053\u308c\u3067\u6b63\u3057\u3044\u306e\u3060\u304c\uff0c\u898b\u3084\u3059\u304f\u3059\u308b\u305f\u3081\u306b\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b $\\boldsymbol{E}$ \u306e\u5411\u304d\u3092\u8868\u3059\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u5834\uff08\u5927\u304d\u3055\u304c $1$\uff09\u3092\u5b9a\u7fa9\u3057\u3066\uff0c\u30d9\u30af\u30c8\u30eb\u306e\u5411\u304d\u306e\u307f\u3092\u6b63\u3057\u304f\u63cf\u753b\u3059\u308b\u3002<\/p>\n<p>$$\\hat{\\boldsymbol{E}} \\equiv \\frac{\\boldsymbol{E}}{\\sqrt{\\boldsymbol{E}\\cdot\\boldsymbol{E}}} $$<\/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=\"\u6b63\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\">\u6b63\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u96fb\u5834 E *\/<\/span>\r\n<span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">x<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span>3$\r\n<span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">y<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span>3$\r\n\r\n<span class=\"cm\">\/* \u898f\u683c\u5316\u3055\u308c\u305f\u96fb\u5834 E *\/<\/span>\r\n<span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">hEx<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">hEy<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">vechE<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">vector<\/span><span class=\"p\">([<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nf\">hEx<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">-<\/span><span class=\"nv\">x1<\/span>, <span class=\"nv\">y<\/span><span class=\"o\">-<\/span><span class=\"nv\">y1<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">hEy<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">-<\/span><span class=\"nv\">x1<\/span>, <span class=\"nv\">y<\/span><span class=\"o\">-<\/span><span class=\"nv\">y1<\/span><span class=\"p\">)])<\/span>$\r\n\r\n<span class=\"nv\">scaling<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>3$\r\n<span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u5834\u306e\u30c7\u30fc\u30bf *\/<\/span>\r\n<span class=\"nv\">vecfhE<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span><span class=\"nf\">vechE<\/span><span class=\"p\">(<\/span><span class=\"nv\">k<\/span><span class=\"p\">[<\/span>1<span class=\"p\">]<\/span>, <span class=\"nv\">k<\/span><span class=\"p\">[<\/span>2<span class=\"p\">])<\/span>, <span class=\"nv\">k<\/span>, <span class=\"nv\">coordxy<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* title \u306e\u30d5\u30a9\u30f3\u30c8\u30b5\u30a4\u30ba\u306e\u5909\u66f4\u4f8b\u3002gnuplot \u306e\u6d41\u5100\u3002 *\/<\/span>\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/=16 \u6b63\u96fb\u8377\u306b\u3088\u308b\u96fb\u5834\u306e\u5411\u304d}\"<\/span>, \r\n  <span class=\"nv\">xtics<\/span><span class=\"o\">=<\/span><span class=\"no\">false<\/span>, <span class=\"nv\">ytics<\/span><span class=\"o\">=<\/span><span class=\"no\">false<\/span>,\r\n\r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span>, 3<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span>, 3<span class=\"p\">]<\/span>,\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span><span class=\"o\">=<\/span><span class=\"nv\">xy<\/span>,\r\n\r\n  <span class=\"cm\">\/* \u6b63\u96fb\u8377\u306e\u4f4d\u7f6e *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">black<\/span>,\r\n  <span class=\"nv\">point_size<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.5<\/span>, \r\n  <span class=\"nv\">point_type<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">6<\/span>, \r\n  <span class=\"nf\">points<\/span><span class=\"p\">([[<\/span><span class=\"nv\">x1<\/span>, <span class=\"nv\">y1<\/span><span class=\"p\">]])<\/span>,\r\n  <span class=\"nf\">label<\/span><span class=\"p\">([<\/span><span class=\"s\">\"\uff0b\"<\/span>, <span class=\"nv\">x1<\/span>, <span class=\"nv\">y1<\/span><span class=\"p\">])<\/span>, \r\n\r\n  <span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u5834\u306e\u8868\u793a *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">blue<\/span>,\r\n  <span class=\"nv\">head_length<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>,\r\n  <span class=\"nv\">head_angle<\/span>  <span class=\"o\">=<\/span> <span class=\"mi\">20<\/span>, \r\n  <span class=\"nv\">vecfhE<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-3949\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxvec-fig02.svg\" alt=\"\" width=\"600\" height=\"500\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5f18\u5927 JupyterHub \u3067\u306f <\/span>\r\n<span class=\"cm\">   set_draw_defaults(file_name=\"~\/.maxplot\",terminal='svg)$<\/span>\r\n<span class=\"cm\">   \u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3002*\/<\/span>\r\n<span class=\"nf\">system<\/span><span class=\"p\">(<\/span><span class=\"s\">\"cp ~\/.maxplot.svg .\/maxvec-fig02.svg\"<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\">\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u96fb\u5834 E *\/<\/span>\r\n<span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"o\">-<\/span><span class=\"nv\">x<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span>3$\r\n<span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"o\">-<\/span><span class=\"nv\">y<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span>3$\r\n\r\n<span class=\"cm\">\/* \u898f\u683c\u5316\u3055\u308c\u305f\u96fb\u5834 E *\/<\/span>\r\n<span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">hEx<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">hEy<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* 2\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306f vector([\u59cb\u70b9\u306ex, \u59cb\u70b9\u306ey], [x\u6210\u5206, y\u6210\u5206]) *\/<\/span>\r\n<span class=\"nf\">vechE<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">vector<\/span><span class=\"p\">([<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nf\">hEx<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">-<\/span><span class=\"nv\">x2<\/span>, <span class=\"nv\">y<\/span><span class=\"o\">-<\/span><span class=\"nv\">y2<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">hEy<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">-<\/span><span class=\"nv\">x2<\/span>, <span class=\"nv\">y<\/span><span class=\"o\">-<\/span><span class=\"nv\">y2<\/span><span class=\"p\">)])<\/span>$\r\n\r\n<span class=\"cm\">\/* (x2, y2) \u306f\u8ca0\u96fb\u8377\u306e\u4f4d\u7f6e *\/<\/span>\r\n<span class=\"p\">[<\/span><span class=\"nv\">x2<\/span>, <span class=\"nv\">y2<\/span><span class=\"p\">]<\/span><span class=\"o\">:<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, <span class=\"o\">-<\/span>1<span class=\"p\">]<\/span>$\r\n\r\n<span class=\"cm\">\/* -3 &lt;= x &lt;= 3, -3 &lt;= y &lt;= 3 \u3067 1\/2 \u523b\u307f\u306e\u683c\u5b50\u70b9\u3092\u59cb\u70b9\u306b *\/<\/span>\r\n<span class=\"cm\">\/* makelist \u3067\u306f1\u6b21\u5143\u306e\u30ea\u30b9\u30c8\u3057\u304b\u4f5c\u308c\u306a\u3044\u3088\u3046\u306a\u306e\u3067\uff0c\u5c11\u3057\u5de5\u592b *\/<\/span>\r\n<span class=\"cm\">\/* \u5225\u89e3\u3068\u3057\u3066\u3053\u3046\u3044\u3046\u3084\u308a\u65b9\u3082\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3002 *\/<\/span>\r\n<span class=\"cm\">\/* makelist() \u3067\u7a7a\u306e\u30ea\u30b9\u30c8\u3092\u3064\u304f\u308a\uff0cappend() \u3067\u8981\u7d20\u3092\u8ffd\u52a0 *\/<\/span>\r\n<span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">()<\/span>$\r\n<span class=\"k\">for<\/span> <span class=\"nv\">i<\/span><span class=\"o\">:<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">thru<\/span> <span class=\"mi\">12<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"k\">for<\/span> <span class=\"nv\">j<\/span><span class=\"o\">:<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">thru<\/span> <span class=\"mi\">12<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">append<\/span><span class=\"p\">(<\/span><span class=\"nv\">coordxy<\/span>, <span class=\"p\">[[<\/span><span class=\"o\">-<\/span>3<span class=\"o\">+<\/span><span class=\"nv\">i<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span>,<span class=\"o\">-<\/span>3<span class=\"o\">+<\/span><span class=\"nv\">j<\/span><span class=\"o\">\/<\/span>2<span class=\"p\">]])<\/span>\r\n  <span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* \u8ca0\u96fb\u8377\u306e\u4f4d\u7f6e\u3067\u306f\u96fb\u5834\u306e\u5206\u6bcd\u304c\u30bc\u30ed\u306b\u306a\u308b\u306e\u3067\u9664\u304f *\/<\/span>\r\n<span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nf\">delete<\/span><span class=\"p\">([<\/span><span class=\"nv\">x2<\/span>, <span class=\"nv\">y2<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">coordxy<\/span><span class=\"p\">))<\/span>$\r\n\r\n<span class=\"nv\">scaling<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>3$\r\n<span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u5834\u306e\u30c7\u30fc\u30bf *\/<\/span>\r\n<span class=\"nv\">vecfhE<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span><span class=\"nf\">vechE<\/span><span class=\"p\">(<\/span><span class=\"nv\">k<\/span><span class=\"p\">[<\/span>1<span class=\"p\">]<\/span>, <span class=\"nv\">k<\/span><span class=\"p\">[<\/span>2<span class=\"p\">])<\/span>, <span class=\"nv\">k<\/span>, <span class=\"nv\">coordxy<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* title \u306e\u30d5\u30a9\u30f3\u30c8\u30b5\u30a4\u30ba\u306e\u5909\u66f4\u4f8b\u3002gnuplot \u306e\u6d41\u5100\u3002 *\/<\/span>\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/=16 \u8ca0\u96fb\u8377\u306b\u3088\u308b\u96fb\u5834\u306e\u5411\u304d}\"<\/span>, \r\n  <span class=\"nv\">xtics<\/span><span class=\"o\">=<\/span><span class=\"no\">false<\/span>, <span class=\"nv\">ytics<\/span><span class=\"o\">=<\/span><span class=\"no\">false<\/span>,\r\n\r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span>, 3<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span>, 3<span class=\"p\">]<\/span>,\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span><span class=\"o\">=<\/span><span class=\"nv\">xy<\/span>,\r\n\r\n  <span class=\"cm\">\/* \u8ca0\u96fb\u8377\u306e\u4f4d\u7f6e *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">red<\/span>, \r\n  <span class=\"nv\">point_size<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.5<\/span>, \r\n  <span class=\"nv\">point_type<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">6<\/span>, \r\n  <span class=\"nf\">points<\/span><span class=\"p\">([[<\/span><span class=\"nv\">x2<\/span>, <span class=\"nv\">y2<\/span><span class=\"p\">]])<\/span>,\r\n  <span class=\"nf\">label<\/span><span class=\"p\">([<\/span><span class=\"s\">\"\u30fc\"<\/span>, <span class=\"nv\">x2<\/span>, <span class=\"nv\">y2<\/span><span class=\"p\">])<\/span>, \r\n\r\n  <span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u5834\u306e\u8868\u793a *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">blue<\/span>,\r\n  <span class=\"nv\">head_length<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>,\r\n  <span class=\"nv\">head_angle<\/span>  <span class=\"o\">=<\/span> <span class=\"mi\">20<\/span>, \r\n  <span class=\"nv\">vecfhE<\/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-full wp-image-3950\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxvec-fig03.svg\" alt=\"\" width=\"600\" height=\"500\" \/><\/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[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5f18\u5927 JupyterHub \u3067\u306f <\/span>\r\n<span class=\"cm\">   set_draw_defaults(file_name=\"~\/.maxplot\",terminal='svg)$<\/span>\r\n<span class=\"cm\">   \u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3002*\/<\/span>\r\n<span class=\"nf\">system<\/span><span class=\"p\">(<\/span><span class=\"s\">\"cp ~\/.maxplot.svg .\/maxvec-fig03.svg\"<\/span><span class=\"p\">)<\/span>$\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<h4 id=\"\u6b63\u96fb\u8377\u3068\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\">\u6b63\u96fb\u8377\u3068\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d<\/h4>\n<ul>\n<li>\u53c2\u8003\uff1a\u300c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e9%9d%99%e9%9b%bb%e5%a0%b4%ef%bc%9a%e9%9b%bb%e8%8d%b7%e5%af%86%e5%ba%a6%e3%81%8b%e3%82%89%e7%9b%b4%e6%8e%a5%e9%9b%bb%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b\/#2\">2\u3064\u306e\u70b9\u96fb\u8377\u306b\u3088\u308b\u96fb\u5834<\/a>\u300d<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u96fb\u5834 E *\/<\/span>\r\n<span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">x<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span>3$\r\n<span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">y<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span>3$\r\n\r\n<span class=\"cm\">\/* \u6b63\u96fb\u8377\u3068\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834 *\/<\/span>\r\n<span class=\"nf\">E2x<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">-<\/span><span class=\"nv\">x1<\/span>, <span class=\"nv\">y<\/span><span class=\"o\">-<\/span><span class=\"nv\">y1<\/span><span class=\"p\">)<\/span> <span class=\"o\">-<\/span> <span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">-<\/span><span class=\"nv\">x2<\/span>, <span class=\"nv\">y<\/span><span class=\"o\">-<\/span><span class=\"nv\">y2<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">E2y<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">-<\/span><span class=\"nv\">x1<\/span>, <span class=\"nv\">y<\/span><span class=\"o\">-<\/span><span class=\"nv\">y1<\/span><span class=\"p\">)<\/span> <span class=\"o\">-<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">-<\/span><span class=\"nv\">x2<\/span>, <span class=\"nv\">y<\/span><span class=\"o\">-<\/span><span class=\"nv\">y2<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* \u898f\u683c\u5316\u3055\u308c\u305f\u96fb\u5834 hat E *\/<\/span>\r\n<span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nf\">E2x<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nf\">E2y<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">hE2x<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">E2x<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">hE2y<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">E2y<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* 2\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306f vector([\u59cb\u70b9\u306ex, \u59cb\u70b9\u306ey], [x\u6210\u5206, y\u6210\u5206]) *\/<\/span>\r\n<span class=\"nf\">vechE<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">vector<\/span><span class=\"p\">([<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nf\">hE2x<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">hE2y<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)])<\/span>$\r\n\r\n<span class=\"cm\">\/* (x1, y1) \u306f\u6b63\u96fb\u8377\u306e\u4f4d\u7f6e *\/<\/span>\r\n<span class=\"p\">[<\/span><span class=\"nv\">x1<\/span>, <span class=\"nv\">y1<\/span><span class=\"p\">]<\/span><span class=\"o\">:<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 1<span class=\"p\">]<\/span>$\r\n<span class=\"cm\">\/* (x2, y2) \u306f\u8ca0\u96fb\u8377\u306e\u4f4d\u7f6e *\/<\/span>\r\n<span class=\"p\">[<\/span><span class=\"nv\">x2<\/span>, <span class=\"nv\">y2<\/span><span class=\"p\">]<\/span><span class=\"o\">:<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, <span class=\"o\">-<\/span>1<span class=\"p\">]<\/span>$\r\n\r\n<span class=\"cm\">\/* -3 &lt;= x &lt;= 3, -3 &lt;= y &lt;= 3 \u3067 1\/3 \u523b\u307f\u306e\u683c\u5b50\u70b9\u3092\u59cb\u70b9\u306b *\/<\/span>\r\n<span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">()<\/span>$\r\n<span class=\"k\">for<\/span> <span class=\"nv\">i<\/span><span class=\"o\">:<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">thru<\/span> <span class=\"mi\">18<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"k\">for<\/span> <span class=\"nv\">j<\/span><span class=\"o\">:<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">thru<\/span> <span class=\"mi\">18<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">append<\/span><span class=\"p\">(<\/span><span class=\"nv\">coordxy<\/span>, <span class=\"p\">[[<\/span><span class=\"o\">-<\/span>3<span class=\"o\">+<\/span><span class=\"nv\">i<\/span><span class=\"o\">\/<\/span><span class=\"mi\">3<\/span>,<span class=\"o\">-<\/span>3<span class=\"o\">+<\/span><span class=\"nv\">j<\/span><span class=\"o\">\/<\/span>3<span class=\"p\">]])<\/span>\r\n  <span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* \u96fb\u8377\u306e\u4f4d\u7f6e\u3067\u306f\u96fb\u5834\u306e\u5206\u6bcd\u304c\u30bc\u30ed\u306b\u306a\u308b\u306e\u3067\u9664\u304f *\/<\/span>\r\n<span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nf\">delete<\/span><span class=\"p\">([<\/span><span class=\"nv\">x2<\/span>, <span class=\"nv\">y2<\/span><span class=\"p\">]<\/span>, <span class=\"nf\">delete<\/span><span class=\"p\">([<\/span><span class=\"nv\">x1<\/span>, <span class=\"nv\">y1<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">coordxy<\/span><span class=\"p\">)))<\/span>$\r\n\r\n<span class=\"nv\">scaling<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>2$\r\n<span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u5834\u306e\u30c7\u30fc\u30bf *\/<\/span>\r\n<span class=\"nv\">vecfhE<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span><span class=\"nf\">vechE<\/span><span class=\"p\">(<\/span><span class=\"nv\">k<\/span><span class=\"p\">[<\/span>1<span class=\"p\">]<\/span>, <span class=\"nv\">k<\/span><span class=\"p\">[<\/span>2<span class=\"p\">])<\/span>, <span class=\"nv\">k<\/span>, <span class=\"nv\">coordxy<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"cm\">\/* title \u306e\u30d5\u30a9\u30f3\u30c8\u30b5\u30a4\u30ba\u306e\u5909\u66f4\u4f8b\u3002gnuplot \u306e\u6d41\u5100\u3002 *\/<\/span>\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/=16 \u6b63\u96fb\u8377\u3068\u8ca0\u96fb\u8377\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d}\"<\/span>, \r\n  <span class=\"nv\">xtics<\/span><span class=\"o\">=<\/span><span class=\"no\">false<\/span>, <span class=\"nv\">ytics<\/span><span class=\"o\">=<\/span><span class=\"no\">false<\/span>,\r\n\r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span>, 3<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span>, 3<span class=\"p\">]<\/span>,\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span><span class=\"o\">=<\/span><span class=\"nv\">xy<\/span>,\r\n  \r\n  <span class=\"cm\">\/* \u6b63\u96fb\u8377\u306e\u4f4d\u7f6e *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">black<\/span>,\r\n  <span class=\"nv\">point_size<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.5<\/span>, \r\n  <span class=\"nv\">point_type<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">6<\/span>, \r\n  <span class=\"nf\">points<\/span><span class=\"p\">([[<\/span><span class=\"nv\">x1<\/span>, <span class=\"nv\">y1<\/span><span class=\"p\">]])<\/span>,\r\n  <span class=\"nf\">label<\/span><span class=\"p\">([<\/span><span class=\"s\">\"\uff0b\"<\/span>, <span class=\"nv\">x1<\/span>, <span class=\"nv\">y1<\/span><span class=\"p\">])<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u8ca0\u96fb\u8377\u306e\u4f4d\u7f6e *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">red<\/span>, \r\n  <span class=\"nv\">point_size<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.5<\/span>, \r\n  <span class=\"nv\">point_type<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">6<\/span>, \r\n  <span class=\"nf\">points<\/span><span class=\"p\">([[<\/span><span class=\"nv\">x2<\/span>, <span class=\"nv\">y2<\/span><span class=\"p\">]])<\/span>,\r\n  <span class=\"nf\">label<\/span><span class=\"p\">([<\/span><span class=\"s\">\"\u30fc\"<\/span>, <span class=\"nv\">x2<\/span>, <span class=\"nv\">y2<\/span><span class=\"p\">])<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u5834\u306e\u8868\u793a *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">blue<\/span>,\r\n  <span class=\"nv\">head_length<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>,\r\n  <span class=\"nv\">head_angle<\/span>  <span class=\"o\">=<\/span> <span class=\"mi\">20<\/span>, \r\n  <span class=\"nv\">vecfhE<\/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-full wp-image-3951\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxvec-fig04.svg\" alt=\"\" width=\"600\" height=\"500\" \/><\/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[8]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5f18\u5927 JupyterHub \u3067\u306f <\/span>\r\n<span class=\"cm\">   set_draw_defaults(file_name=\"~\/.maxplot\",terminal='svg)$<\/span>\r\n<span class=\"cm\">   \u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3002*\/<\/span>\r\n<span class=\"nf\">system<\/span><span class=\"p\">(<\/span><span class=\"s\">\"cp ~\/.maxplot.svg .\/maxvec-fig04.svg\"<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u96fb\u6c17\u53cc\u6975\u5b50\u304c\u3064\u304f\u308b\u96fb\u5834\">\u96fb\u6c17\u53cc\u6975\u5b50\u304c\u3064\u304f\u308b\u96fb\u5834<\/h3>\n<ul>\n<li>\u53c2\u8003\uff1a\u300c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e9%9d%99%e9%9b%bb%e5%a0%b4%ef%bc%9a%e9%9b%bb%e8%8d%b7%e5%af%86%e5%ba%a6%e3%81%8b%e3%82%89%e7%9b%b4%e6%8e%a5%e9%9b%bb%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b\/#i-3\">\u96fb\u6c17\u53cc\u6975\u5b50\u306b\u3088\u308b\u96fb\u5834<\/a>\u300d<\/li>\n<\/ul>\n<p>$$\\boldsymbol{E} = 3 \\frac{\\boldsymbol{r}\\cdot\\boldsymbol{p}}{r^5} \\boldsymbol{r}<br \/>\n&#8211; \\frac{\\boldsymbol{p}}{r^3}$$<\/p>\n<p>$\\boldsymbol{p} = (0, 1, 0), \\quad z = 0$ \u3068\u3057\u3066<\/p>\n<p>\\begin{eqnarray}<br \/>\nE_x &amp;=&amp; \\frac{3}{\\left( x^2 + y^2 \\right)^{5\/2}} x y \\\\<br \/>\nE_y &amp;=&amp; \\frac{3}{\\left( x^2 + y^2 \\right)^{5\/2}} y^2 &#8211; \\frac{1}{\\left( x^2 + y^2 \\right)^{3\/2}} \\\\<br \/>\n\\end{eqnarray}<\/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=\"\u96fb\u6c17\u53cc\u6975\u5b50\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d\">\u96fb\u6c17\u53cc\u6975\u5b50\u304c\u3064\u304f\u308b\u96fb\u5834\u306e\u5411\u304d<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u96fb\u5834 E *\/<\/span>\r\n<span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> 3<span class=\"o\">*<\/span> <span class=\"nv\">x<\/span><span class=\"o\">*<\/span><span class=\"nv\">y<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span>5$\r\n<span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> 3<span class=\"o\">*<\/span> <span class=\"nv\">y<\/span><span class=\"o\">*<\/span><span class=\"nv\">y<\/span><span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">5<\/span> <span class=\"o\">-<\/span> 1<span class=\"o\">\/<\/span><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span>3$\r\n\r\n<span class=\"cm\">\/* \u898f\u683c\u5316\u3055\u308c\u305f\u96fb\u5834 E *\/<\/span>\r\n<span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">hEx<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">Ex<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">hEy<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">Ey<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">E<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* 2\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306f vector([\u59cb\u70b9\u306ex, \u59cb\u70b9\u306ey], [x\u6210\u5206, y\u6210\u5206]) *\/<\/span>\r\n<span class=\"nf\">vechE<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">vector<\/span><span class=\"p\">([<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nf\">hEx<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">hEy<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)])<\/span>$\r\n\r\n<span class=\"cm\">\/* (x0, y0) \u306f\u96fb\u6c17\u53cc\u6975\u5b50\u306e\u4f4d\u7f6e *\/<\/span>\r\n<span class=\"p\">[<\/span><span class=\"nv\">x0<\/span>, <span class=\"nv\">y0<\/span><span class=\"p\">]<\/span><span class=\"o\">:<\/span> <span class=\"p\">[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"p\">]<\/span>$\r\n\r\n<span class=\"cm\">\/* -3 &lt;= x &lt;= 3, -3 &lt;= y &lt;= 3 \u3067 1\/3 \u523b\u307f\u306e\u683c\u5b50\u70b9\u3092\u59cb\u70b9\u306b *\/<\/span>\r\n<span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">()<\/span>$\r\n<span class=\"k\">for<\/span> <span class=\"nv\">i<\/span><span class=\"o\">:<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">thru<\/span> <span class=\"mi\">18<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"k\">for<\/span> <span class=\"nv\">j<\/span><span class=\"o\">:<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">thru<\/span> <span class=\"mi\">18<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">append<\/span><span class=\"p\">(<\/span><span class=\"nv\">coordxy<\/span>, <span class=\"p\">[[<\/span><span class=\"o\">-<\/span>3<span class=\"o\">+<\/span><span class=\"nv\">i<\/span><span class=\"o\">\/<\/span><span class=\"mi\">3<\/span>,<span class=\"o\">-<\/span>3<span class=\"o\">+<\/span><span class=\"nv\">j<\/span><span class=\"o\">\/<\/span>3<span class=\"p\">]])<\/span>\r\n  <span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* \u96fb\u6c17\u53cc\u6975\u5b50\u306e\u4f4d\u7f6e\u3067\u306f\u96fb\u5834\u306e\u5206\u6bcd\u304c\u30bc\u30ed\u306b\u306a\u308b\u306e\u3067\u9664\u304f *\/<\/span>\r\n<span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nf\">delete<\/span><span class=\"p\">([<\/span><span class=\"nv\">x0<\/span>, <span class=\"nv\">y0<\/span><span class=\"p\">]<\/span>, <span class=\"nv\">coordxy<\/span><span class=\"p\">))<\/span>$\r\n\r\n<span class=\"nv\">scaling<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>25$\r\n<span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u5834\u306e\u30c7\u30fc\u30bf *\/<\/span>\r\n<span class=\"nv\">vecfhE<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span><span class=\"nf\">vechE<\/span><span class=\"p\">(<\/span><span class=\"nv\">k<\/span><span class=\"p\">[<\/span>1<span class=\"p\">]<\/span>, <span class=\"nv\">k<\/span><span class=\"p\">[<\/span>2<span class=\"p\">])<\/span>, <span class=\"nv\">k<\/span>, <span class=\"nv\">coordxy<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">xaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>, <span class=\"nv\">yaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"cm\">\/* title \u306e\u30d5\u30a9\u30f3\u30c8\u30b5\u30a4\u30ba\u306e\u5909\u66f4\u4f8b\u3002gnuplot \u306e\u6d41\u5100\u3002 *\/<\/span>\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/=16 \u96fb\u6c17\u53cc\u6975\u5b50\u306b\u3088\u308b\u96fb\u5834\u306e\u5411\u304d}\"<\/span>, \r\n  <span class=\"nv\">xtics<\/span><span class=\"o\">=<\/span><span class=\"no\">false<\/span>, <span class=\"nv\">ytics<\/span><span class=\"o\">=<\/span><span class=\"no\">false<\/span>,\r\n  \r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span>, 3<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span>, 3<span class=\"p\">]<\/span>,\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span><span class=\"o\">=<\/span><span class=\"nv\">xy<\/span>,\r\n  \r\n  <span class=\"cm\">\/* \u96fb\u6c17\u53cc\u6975\u5b50\u306e\u4f4d\u7f6e *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">red<\/span>, \r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">5<\/span>,\r\n  <span class=\"nv\">head_length<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>,\r\n  <span class=\"nv\">head_angle<\/span>  <span class=\"o\">=<\/span> <span class=\"mi\">30<\/span>, \r\n  <span class=\"nf\">vector<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span>,<span class=\"o\">-<\/span>0<span class=\"o\">.<\/span>15<span class=\"p\">]<\/span>,<span class=\"p\">[<\/span><span class=\"mi\">0<\/span>,0<span class=\"o\">.<\/span>3<span class=\"p\">])<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u5834\u306e\u8868\u793a *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">blue<\/span>,\r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>,\r\n  <span class=\"nv\">head_length<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>,\r\n  <span class=\"nv\">head_angle<\/span>  <span class=\"o\">=<\/span> <span class=\"mi\">20<\/span>, \r\n  <span class=\"nv\">vecfhE<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-3952\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxvec-fig05.svg\" alt=\"\" width=\"600\" height=\"500\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[10]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5f18\u5927 JupyterHub \u3067\u306f <\/span>\r\n<span class=\"cm\">   set_draw_defaults(file_name=\"~\/.maxplot\",terminal='svg)$<\/span>\r\n<span class=\"cm\">   \u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3002*\/<\/span>\r\n<span class=\"nf\">system<\/span><span class=\"p\">(<\/span><span class=\"s\">\"cp ~\/.maxplot.svg .\/maxvec-fig05.svg\"<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834-$\\boldsymbol{B}$\">\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834 $\\boldsymbol{B}$<\/h3>\n<ul>\n<li>\u53c2\u8003\uff1a\u300c<a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e9%9d%99%e7%a3%81%e5%a0%b4%ef%bc%9a%e9%9b%bb%e6%b5%81%e5%af%86%e5%ba%a6%e3%81%8b%e3%82%89%e7%9b%b4%e6%8e%a5%e9%9d%99%e7%a3%81%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b\/#i-2\">\u76f4\u7dda\u96fb\u6d41\u306b\u3088\u308b\u78c1\u5834<\/a>\u300d<\/li>\n<\/ul>\n<p>$$\\boldsymbol{B} = \\frac{\\boldsymbol{I}\\times\\boldsymbol{\\rho}}{\\rho^2}$$$$ \\boldsymbol{I} = (0, 0, I), \\quad \\boldsymbol{\\rho} = (x, y, 0)$$\\begin{eqnarray}<br \/>\nB_x &amp;=&amp; &#8211; \\frac{ I y}{x^2 + y^2} \\\\<br \/>\nB_y &amp;=&amp; \\frac{ I x}{x^2 + y^2}<br \/>\n\\end{eqnarray}<\/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=\"\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834\">\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[11]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u78c1\u5834 B *\/<\/span>\r\n<span class=\"nf\">Bx<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">y<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">By<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span>   <span class=\"nv\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">x<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* 2\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306f vector([\u59cb\u70b9\u306ex, \u59cb\u70b9\u306ey], [x\u6210\u5206, y\u6210\u5206]) *\/<\/span>\r\n<span class=\"nf\">vecB<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">vector<\/span><span class=\"p\">([<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nf\">Bx<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">By<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)])<\/span>$\r\n\r\n<span class=\"cm\">\/* -3 &lt;= x &lt;= 3, -3 &lt;= y &lt;= 3 \u3067 1\/2 \u523b\u307f\u306e\u683c\u5b50\u70b9\u3092\u59cb\u70b9\u306b *\/<\/span>\r\n<span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">()<\/span>$\r\n<span class=\"k\">for<\/span> <span class=\"nv\">i<\/span><span class=\"o\">:<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">thru<\/span> <span class=\"mi\">12<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"k\">for<\/span> <span class=\"nv\">j<\/span><span class=\"o\">:<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">thru<\/span> <span class=\"mi\">12<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">append<\/span><span class=\"p\">(<\/span><span class=\"nv\">coordxy<\/span>, <span class=\"p\">[[<\/span><span class=\"o\">-<\/span>3<span class=\"o\">+<\/span><span class=\"nv\">i<\/span><span class=\"o\">\/<\/span><span class=\"mi\">2<\/span>,<span class=\"o\">-<\/span>3<span class=\"o\">+<\/span><span class=\"nv\">j<\/span><span class=\"o\">\/<\/span>2<span class=\"p\">]])<\/span>\r\n  <span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* \u539f\u70b9\u3067\u306f\u78c1\u5834\u306e\u5206\u6bcd\u304c\u30bc\u30ed\u306b\u306a\u308b\u306e\u3067\u9664\u304f *\/<\/span>\r\n<span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nf\">delete<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span>, 0<span class=\"p\">]<\/span>, <span class=\"nv\">coordxy<\/span><span class=\"p\">))<\/span>$\r\n\r\n<span class=\"nv\">scaling<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>25$\r\n<span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u5834\u306e\u30c7\u30fc\u30bf *\/<\/span>\r\n<span class=\"nv\">vecfB<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span><span class=\"nf\">vecB<\/span><span class=\"p\">(<\/span><span class=\"nv\">k<\/span><span class=\"p\">[<\/span>1<span class=\"p\">]<\/span>, <span class=\"nv\">k<\/span><span class=\"p\">[<\/span>2<span class=\"p\">])<\/span>, <span class=\"nv\">k<\/span>, <span class=\"nv\">coordxy<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">xaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>, <span class=\"nv\">yaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"cm\">\/* title \u306e\u30d5\u30a9\u30f3\u30c8\u30b5\u30a4\u30ba\u306e\u5909\u66f4\u4f8b\u3002gnuplot \u306e\u6d41\u5100\u3002 *\/<\/span>\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/=16 \u76f4\u7dda\u96fb\u6d41\u306b\u3088\u308b\u78c1\u5834}\"<\/span>, \r\n  <span class=\"nv\">xtics<\/span><span class=\"o\">=<\/span><span class=\"no\">false<\/span>, <span class=\"nv\">ytics<\/span><span class=\"o\">=<\/span><span class=\"no\">false<\/span>,\r\n  \r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span>, 3<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span>, 3<span class=\"p\">]<\/span>,\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span><span class=\"o\">=<\/span><span class=\"nv\">xy<\/span>,\r\n  \r\n  <span class=\"cm\">\/* \u96fb\u7dda\u306e\u4f4d\u7f6e *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">red<\/span>,\r\n  <span class=\"nv\">point_size<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.5<\/span>, \r\n  <span class=\"nv\">point_type<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">6<\/span>, \r\n  <span class=\"nf\">points<\/span><span class=\"p\">([[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"p\">]])<\/span>,\r\n  <span class=\"nf\">label<\/span><span class=\"p\">([<\/span><span class=\"s\">\"\u30fb\"<\/span>, <span class=\"mi\">0<\/span>, 0<span class=\"p\">])<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u5834\u306e\u8868\u793a *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">green<\/span>,\r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.5<\/span>,\r\n  <span class=\"nv\">head_length<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>,\r\n  <span class=\"nv\">head_angle<\/span>  <span class=\"o\">=<\/span> <span class=\"mi\">20<\/span>, \r\n  <span class=\"nv\">vecfB<\/span>\r\n<span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_svg output_subarea \">\n<p><!--?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-3953\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxvec-fig06.svg\" alt=\"\" width=\"600\" height=\"500\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[12]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5f18\u5927 JupyterHub \u3067\u306f <\/span>\r\n<span class=\"cm\">   set_draw_defaults(file_name=\"~\/.maxplot\",terminal='svg)$<\/span>\r\n<span class=\"cm\">   \u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3002*\/<\/span>\r\n<span class=\"nf\">system<\/span><span class=\"p\">(<\/span><span class=\"s\">\"cp ~\/.maxplot.svg .\/maxvec-fig06.svg\"<\/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<h4 id=\"\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834\u306e\u5411\u304d\">\u76f4\u7dda\u96fb\u6d41\u304c\u3064\u304f\u308b\u78c1\u5834\u306e\u5411\u304d<\/h4>\n<p>\u78c1\u5834 $\\boldsymbol{B}$ \u306e\u5927\u304d\u3055\u306f\u96fb\u7dda\u304b\u3089\u306e\u8ddd\u96e2\u306b\u53cd\u6bd4\u4f8b\u3059\u308b\u306e\u3067\uff0c\u4e0a\u56f3\u306e\u3088\u3046\u306b\u30d9\u30af\u30c8\u30eb\u306e\u9577\u3055\u304c\u5927\u304d\u304f\u5909\u5316\u3059\u308b\u3002\u3053\u308c\u306f\u3053\u308c\u3067\u6b63\u3057\u3044\u306e\u3060\u304c\uff0c\u898b\u3084\u3059\u304f\u3059\u308b\u305f\u3081\u306b\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b $\\boldsymbol{B}$ \u306e\u5411\u304d\u3092\u8868\u3059\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u5834\uff08\u5927\u304d\u3055\u304c $1$\uff09\u3092\u5b9a\u7fa9\u3057\u3066\uff0c\u30d9\u30af\u30c8\u30eb\u306e\u5411\u304d\u306e\u307f\u3092\u6b63\u3057\u304f\u63cf\u753b\u3059\u308b\u3002<\/p>\n<p>$$\\hat{\\boldsymbol{B}} \\equiv \\frac{\\boldsymbol{B}}{\\sqrt{\\boldsymbol{B}\\cdot\\boldsymbol{B}}}$$<\/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-maxima\">\n<pre><span class=\"cm\">\/* \u78c1\u5834 B *\/<\/span>\r\n<span class=\"nf\">Bx<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"o\">-<\/span> <span class=\"nv\">y<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">By<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span>   <span class=\"nv\">x<\/span><span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* \u898f\u683c\u5316\u3055\u308c\u305f hat B *\/<\/span>\r\n<span class=\"nf\">B<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"nf\">Bx<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"nf\">By<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">hBx<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">Bx<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">B<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nf\">hBy<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">scaling<\/span> <span class=\"o\">*<\/span> <span class=\"nf\">By<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">\/<\/span><span class=\"nf\">B<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* 2\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u306f vector([\u59cb\u70b9\u306ex, \u59cb\u70b9\u306ey], [x\u6210\u5206, y\u6210\u5206]) *\/<\/span>\r\n<span class=\"nf\">vechB<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nf\">vector<\/span><span class=\"p\">([<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nf\">hBx<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)<\/span>, <span class=\"nf\">hBy<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">)])<\/span>$\r\n\r\n<span class=\"cm\">\/* -3 &lt;= x &lt;= 3, -3 &lt;= y &lt;= 3 \u3067 1\/3 \u523b\u307f\u306e\u683c\u5b50\u70b9\u3092\u59cb\u70b9\u306b *\/<\/span>\r\n<span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">()<\/span>$\r\n<span class=\"k\">for<\/span> <span class=\"nv\">i<\/span><span class=\"o\">:<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">thru<\/span> <span class=\"mi\">18<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"k\">for<\/span> <span class=\"nv\">j<\/span><span class=\"o\">:<\/span> <span class=\"mi\">0<\/span> <span class=\"k\">thru<\/span> <span class=\"mi\">18<\/span> <span class=\"k\">do<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">append<\/span><span class=\"p\">(<\/span><span class=\"nv\">coordxy<\/span>, <span class=\"p\">[[<\/span><span class=\"o\">-<\/span>3<span class=\"o\">+<\/span><span class=\"nv\">i<\/span><span class=\"o\">\/<\/span><span class=\"mi\">3<\/span>,<span class=\"o\">-<\/span>3<span class=\"o\">+<\/span><span class=\"nv\">j<\/span><span class=\"o\">\/<\/span>3<span class=\"p\">]])<\/span>\r\n  <span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* \u539f\u70b9\u3067\u306f\u78c1\u5834\u306e\u5206\u6bcd\u304c\u30bc\u30ed\u306b\u306a\u308b\u306e\u3067\u9664\u304f *\/<\/span>\r\n<span class=\"nv\">coordxy<\/span><span class=\"o\">:<\/span> <span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nf\">delete<\/span><span class=\"p\">([<\/span><span class=\"mi\">0<\/span>, 0<span class=\"p\">]<\/span>, <span class=\"nv\">coordxy<\/span><span class=\"p\">))<\/span>$\r\n\r\n<span class=\"nv\">scaling<\/span><span class=\"o\">:<\/span> 0<span class=\"o\">.<\/span>25$\r\n<span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u5834\u306e\u30c7\u30fc\u30bf *\/<\/span>\r\n<span class=\"nv\">vecfhB<\/span><span class=\"o\">:<\/span> <span class=\"nf\">makelist<\/span><span class=\"p\">(<\/span><span class=\"nf\">vechB<\/span><span class=\"p\">(<\/span><span class=\"nv\">k<\/span><span class=\"p\">[<\/span>1<span class=\"p\">]<\/span>, <span class=\"nv\">k<\/span><span class=\"p\">[<\/span>2<span class=\"p\">])<\/span>, <span class=\"nv\">k<\/span>, <span class=\"nv\">coordxy<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"nf\">draw2d<\/span><span class=\"p\">(<\/span>\r\n  <span class=\"nv\">xaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>, <span class=\"nv\">yaxis<\/span> <span class=\"o\">=<\/span> <span class=\"no\">true<\/span>,\r\n  <span class=\"cm\">\/* title \u306e\u30d5\u30a9\u30f3\u30c8\u30b5\u30a4\u30ba\u306e\u5909\u66f4\u4f8b\u3002gnuplot \u306e\u6d41\u5100\u3002 *\/<\/span>\r\n  <span class=\"nv\">title<\/span> <span class=\"o\">=<\/span> <span class=\"s\">\"{\/=16 \u76f4\u7dda\u96fb\u6d41\u306b\u3088\u308b\u78c1\u5834\u306e\u5411\u304d}\"<\/span>, \r\n  <span class=\"nv\">xtics<\/span><span class=\"o\">=<\/span><span class=\"no\">false<\/span>, <span class=\"nv\">ytics<\/span><span class=\"o\">=<\/span><span class=\"no\">false<\/span>,\r\n  \r\n  <span class=\"cm\">\/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  <span class=\"nv\">xrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span>, 3<span class=\"p\">]<\/span>, <span class=\"nv\">yrange<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span>, 3<span class=\"p\">]<\/span>,\r\n  <span class=\"cm\">\/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  <span class=\"nv\">proportional_axes<\/span><span class=\"o\">=<\/span><span class=\"nv\">xy<\/span>,\r\n  \r\n  <span class=\"cm\">\/* \u96fb\u7dda\u306e\u4f4d\u7f6e *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">red<\/span>,\r\n  <span class=\"nv\">point_size<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.5<\/span>, \r\n  <span class=\"nv\">point_type<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">6<\/span>, \r\n  <span class=\"nf\">points<\/span><span class=\"p\">([[<\/span><span class=\"mi\">0<\/span>, 0<span class=\"p\">]])<\/span>,\r\n  <span class=\"nf\">label<\/span><span class=\"p\">([<\/span><span class=\"s\">\"\u30fb\"<\/span>, <span class=\"mi\">0<\/span>, 0<span class=\"p\">])<\/span>, \r\n  \r\n  <span class=\"cm\">\/* \u30d9\u30af\u30c8\u30eb\u5834\u306e\u8868\u793a *\/<\/span>\r\n  <span class=\"nv\">color<\/span> <span class=\"o\">=<\/span> <span class=\"nv\">green<\/span>,\r\n  <span class=\"nv\">line_width<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.5<\/span>,\r\n  <span class=\"nv\">head_length<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>,\r\n  <span class=\"nv\">head_angle<\/span>  <span class=\"o\">=<\/span> <span class=\"mi\">20<\/span>, \r\n  <span class=\"nv\">vecfhB<\/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-full wp-image-3954\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxvec-fig07.svg\" alt=\"\" width=\"600\" height=\"500\" \/><\/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[14]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5f18\u5927 JupyterHub \u3067\u306f <\/span>\r\n<span class=\"cm\">   set_draw_defaults(file_name=\"~\/.maxplot\",terminal='svg)$<\/span>\r\n<span class=\"cm\">   \u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3002*\/<\/span>\r\n<span class=\"nf\">system<\/span><span class=\"p\">(<\/span><span class=\"s\">\"cp ~\/.maxplot.svg .\/maxvec-fig07.svg\"<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u96fb\u78c1\u6c17\u5b66\u306e\u6388\u696d\u306e\u6e96\u5099\u300cgnuplot \u3067\u30d9\u30af\u30c8\u30eb\u5834\uff08\u96fb\u5834\u30fb\u78c1\u5834\uff09\u3092\u63cf\u304f\u300d\u306e Maxima \u7248\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3934\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\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":[14,19],"tags":[],"class_list":["post-3934","post","type-post","status-publish","format-standard","hentry","category-maxima","category-19","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 4.9.10 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u96fb\u78c1\u6c17\u5b66\u306e\u6388\u696d\u306e\u6e96\u5099\u300cgnuplot \u3067\u30d9\u30af\u30c8\u30eb\u5834\uff08\u96fb\u5834\u30fb\u78c1\u5834\uff09\u3092\u63cf\u304f\u300d\u306e Maxima \u7248\u3002 \u70b9\u96fb\u8377\u304c\u3064\u304f\u308b\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"kasai\"\/>\n\t<link rel=\"canonical\" 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