{"id":4593,"date":"2023-12-18T10:31:00","date_gmt":"2023-12-18T01:31:00","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=4593"},"modified":"2023-12-18T10:37:25","modified_gmt":"2023-12-18T01:37:25","slug":"maxima-%e3%81%a6%e3%82%99%e5%be%ae%e5%88%86%e7%a9%8d%e5%88%86%e3%83%bb%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%ae%e8%a7%a3","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8f%82%e8%80%83%ef%bc%9amaxima-%e7%b7%a8\/maxima-%e3%81%ab%e3%82%88%e3%82%8b%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/maxima-%e3%81%a6%e3%82%99%e5%be%ae%e5%88%86%e7%a9%8d%e5%88%86%e3%83%bb%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%ae%e8%a7%a3\/","title":{"rendered":"Maxima \u3066\u3099\u5fae\u5206\u7a4d\u5206\u30fb\u65b9\u7a0b\u5f0f\u306e\u89e3"},"content":{"rendered":"<p>Maxima \u306e\u57fa\u672c\u304b\u3089\uff0c\u95a2\u6570\uff0c\u5fae\u5206\u30fb\u7a4d\u5206\uff0c\u65b9\u7a0b\u5f0f\u306e\u89e3\u307e\u3067\u3002<!--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=\"JupyterHub-\u3067\u306e\u8a08\u7b97\u306e\u5b9f\u884c\u3068\u884c\u672b\u8a18\u53f7\">JupyterHub \u3067\u306e\u8a08\u7b97\u306e\u5b9f\u884c\u3068\u884c\u672b\u8a18\u53f7<\/h3>\n<ol>\n<li>Maxima \u3067\u306f\u30bb\u30eb\u306b\u5b9f\u884c\u6587\u3092\u66f8\u304d\uff0c<\/li>\n<li>\u884c\u672b\u306b\u30bb\u30df\u30b3\u30ed\u30f3 <code>;<\/code> \u3092\u5165\u529b\u5f8c\uff0c<\/li>\n<li>Shift \u30ad\u30fc\u3092\u62bc\u3057\u306a\u304c\u3089 Enter \u30ad\u30fc\uff08Return \u30ad\u30fc\uff09\u3092\u62bc\u3059\u3068\u5b9f\u884c\u3057\u307e\u3059\u3002<\/li>\n<li>SHift + Enter \u306e\u304b\u308f\u308a\u306b\uff0c\u30e1\u30cb\u30e5\u30fc\u306e\u300c\u25b6\ufe0e Run\u300d\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u3082\u3088\u3044\u3067\u3059\u3002<\/li>\n<li>\u884c\u672b\u306b\u30bb\u30df\u30b3\u30ed\u30f3 <code>;<\/code> \u306e\u4ee3\u308f\u308a\u306b <code>$<\/code> \u3092\u5165\u529b\u5f8c\uff0c\u5b9f\u884c\u3059\u308b\u3068\uff0c\u7d50\u679c\u304c\u8868\u793a\u3055\u308c\u307e\u305b\u3093\u3002<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u307e\u305a\u306f\u7c21\u5358\u306a\u304b\u3051\u7b97 123\u00d7456 \u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[1]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"mi\">123<\/span> <span class=\"o\">*<\/span> <span class=\"mi\">456<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[1]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{1}$}56088\\]<\/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>2 \u306e 100 \u4e57 ($2^{100}$) \u306e\u3088\u3046\u306a\u5927\u304d\u3044\u6570\u3067\u3082\uff0c\u53b3\u5bc6\u306a\u7d50\u679c\u3092\u51fa\u529b\u3057\u307e\u3059\u3002\uff08<code>**<\/code> \u306f\u7d2f\u4e57\u3092\u8868\u3057\u307e\u3059\u3002<code>^<\/code> \u3067\u3082\u3044\u3044\u3067\u3059\u304c\uff0c\u4ed6\u306e\u8a00\u8a9e\u3067\u306f <code>**<\/code> \u3092\u4f7f\u3046\u3053\u3068\u304c\u591a\u3044\u306e\u3067\uff0c\u3053\u3061\u3089\u306b\u7d71\u4e00\u3057\u307e\u3059\u3002\uff09<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[2]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre>2<span class=\"o\">**<\/span><span class=\"mi\">100<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[2]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{2}$}1267650600228229401496703205376\\]<\/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><code>float<\/code> \u95a2\u6570\u3092\u4f7f\u3063\u3066\u6d6e\u52d5\u5c0f\u6570\u70b9\u8868\u793a\u3067\u8fd1\u4f3c\u5024\u3092\u51fa\u529b\u3055\u305b\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[3]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">float<\/span><span class=\"p\">(<\/span>2<span class=\"o\">**<\/span><span class=\"mi\">100<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[3]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{3}$}1.26765060022823 \\times 10^{+30}\\]<\/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=\"\u8868\u8a18\u306a\u3068\u3099\u306e\u7d04\u675f\u4e8b\">\u8868\u8a18\u306a\u3068\u3099\u306e\u7d04\u675f\u4e8b<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Maxima \u306e\u5b9f\u884c\u306b\u969b\u3057\u3066\uff0c\u3044\u304f\u3064\u304b\u8868\u8a18\u306b\u3064\u3044\u3066\u306e\u7d04\u675f\u4e8b\u304b\u3099\u3042\u308a\u307e\u3059\u3002\u4ee3\u8868\u7684\u306a\u3082\u306e\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n<p>\u30b3\u30e1\u30f3\u30c8(\u5b9f\u884c\u306b\u5f71\u97ff\u3057\u306a\u3044\u6ce8\u91c8)\u3092 \u5165\u308c\u305f\u3044\u3068\u304d\u306f\uff0c<code>\/* ... *\/<\/code> \u3066\u3099\u30b3\u30e1\u30f3\u30c8\u90e8\u5206\u3092\u56f2\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[4]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"mi\">1<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">3<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[4]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{4}$}6\\]<\/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[5]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"mi\">1<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">2<\/span> <span class=\"cm\">\/* + 3 *\/<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[5]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{5}$}3\\]<\/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>\u52a0\u6cd5 <code>+<\/code>\uff0c\u6e1b\u6cd5 <code>-<\/code>\uff0c\u4e57\u6cd5 <code>*<\/code>\uff0c\u9664\u6cd5 <code>\/<\/code> \u306b\u304a\u3051\u308b\u512a\u5148\u9806\u4f4d\u306f\u6570\u5b66\u3068\u540c\u3057\u3099\u3066\u3099\u3059\u3002\u512a\u5148\u3057\u3066\u8a08\u7b97\u3057\u305f\u3044\u7b87\u6240\u306f <code>( )<\/code> \u3066\u3099 \u56f2\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[6]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u6697\u7b97\u3067\u3082\u3067\u304d\u308b\uff01*\/<\/span>\r\n<span class=\"mi\">1<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">2<\/span> <span class=\"o\">*<\/span> <span class=\"mi\">3<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[6]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{6}$}7\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[7]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"p\">(<\/span><span class=\"mi\">1<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">2<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"mi\">3<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[7]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{7}$}9\\]<\/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>\u305f\u305f\u3099\u3057\uff0c\u5927\u30ab\u30c3\u30b3 <code>[ ]<\/code> \u3084\u4e2d\u30ab\u30c3\u30b3 <code>{ }<\/code> \u306f\u512a\u5148\u9806\u4f4d\u306e\u6307\u5b9a\u306b\u306f\u7528\u3044\u307e\u305b\u3093\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u4ee3\u5165\">\u4ee3\u5165<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5909\u6570\u306b\u5f0f\u3084\u5024\u3092\u4ee3\u5165\u3059\u308b\u3068\u304d\u306f <code>:<\/code> (\u30b3\u30ed\u30f3)\u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5909\u6570 a \u306b\uff0c$100 + 3\/21$ \u3092\u4ee3\u5165\u3057\u3066\uff0c<br \/>\na \u3092\u4f7f\u3063\u3066\u8a08\u7b97\u3092\u7d9a\u3051\u307e\u3059.<\/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-maxima\">\n<pre><span class=\"nv\">a<\/span><span class=\"o\">:<\/span> <span class=\"mi\">100<\/span> <span class=\"o\">+<\/span> 3<span class=\"o\">\/<\/span><span class=\"mi\">21<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[8]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{8}$}\\frac{701}{7}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[9]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"p\">(<\/span><span class=\"nv\">a<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">100<\/span><span class=\"p\">)<\/span> <span class=\"o\">*<\/span> <span class=\"mi\">7<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[9]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{9}$}1\\]<\/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=\"nv\">a<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[10]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{10}$}\\frac{701}{7}\\]<\/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=\"\u95a2\u6570\u306e\u5b9a\u7fa9\">\u95a2\u6570\u306e\u5b9a\u7fa9<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Maxima \u3067\u306f\uff0c\u95a2\u6570\u306e\u5b9a\u7fa9\u306b\u306f <code>:=<\/code> \u3092\u4f7f\u3044\u307e\u3059\u3002$f(x) := x^2$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[11]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[11]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{11}$}f\\left(x\\right):=x^2\\]<\/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>$f(4) = 4^2 = 16$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[12]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"mi\">4<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[12]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{12}$}16\\]<\/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=\"\u5b9f\u884c\u7d50\u679c\u306e\u975e\u8868\u793a\">\u5b9f\u884c\u7d50\u679c\u306e\u975e\u8868\u793a<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u6587\u672b\u306b <code>$<\/code> \u3092\u3064\u3051\u308b\u3068\u5b9f\u884c\u7d50\u679c\u306e\u51fa\u529b\u3092\u7701\u7565\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[13]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">eq<\/span><span class=\"o\">:<\/span> <span class=\"nv\">x<\/span><span class=\"o\">^<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> 3<span class=\"o\">*<\/span><span class=\"nv\">x<\/span> <span class=\"o\">+<\/span> 2$\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>\u5909\u6570 <code>eq<\/code> \u3092\u51fa\u529b\u3055\u305b\u308b\u3068&#8230;<br \/>\n\u78ba\u304b\u306b\u5f0f $x^2 +3x+2$ \u3066\u3099\u3059\u306d.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[14]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">eq<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[14]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{14}$}x^2+3\\,x+2\\]<\/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=\"\u524d\u306e\u51fa\u529b\u7d50\u679c\u306e\u53c2\u7167\">\u524d\u306e\u51fa\u529b\u7d50\u679c\u306e\u53c2\u7167<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u76f4\u524d\u306e\u51fa\u529b\u7d50\u679c\u306f <code>%<\/code> \u3068\u8868\u3057\u307e\u3059\u3002\u3053\u308c\u3092\u53c2\u7167\u3057\u3066\u3055\u3089\u306b\u8a08\u7b97\u3059\u308b\u3053\u3068\u304b\u3099\u3066\u3099\u304d\u307e\u3059\u3002\u307e\u305f\uff0c\u4ee5\u524d\u306e\u7d50\u679c\u3092\u53c2\u7167\u3059\u308b\u5834\u5408\u306f\uff0c\u4f8b\u3048\u3070 <code>%o14<\/code> \u306e\u3088\u3046\u306b\u884c\u756a\u53f7\u3092\u6307\u5b9a\u3059\u308b\u3053\u3068\u3082\u3066\u3099\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><code>expand<\/code> \u95a2\u6570\u3092\u4f7f\u3063\u3066\u5c55\u958b\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[15]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">expand<\/span><span class=\"p\">((<\/span><span class=\"nv\">x<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">2<\/span><span class=\"p\">)<\/span><span class=\"o\">**<\/span><span class=\"mi\">4<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[15]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{15}$}x^4-8\\,x^3+24\\,x^2-32\\,x+16\\]<\/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>\u76f4\u524d\u306e\u7d50\u679c\u3092 <code>factor<\/code> \u95a2\u6570\u3066\u3099\u56e0\u6570\u5206\u89e3\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[16]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">factor<\/span><span class=\"p\">(<\/span><span class=\"nv\">%<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[16]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{16}$}\\left(x-2\\right)^4\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[17]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u884c\u756a\u53f7\u3092\u6307\u5b9a\u3057\u3066\u4ee5\u524d\u306e\u7d50\u679c\u3092\u8868\u793a\u3055\u305b\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002*\/<\/span>\r\n\r\n<span class=\"nf\">factor<\/span><span class=\"p\">(<\/span><span class=\"nv\">%o15<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[17]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{17}$}\\left(x-2\\right)^4\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u6570\u306e\u8a08\u7b97\u30fb\u57fa\u672c\u7684\u306a\u95a2\u6570\">\u6570\u306e\u8a08\u7b97\u30fb\u57fa\u672c\u7684\u306a\u95a2\u6570<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u57fa\u672c\u7684\u306a\u56db\u5247\u6f14\u7b97 (<code>+ - * \/<\/code>) \u4ee5\u5916\u306b\u3088\u304f\u4f7f\u308f\u308c\u308b\u6f14\u7b97\u8a18\u53f7\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>4 \u306e\u968e\u4e57\u306e\u8a08\u7b97\u3092\u3057\u307e\u3059. <code>4! = 4*3*2*1 = 24<\/code> \u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[18]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre>4<span class=\"o\">!<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[18]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{18}$}24\\]<\/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><code>!!<\/code> \u306f\uff0c\u4e00\u3064\u304a\u304d\u306e\u968e\u4e57\u306e\u8a08\u7b97\u3092\u3057\u307e\u3059\u3002<code>5!! = 5*3*1<\/code> \u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[19]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre>5<span class=\"o\">!!<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[19]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{19}$}15\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[20]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre>6<span class=\"o\">!!<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[20]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{20}$}48\\]<\/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[21]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"mi\">6<\/span> <span class=\"o\">*<\/span> <span class=\"mi\">4<\/span> <span class=\"o\">*<\/span> <span class=\"mi\">2<\/span> ;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[21]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{21}$}48\\]<\/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=\"\u7df4\u7fd2-1-1\">\u7df4\u7fd2 1-1<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><strong>(\u7df4\u7fd2) 3, 2, 1 \u3067\u3064\u304f\u308b\u6700\u5927\u306e\u6570<\/strong><\/p>\n<p>\u6570\u5b57\u306e 3 \u3068 2 \u3068 1 \u3092 1 \u500b\u305a\u3064\u4f7f\u3063\u305f\u6f14\u7b97\u3067\u3064\u304f\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u6700\u5927\u306e\u6574\u6570\u306f?<\/p>\n<p><strong>\u30d2\u30f3\u30c8:<\/strong><\/p>\n<p><code>(1 + 2) \u00d7 3 = 9<\/code> \u3058\u3083\u5168\u7136\u3060\u3081\u3002\u305d\u306e\u307e\u307e\u4e26\u3079\u308b\u3068 <code>321<\/code> \u3067\u3059\u304c\uff0c\u7d2f\u4e57\u3092\u4f7f\u3046\u3068\u3082\u3063\u3068\u5927\u304d\u3044\u6570\u3092\u3064\u304f\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<br \/>\n$21^3$ \u3068\u304b\uff0c$31^2$ \u3068\u304b\uff0c$2^{31}$ \u3068\u304b&#8230;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u57fa\u672c\u7684\u306a\u5b9a\u6570\">\u57fa\u672c\u7684\u306a\u5b9a\u6570<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Maxima \u306e\u57fa\u672c\u7684\u306a\u5b9a\u6570\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<table>\n<thead>\n<tr>\n<td style=\"text-align: center;\"><strong><span style=\"font-family: helvetica, arial, sans-serif;\">\u3000\u3000\u5186\u5468\u7387 $\\pi$\u3000\u3000<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"><strong><span style=\"font-family: helvetica, arial, sans-serif;\">\u3000\u3000\u7121\u9650\u5927 $\\infty$\u3000\u3000<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"><strong><span style=\"font-family: helvetica, arial, sans-serif;\">\u3000\u3000\u81ea\u7136\u5bfe\u6570\u306e\u5e95 $e$\u3000\u3000<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"><strong><span style=\"font-family: helvetica, arial, sans-serif;\">\u3000\u3000\u865a\u6570\u5358\u4f4d $i$\u3000\u3000<\/span><\/strong><\/td>\n<td><\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><code>%pi<\/code><\/td>\n<td style=\"text-align: center;\"><code>inf<\/code><\/td>\n<td style=\"text-align: center;\"><code>%e<\/code><\/td>\n<td style=\"text-align: center;\"><code>%i<\/code><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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>\u7121\u7406\u6570 $e$\uff0c$\\pi$ \u3068\u865a\u6570\u5358\u4f4d $i$ \u3068\u6574\u6570 $\u22121$ \u306e\u9593\u306e\u3059\u3066\u304d\u306a\u95a2\u4fc2\uff0c\u30aa\u30a4\u30e9\u30fc\u306e\u7b49\u5f0f $$e^{i\\pi} = -1$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[22]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">%e<\/span><span class=\"o\">**<\/span><span class=\"p\">(<\/span><span class=\"nv\">%i<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[22]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{22}$}-1\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u53c2\u8003\uff1a<code>display()<\/code> \u3092\u4f7f\u3063\u3066\u8868\u793a\u3055\u305b\u308b\u4f8b\u3002\u8a55\u4fa1\u3059\u308b\u524d\u306e\u5f0f\u3092\u5de6\u8fba\u306b\uff0c\u8a55\u4fa1\u5f8c\u306e\u5024\u3092\u53f3\u8fba\u306b\u3057\u305f\u5f0f\u3092\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[23]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">display<\/span><span class=\"p\">(<\/span><span class=\"nv\">%e<\/span><span class=\"o\">**<\/span><span class=\"p\">(<\/span><span class=\"nv\">%i<\/span> <span class=\"o\">*<\/span> <span class=\"nv\">%pi<\/span><span class=\"p\">))<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\[e^{i\\,\\pi}=-1\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre><\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u6d6e\u52d5\u5c0f\u6570\u70b9\u3067\u8fd1\u4f3c\u5024\u3092\u8868\u793a\u3059\u308b\u306b\u306f <code>float<\/code> \u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[24]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">%pi<\/span>; \r\n<span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[24]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{24}$}\\pi\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[24]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{25}$}3.141592653589793\\]<\/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=\"\u57fa\u672c\u7684\u306a\u95a2\u6570\">\u57fa\u672c\u7684\u306a\u95a2\u6570<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u57fa\u672c\u7684\u306a\u95a2\u6570\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u8a18\u3055\u308c\u307e\u3059\u3002<\/p>\n<table style=\"width: 100%;\">\n<tbody>\n<tr>\n<th style=\"text-align: center; width: 11.8667%;\"><span style=\"font-family: helvetica, arial, sans-serif;\">\u5e73\u65b9\u6839<\/span><\/th>\n<th style=\"text-align: center; width: 14.2667%;\"><span style=\"font-family: helvetica, arial, sans-serif;\">\u3000\u6307\u6570\u95a2\u6570<\/span><\/th>\n<th style=\"text-align: center; width: 14.2667%;\"><span style=\"font-family: helvetica, arial, sans-serif;\">\u3000\u81ea\u7136\u5bfe\u6570<\/span><\/th>\n<th style=\"text-align: center; width: 11.8667%;\"><span style=\"font-family: helvetica, arial, sans-serif;\">\u3000\u7d76\u5bfe\u5024<\/span><\/th>\n<th style=\"text-align: center; width: 14.2667%;\"><span style=\"font-family: helvetica, arial, sans-serif;\">\u3000\u4e09\u89d2\u95a2\u6570<\/span><\/th>\n<th style=\"text-align: center; width: 18.9333%;\"><span style=\"font-family: helvetica, arial, sans-serif;\">\u3000\u9006\u4e09\u89d2\u95a2\u6570<\/span><\/th>\n<th style=\"text-align: center; width: 14.2667%;\"><span style=\"font-family: helvetica, arial, sans-serif;\">\u3000\u53cc\u66f2\u7dda\u95a2\u6570<\/span><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center; width: 11.8667%;\"><code>sqrt<\/code><\/td>\n<td style=\"text-align: center; width: 14.2667%;\"><code>exp<\/code><\/td>\n<td style=\"text-align: center; width: 14.2667%;\"><code>log<\/code><\/td>\n<td style=\"text-align: center; width: 11.8667%;\"><code>abs<\/code><\/td>\n<td style=\"text-align: center; width: 14.2667%;\"><code>sin<\/code><br \/>\n<code>cos<\/code><br \/>\n<code>tan<\/code><\/td>\n<td style=\"text-align: center; width: 18.9333%;\"><code>asin<\/code><br \/>\n<code>acos<\/code><br \/>\n<code>atan<\/code><\/td>\n<td style=\"text-align: center; width: 14.2667%;\"><code>sinh<\/code><br \/>\n<code>cosh<\/code><br \/>\n<code>tanh<\/code><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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>\u3046\u3063\u304b\u308a $\\sqrt{x^2} = x$ \u3068\u3057\u306a\u3044\u3088\u3046\u306b\u3002 $\\sqrt{x^2} = |x|$ \u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[25]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><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=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[25]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{26}$}\\left| x\\right| \\]<\/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>\u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u5b9a\u7406\u3092\u307f\u305f\u3059\u6574\u6570\u306e\u4f8b\u3002<br \/>\n$\\sqrt{3^2 + 4^2} = 5$ \u3067\u3059\u306d\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[26]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">sqrt<\/span><span class=\"p\">(<\/span>3<span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> 4<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 class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[26]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{27}$}5\\]<\/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>$\\exp(1) = e$ \u306e\u3053\u3068\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$e^{\\log x}$ \u3084 $\\log(e^2)$ \u306e\u8a08\u7b97\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[27]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">display<\/span><span class=\"p\">(<\/span><span class=\"nf\">exp<\/span><span class=\"p\">(<\/span><span class=\"nf\">log<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)))<\/span>$\r\n<span class=\"nf\">display<\/span><span class=\"p\">(<\/span><span class=\"nf\">log<\/span><span class=\"p\">(<\/span><span class=\"nv\">%e<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">))<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\[\\exp \\log x=x\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre><\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_latex output_subarea \">\\[\\log e^2=2\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stdout output_text\">\n<pre><\/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=\"\u4e09\u89d2\u95a2\u6570\u306e\u5024\u30fb\u5f15\u6570\u306e\u5358\u4f4d\">\u4e09\u89d2\u95a2\u6570\u306e\u5024\u30fb\u5f15\u6570\u306e\u5358\u4f4d<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4e09\u89d2\u95a2\u6570\u306e\u5024\u3092\u6570\u5024\u3067\u6c42\u3081\u305f\u3044\u3068\u304d\u306b\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$\\displaystyle \\sin\\frac{\\pi}{3}$ \u306e\u5024\u306f&#8230;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[28]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">%pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">3<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[28]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{30}$}\\frac{\\sqrt{3}}{2}\\]<\/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><code>float<\/code> \u95a2\u6570\u3092\u4f7f\u3063\u3066\uff0c\u76f4\u524d\u306e\u7d50\u679c\u3092<br \/>\n\u6d6e\u52d5\u5c0f\u6570\u70b9\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[29]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nv\">%<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[29]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{31}$}0.8660254037844386\\]<\/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>\u5909\u6570 <code>pi<\/code> \u306b\u6d6e\u52d5\u5c0f\u6570\u70b9\u8868\u793a\u306e $\\pi$ \u306e\u5024\u3092\u4ee3\u5165\u3057\u307e\u3059\u3002 \u6d6e\u52d5\u5c0f\u6570\u70b9\u8868\u793a\u3067\u6570\u5024\u3092\u5165\u308c\u308b\u3068\uff0c <code>sin<\/code> \u3082\u6d6e\u52d5\u5c0f\u6570\u70b9\u8868\u793a\u3067\u7b54\u3048\u3092\u8fd4\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[30]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">pi<\/span><span class=\"o\">:<\/span> <span class=\"nf\">float<\/span><span class=\"p\">(<\/span><span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span>;\r\n<span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">pi<\/span><span class=\"o\">\/<\/span><span class=\"mi\">3<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[30]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{32}$}3.141592653589793\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[30]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{33}$}0.8660254037844386\\]<\/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>\u4e09\u89d2\u95a2\u6570\u306e\u5f15\u6570\u306f\u30e9\u30b8\u30a2\u30f3\u3067\u3059\u3002\u5ea6\u3092\u4f7f\u3063\u3066\u6c42\u3081\u305f\u3044\u3068\u304d\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5ea6\u3092\u30e9\u30b8\u30a2\u30f3\u306b\u5909\u63db\u3059\u308b\u95a2\u6570 <code>degrad<\/code> \u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<p><code>degrad(60)<\/code> \u3092\u5f15\u6570\u306b\u3057\u3066 <code>sin<\/code> \u306e\u5024\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[31]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">degrad<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">x<\/span><span class=\"o\">\/<\/span>180<span class=\"o\">*<\/span><span class=\"nv\">%pi<\/span>$\r\n<span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nf\">degrad<\/span><span class=\"p\">(<\/span><span class=\"mi\">60<\/span><span class=\"p\">))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[31]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{35}$}\\frac{\\sqrt{3}}{2}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[32]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nf\">degrad<\/span><span class=\"p\">(<\/span><span class=\"mi\">30<\/span><span class=\"p\">))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[32]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{36}$}\\frac{1}{2}\\]<\/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=\"\u7df4\u7fd2-1-2\">\u7df4\u7fd2 1-2<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><strong>\uff08\u7df4\u7fd2\uff09\u5c4b\u6839\u52fe\u914d<\/strong><\/p>\n<p>\u5bb6\u306e\u5c4b\u6839\u306e\u52fe\u914d\u306f\u89d2\u5ea6\u3067\u306f\u306a\u304f\uff0c\u4f1d\u7d71\u7684\u306b 3 \u5bf8\u52fe\u914d\uff0c4 \u5bf8\u52fe\u914d\u306e\u3088\u3046\u306b\u6c34\u5e73\u65b9\u5411\u306b 1 \u5c3a(10 \u5bf8)\u306b\u5bfe\u3057\u3066\u5782\u76f4\u65b9\u5411\u306b\u4f55\u5bf8\u7acb\u3061\u4e0a\u304c\u308b\u304b\u3067\u793a\u3057\u307e\u3059\u3002<\/p>\n<p>\u56f3\u306e\u30ed\u30b0\u30cf\u30a6\u30b9\u306e\u5c4b\u6839\u306f 8 \u5bf8\u52fe\u914d\u3067\u3059\u3002<br \/>\n\u50be\u659c\u89d2\u5ea6\u306b\u3059\u308b\u3068\u4f55\u5ea6\u3067\u3059\u304b?<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/home.hirosaki-u.ac.jp\/jupyter\/maxima\/ritsumen.png\" width=\"400px\" \/><\/p>\n<p>\u4ee5\u4e0b\u306b\u5404\u5bf8\u52fe\u914d\u306e\u89d2\u5ea6\u306e\u8868\u304c\u3042\u308a\u307e\u3059\u300210 \u5bf8\u52fe\u914d\u307e\u3067\u8868<br \/>\n\u3092\u5b8c\u6210\u3055\u305b\u307e\u3057\u3087\u3046\u3002<\/p>\n<table>\n<thead>\n<tr>\n<th style=\"text-align: left;\"><span style=\"font-family: helvetica, arial, sans-serif;\">\u52fe\u914d\u3000\u3000<\/span><\/th>\n<th style=\"text-align: left;\"><span style=\"font-family: helvetica, arial, sans-serif;\">1\u5bf8\u52fe\u914d\u3000\u3000\u3000<\/span><\/th>\n<th style=\"text-align: left;\"><span style=\"font-family: helvetica, arial, sans-serif;\">2\u5bf8\u52fe\u914d\u3000\u3000\u3000<\/span><\/th>\n<th style=\"text-align: left;\"><span style=\"font-family: helvetica, arial, sans-serif;\">3\u5bf8\u52fe\u914d\u3000\u3000\u3000<\/span><\/th>\n<th><span style=\"font-family: helvetica, arial, sans-serif;\">&#8230;<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><\/td>\n<td><code>atan(0.1)<\/code><\/td>\n<td><code>atan(0.2)<\/code><\/td>\n<td><code>atan(0.3)<\/code><\/td>\n<td>&#8230;<\/td>\n<\/tr>\n<tr>\n<td>rad<\/td>\n<td>0.0997<\/td>\n<td>0.1974<\/td>\n<td>0.2915<\/td>\n<td>&#8230;<\/td>\n<\/tr>\n<tr>\n<td>\u5ea6<\/td>\n<td>5.7106\u00b0<\/td>\n<td>11.3099\u00b0<\/td>\n<td>16.6992\u00b0<\/td>\n<td>&#8230;<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u7df4\u7fd2-1-3\">\u7df4\u7fd2 1-3<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><strong>(\u7df4\u7fd2)\u52a0\u6cd5\u5b9a\u7406\u30fb\u4e09\u500d\u89d2\u306e\u516c\u5f0f<\/strong><\/p>\n<ol>\n<li>\u4e09\u89d2\u95a2\u6570\u53ca\u3072\u3099\u53cc\u66f2\u7dda\u95a2\u6570\u306e\u52a0\u6cd5\u5b9a\u7406\u3092\u78ba\u8a8d\u3057\u306a\u3055\u3044\u3002<\/li>\n<li>$\\sin 3x$ \u3092 $\\sin x$ \u305f\u3099\u3051\u3092\u4f7f\u3063\u3066\u8868\u3057\u306a\u3055\u3044\u3002<\/li>\n<li>$\\tan 3x$ \u3092 $\\tan x$ \u305f\u3099\u3051\u3092\u4f7f\u3063\u3066\u8868\u3057\u306a\u3055\u3044.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[33]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* 1. \u306e\u30d2\u30f3\u30c8 *\/<\/span>\r\n<span class=\"cm\">\/* trigexpand \u3067\u5c55\u958b\u3057\u307e\u3059\u3002*\/<\/span>\r\n<span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">trigexpand<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span><span class=\"p\">))<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[34]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* 2. \u3084 3. \u306e\u30d2\u30f3\u30c8 *\/<\/span>\r\n<span class=\"nf\">sin<\/span><span class=\"p\">(<\/span>3<span class=\"o\">*<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"nf\">trigexpand<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span>3<span class=\"o\">*<\/span><span class=\"nv\">x<\/span><span class=\"p\">))<\/span>$\r\n<span class=\"nf\">trigsimp<\/span><span class=\"p\">(<\/span><span class=\"nv\">%<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$\\cos(x)^2$ \u3092 $1-\\sin(x)^2$ \u3066\u3099\u7f6e\u304d\u63db\u3048\u308b\u4f8b\u3066\u3099\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[35]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">ratsubst<\/span><span class=\"p\">(<\/span>1<span class=\"o\">-<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">^<\/span><span class=\"mi\">2<\/span>, <span class=\"nf\">cos<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">^<\/span><span class=\"mi\">2<\/span>, <span class=\"nv\">%<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u5fae\u5206\u30fb\u7a4d\u5206\u30fb\u6570\u5024\u7a4d\u5206\">\u5fae\u5206\u30fb\u7a4d\u5206\u30fb\u6570\u5024\u7a4d\u5206<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5fae\u5206\u30fb\u7a4d\u5206\u3092\u884c\u3046\u95a2\u6570\u306e\u8868\u8a18\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n<table style=\"width: 100%; height: 259px;\">\n<thead>\n<tr style=\"height: 41px;\">\n<td style=\"text-align: right; border-style: none; width: 18.2667%; height: 41px;\"><strong><span style=\"font-family: helvetica, arial, sans-serif;\">\u64cd\u4f5c<\/span><\/strong><\/td>\n<td style=\"text-align: left; width: 3.2%; height: 41px;\"><strong><span style=\"font-family: helvetica, arial, sans-serif;\">\u00a0<\/span><\/strong><\/td>\n<th style=\"text-align: left; width: 78.4667%; height: 41px;\"><strong><span style=\"font-family: helvetica, arial, sans-serif;\">\u3000\u8868\u8a18\u4f8b<\/span><\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 39px;\">\n<td style=\"text-align: right; border-style: none; width: 18.2667%; height: 39px;\">\u5fae\u5206<\/td>\n<td style=\"text-align: left; width: 3.2%; height: 39px;\"><\/td>\n<td style=\"text-align: left; width: 78.4667%; height: 39px;\"><code>diff(f(x), x)<\/code><\/td>\n<\/tr>\n<tr style=\"height: 39px;\">\n<td style=\"text-align: right; border-style: none; width: 18.2667%; height: 39px;\">n \u968e\u5fae\u5206<\/td>\n<td style=\"text-align: left; width: 3.2%; height: 39px;\"><\/td>\n<td style=\"text-align: left; width: 78.4667%; height: 39px;\"><code>diff(f(x), x, n)<\/code><\/td>\n<\/tr>\n<tr style=\"height: 39px;\">\n<td style=\"text-align: right; border-style: none; width: 18.2667%; height: 39px;\">\u4e0d\u5b9a\u7a4d\u5206<\/td>\n<td style=\"text-align: left; width: 3.2%; height: 39px;\"><\/td>\n<td style=\"text-align: left; width: 78.4667%; height: 39px;\"><code>integrate(f(x), x)<\/code><\/td>\n<\/tr>\n<tr style=\"height: 39px;\">\n<td style=\"text-align: right; border-style: none; width: 18.2667%; height: 39px;\">\u5b9a\u7a4d\u5206<\/td>\n<td style=\"text-align: left; width: 3.2%; height: 39px;\"><\/td>\n<td style=\"text-align: left; width: 78.4667%; height: 39px;\"><code>integrate(f(x), x, a, b)<\/code><\/td>\n<\/tr>\n<tr style=\"height: 62px;\">\n<td style=\"text-align: right; border-style: none; width: 18.2667%; height: 62px;\">\u6570\u5024\u7a4d\u5206<\/td>\n<td style=\"text-align: left; width: 3.2%; height: 62px;\"><\/td>\n<td style=\"text-align: left; width: 78.4667%; height: 62px;\"><code>romberg(f(x), x, a, b)<\/code>, <code>quad_qags(f(x), x, a, b)<\/code><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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=\"\u5fae\u5206\u30fb\u7a4d\u5206\">\u5fae\u5206\u30fb\u7a4d\u5206<\/h4>\n<p>\u7406\u5de5\u7cfb\u306e\u6570\u5b66B\u3067 Maxima \u3092\u4f7f\u3063\u305f\u5fae\u5206\u30fb\u7a4d\u5206\u306b\u3064\u3044\u3066\u3084\u3063\u3066\u3044\u307e\u3059\u3002\u4ee5\u4e0b\u3092\u53c2\u7167\u306e\u3053\u3068\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\/maxima-%e3%81%a7%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/maxima-%e3%81%a6%e3%82%99-1-%e5%a4%89%e6%95%b0%e9%96%a2%e6%95%b0%e3%81%ae%e5%be%ae%e5%88%86\/\">Maxima \u3066\u3099 1 \u5909\u6570\u95a2\u6570\u306e\u5fae\u5206<\/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\/maxima-%e3%81%a7%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/maxima-%e3%81%a6%e3%82%99%e3%83%86%e3%82%a4%e3%83%a9%e3%83%bc%e5%b1%95%e9%96%8b%e3%83%bb%e3%82%aa%e3%82%a4%e3%83%a9%e3%83%bc%e3%81%ae%e5%85%ac%e5%bc%8f\/\">Maxima \u3066\u3099\u30c6\u30a4\u30e9\u30fc\u5c55\u958b\u30fb\u30aa\u30a4\u30e9\u30fc\u306e\u516c\u5f0f<\/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\/maxima-%e3%81%a7%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/maxima-%e3%81%a6%e3%82%99-1-%e5%a4%89%e6%95%b0%e9%96%a2%e6%95%b0%e3%81%ae%e7%a9%8d%e5%88%86\/\">Maxima \u3067 1 \u5909\u6570\u95a2\u6570\u306e\u7a4d\u5206<\/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=\"\u6570\u5024\u7a4d\u5206\uff1aromberg()\">\u6570\u5024\u7a4d\u5206\uff1a<code>romberg()<\/code><\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3067\u306f\uff0c\u89e3\u6790\u7684\u306b\u7a4d\u5206\u3067\u304d\u306a\u3044\u5834\u5408\u306f\u3069\u3046\u3059\u308b\u304b\uff1f<\/p>\n<p>\u5b9f\u969b\uff0c\u5927\u5b66\u3067\u7fd2\u3046\u300c\u521d\u7b49\u95a2\u6570\u300d\u304a\u3088\u3073\u305d\u306e\u5408\u6210\u95a2\u6570\u306f\u5168\u3066\u5fae\u5206\u3067\u304d\u307e\u3059\u304c\uff0c\u3067\u306f\u521d\u7b49\u95a2\u6570\u304a\u3088\u3073\u305d\u306e\u5408\u6210\u95a2\u6570\uff08\u521d\u7b49\u95a2\u6570\u3092\u4f7f\u3063\u3066\u66f8\u304b\u308c\u308b\u95a2\u6570\uff09\u306f\u5168\u3066\u7a4d\u5206\u3067\u304d\u308b\u304b\u3068\u3044\u3046\u3068\uff0c\u305d\u3046\u3067\u306f\u306a\u3044\u3002<\/p>\n<p>\u5927\u5b66\u306e\u6388\u696d\uff0c\u305f\u3068\u3048\u3070\u7406\u5de5\u7cfb\u306e\u6570\u5b66B\u306a\u3069\u3067\u306f\uff0c\u89e3\u6790\u7684\u306b\u7a4d\u5206\u3067\u304d\u308b\u3088\u3046\u306a\u4f8b\u984c\u3060\u3051\u3092\u6271\u3044\u307e\u3059\u304c\uff0c\u5b9f\u969b\u306b\u306f\uff0c\u4ee5\u4e0b\u306e\u4f8b\u306e\u3088\u3046\u306b $\\sin(\\sin x)$ \u306a\u3069\u306e\u3088\u3046\u306a\u5358\u7d14\u306a\u4f8b\u3067\u3082\uff0c\u89e3\u6790\u7684\u306b\u306f\u7a4d\u5206\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n<p>\u89e3\u6790\u7684\u306b\u7a4d\u5206\u3066\u3099\u304d\u306a\u3044\u5834\u5408\u306f\uff0c\u6570\u5024\u7a4d\u5206\u306b\u3088\u3063\u3066\u8fd1\u4f3c\u5024\u3092\u6c42\u3081\u307e\u3059\u3002Maxima \u306b\u306f\u6570\u5024\u7a4d\u5206\u3092\u884c\u3046\u95a2\u6570\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$\\displaystyle \\int_0^{\\pi} \\sin(\\sin x)\\ dx$ \u306e\u8a08\u7b97\u3092\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[36]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">integrate<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">))<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[36]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{41}$}\\int_{0}^{\\pi}{\\sin \\sin x\\;dx}\\]<\/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>\u89e3\u6790\u7684\u306b\u89e3\u3051\u306a\u3044\u3068\uff0c\u305d\u306e\u307e\u307e\u3067\u8fd4\u3057\u307e\u3059\u3002<\/p>\n<p><code>romberg<\/code> \u95a2\u6570\u3092\u4f7f\u3046\u3068\uff0c\u6570\u5024\u7684\u306b\u7a4d\u5206\u3057\u305f\u8fd1\u4f3c\u89e3\u3092\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[37]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">r1<\/span><span class=\"o\">:<\/span> <span class=\"nf\">romberg<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">))<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[37]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{42}$}1.786487487137068\\]<\/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>\u6570\u5024\u7a4d\u5206 <code>romberg<\/code> \u306e\u7cbe\u5ea6\u306f\uff0c\u5927\u57df\u5909\u6570 <code>rombergtol<\/code> \u3066\u3099\u6c7a\u307e\u308a\u307e\u3059\u3002<\/p>\n<p><code>rombergtol<\/code> \u306e\u5024\u3092\u5c0f\u3055\u304f\u3059\u308b\u3053\u3068\u3066\u3099\u7cbe\u5ea6\u3092\u3042\u3051\u3099\u308b\u3053\u3068\u304b\u3099\u3066\u3099\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30c7\u30d5\u30a9\u30eb\u30c8\u306e <code>rombergtol<\/code> \u306e\u5024\u306f&#8230;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[38]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">rombergtol<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[38]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{43}$}1.0 \\times 10^{-4}\\]<\/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><code>rombergtol<\/code> \u3092 $10^{-10}$ \u306b\u3057\u3066\u3082\u3046\u4e00\u5ea6\u540c\u3058\u6570\u5024\u7a4d\u5206\u3092\u884c\u3046\u3068&#8230;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[39]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">rombergtol<\/span><span class=\"o\">:<\/span> 1<span class=\"o\">.<\/span><span class=\"nv\">e<\/span><span class=\"o\">-<\/span>10$\r\n<span class=\"nv\">r2<\/span><span class=\"o\">:<\/span> <span class=\"nf\">romberg<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">))<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[39]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{45}$}1.78648748195006\\]<\/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><code>rombergtol<\/code> \u3092 $10^{-12}$ \u306b\u3057\u3066\u3082\u3046\u4e00\u5ea6\u540c\u3058\u6570\u5024\u7a4d\u5206\u3092\u884c\u3046\u3068&#8230;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[40]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">rombergtol<\/span><span class=\"o\">:<\/span> 1<span class=\"o\">.<\/span><span class=\"nv\">e<\/span><span class=\"o\">-<\/span>12$\r\n<span class=\"nv\">r3<\/span><span class=\"o\">:<\/span> <span class=\"nf\">romberg<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">))<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[40]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{47}$}1.786487481950052\\]<\/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>\u4ee5\u4e0a\u306e\u3053\u3068\u304b\u3089\uff0c\u6570\u5024\u7a4d\u5206\u306f\uff0c\u3042\u304f\u307e\u3067\u8fd1\u4f3c\u7684\u89e3\u3092\u6c42\u3081\u308b\u3082\u306e\u3060\u304c\uff0c\u3069\u306e\u304f\u3089\u3044\u307e\u3067\u6b63\u3057\u304f\uff0c\u3069\u306e\u304f\u3089\u3044\u306e\u8aa4\u5dee\u304c\u3042\u308b\u304b\u306f\uff0c\u81ea\u5206\u3067\u30b3\u30f3\u30c8\u30ed\u30fc\u30eb\u3067\u304d\u308b\u3002<code>rombergtol<\/code> \u306f\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u306f $10^{-4}$ \u306a\u306e\u3067\uff0c\u3082\u3063\u3068\u7cbe\u5ea6\u3092\u6c42\u3081\u308b\u5834\u5408\u306f $10^{-10}$ \u3068\u304b $10^{-12}$ \u306b\u3057\u3066\u304a\u3051\u3070\uff0c\u305d\u308c\u306a\u308a\u306e\u7cbe\u5ea6\u3092\u3082\u3064\u6570\u5024\u89e3\u304c\u6c42\u3081\u3089\u308c\u308b\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u6570\u5024\u7a4d\u5206\uff1aquad_qags()\">\u6570\u5024\u7a4d\u5206\uff1a<code>quad_qags()<\/code><\/h4>\n<p>Maxima \u306b\u306f\u6570\u5024\u7a4d\u5206\u3092\u884c\u3046\u95a2\u6570\u3068\u3057\u3066 <code>quad_qags()<\/code> \u3082\u3042\u308a\u307e\u3059\u3002<code>romberg()<\/code> \u306b\u5bfe\u3059\u308b <code>quad_qags()<\/code> \u306e\u5229\u70b9\u306b\u3064\u3044\u3066\u306f\uff0c\u4ee5\u4e0b\u306e\u30ea\u30f3\u30af\u306b\u7c21\u5358\u306b\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e6%ba%96\/maxima-%e3%81%a6%e3%82%99%e5%8d%98%e6%8c%af%e3%82%8a%e5%ad%90%e3%81%ae%e3%82%a8%e3%83%8d%e3%83%ab%e3%82%ae%e3%83%bc%e4%bf%9d%e5%ad%98%e5%89%87%e3%81%8b%e3%82%89%e5%91%a8%e6%9c%9f%e3%82%92%e6%b1%82\/#_quad_qags\">\u6570\u5024\u7a4d\u5206 <code>quad_qags()<\/code><\/a><\/li>\n<\/ul>\n<p><code>quad_qags()<\/code> \u3067 $\\displaystyle \\int_0^{\\pi} \\sin(\\sin x)\\ dx$ \u306e\u8a08\u7b97\u3092\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[41]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">quad_qags<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">))<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">%pi<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[41]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{48}$}\\left[ 1.786487481950052 , 2.468727406962818 \\times 10^{-11} , 21 , 0 \\right] \\]<\/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><code>quad_qags()<\/code> \u306f4\u3064\u306e\u8981\u7d20\u306e\u30ea\u30b9\u30c8\u3092\u8fd4\u3057\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u7a4d\u5206\u306e\u8fd1\u4f3c\u5024<\/li>\n<li>\u898b\u7a4d\u3082\u3089\u308c\u305f\u8fd1\u4f3c\u306e\u7d76\u5bfe\u8aa4\u5dee<\/li>\n<li>\u88ab\u7a4d\u5206\u95a2\u6570\u306e\u8a55\u4fa1\u6570<\/li>\n<li>\u30a8\u30e9\u30fc\u30b3\u30fc\u30c9<\/li>\n<\/ul>\n<p>\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u306f $10^{-11}$ \u7a0b\u5ea6\u306e\u8aa4\u5dee\u306e\u6570\u5024\u7a4d\u5206\u5024\u3092\u8fd4\u3057\u307e\u3059\u3002<\/p>\n<p>\u6570\u5024\u7a4d\u5206\u306e\u7cbe\u5ea6\u3092\u8a2d\u5b9a\u3057\uff08\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u306f <code><span class=\"nv\">epsrel<\/span><span class=\"o\">=<\/span><span class=\"mf\">1d-8<\/span><\/code> \uff09\uff0c\u7a4d\u5206\u5024\u306e\u307f\u3092\u53d6\u308a\u51fa\u3059\u4f8b\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[42]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nv\">ans<\/span><span class=\"o\">:<\/span> \r\n  <span class=\"nf\">quad_qags<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nf\">sin<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">))<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"nv\">%pi<\/span>, \r\n            <span class=\"o\">'<\/span><span class=\"nv\">epsrel<\/span><span class=\"o\">=<\/span><span class=\"mf\">1d-12<\/span><span class=\"p\">)<\/span>$\r\n<span class=\"nv\">ans<\/span><span class=\"p\">[<\/span>1<span class=\"p\">]<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[42]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{50}$}1.786487481950052\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u65b9\u7a0b\u5f0f\">\u65b9\u7a0b\u5f0f<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u591a\u9805\u5f0f\u65b9\u7a0b\u5f0f\u30fb\u9023\u7acb\u65b9\u7a0b\u5f0f\">\u591a\u9805\u5f0f\u65b9\u7a0b\u5f0f\u30fb\u9023\u7acb\u65b9\u7a0b\u5f0f<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>Maxima \u306f\uff0c\u5f0f\u306e\u8a08\u7b97\u305f\u3099\u3051\u3066\u3099\u306a\u304f\uff0c\u4ee3\u6570\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u304b\u3099\u3066\u3099\u304d\u307e\u3059.\u4f8b\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n<p>$x^2 +2x\u22122 = 0$ \u3092 $x$ \u306b\u3064\u3044\u3066\u89e3\u304d<br \/>\n\u307e\u3059.<\/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[43]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">solve<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span> <span class=\"o\">+<\/span> 2<span class=\"o\">*<\/span><span class=\"nv\">x<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">2<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"nv\">x<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[43]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{51}$}\\left[ x=-\\sqrt{3}-1 , x=\\sqrt{3}-1 \\right] \\]<\/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>\u9023\u7acb\u65b9\u7a0b\u5f0f $x^2 + y^2 = 5, \\ x + y = 1$ \u3092 $x, y$ \u306b\u3064\u3044\u3066\u89e3\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[44]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">solve<\/span><span class=\"p\">(<\/span>\r\n  <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=\"o\">=<\/span> <span class=\"mi\">5<\/span>,  <span class=\"nv\">x<\/span> <span class=\"o\">+<\/span> <span class=\"nv\">y<\/span> <span class=\"o\">=<\/span> 1<span class=\"p\">]<\/span>, \r\n  <span class=\"p\">[<\/span><span class=\"nv\">x<\/span>, <span class=\"nv\">y<\/span><span class=\"p\">]<\/span>\r\n<span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[44]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{52}$}\\left[ \\left[ x=-1 , y=2 \\right] , \\left[ x=2 , y=-1 \\right] \\right] \\]<\/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>3 \u6b21\u65b9\u7a0b\u5f0f $x^3 = 8$ \u3092\u89e3\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[45]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">solve<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">8<\/span>, <span class=\"nv\">x<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[45]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{53}$}\\left[ x=\\sqrt{3}\\,i-1 , x=-\\sqrt{3}\\,i-1 , x=2 \\right] \\]<\/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>\u78ba\u8a8d\u306e\u305f\u3081\uff0c\u4e0a\u8a18\u306e1\u756a\u76ee\u306e\u7b54\u3048\u30923\u4e57\u3057\u3066\u7c21\u5358\u5316\u3059\u308b\u3068&#8230;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[46]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u76f4\u524d\u306e\u7d50\u679c\u306f [] \u3067\u56f2\u307e\u308c\u305f\u30ea\u30b9\u30c8\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002*\/<\/span>\r\n<span class=\"cm\">\/* \u30ea\u30b9\u30c8\u306e1\u756a\u76ee\u3092\u3068\u308b\u306b\u306f %[1] \u306e\u3088\u3046\u306b\u3057\u307e\u3059\u3002*\/<\/span>\r\n<span class=\"nf\">rhs<\/span><span class=\"p\">(<\/span><span class=\"nv\">%<\/span><span class=\"p\">[<\/span>1<span class=\"p\">])<\/span><span class=\"o\">**<\/span><span class=\"mi\">3<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[46]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{54}$}\\left(\\sqrt{3}\\,i-1\\right)^3\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[47]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5c55\u958b\u3057\u307e\u3059\u3002*\/<\/span>\r\n<span class=\"nf\">expand<\/span><span class=\"p\">(<\/span><span class=\"nv\">%<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[47]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{55}$}8\\]<\/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=\"\u7df4\u7fd2-1-4\">\u7df4\u7fd2 1-4<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><strong>\uff08\u7df4\u7fd2\uff09\u9db4\u3068\u4e80\u3068\u87fb<\/strong><\/p>\n<p>\u9db4\u3068\u4e80\u3068\u87fb\uff0c\u500b\u4f53\u6570\u306e\u5408\u8a08\u306f 10\u3002\u8db3\u306e\u6570\u306f\u5168\u90e8\u3066\u3099 34 \u672c\u3002\u87fb\u306f\u4e80\u3088\u308a 1 \u5339\u5c11\u306a\u3044\u3002\u9db4\uff0c\u4e80\uff0c\u87fb\uff0c\u305d\u308c\u305d\u3099\u308c\u4f55\u7fbd\u30fb\u4f55\u5339?<\/p>\n<p>\u9db4\u3068\u4e80\u3068\u87fb\u306e\u500b\u4f53\u6570\u3092\u305d\u308c\u305d\u3099\u308c $x, y, z$ \u3068\u3057\u3066\u9023\u7acb\u65b9\u7a0b\u5f0f\u3092\u305f\u3066\u3066 <code>solve<\/code> \u3057\u307e\u3059\u3002\u87fb\u306e\u8db3\u306f\u4f55\u672c\u304b\u308f\u304b\u308a\u307e\u3059\u3088\u306d?<\/p>\n<p>\u304b\u3064\u3066\u7dda\u5f62\u4ee3\u6570\u306e\u6388\u696d\u3067\u3053\u306e\u554f\u984c\u3092\u51fa\u3057\u305f\u3068\u304d\uff0c\u771f\u3063\u5148\u306b\u51fa\u305f\u8cea\u554f\u304c\u300c\u5148\u751f\uff0c\u87fb\u306e\u8db3\u306f\u4f55\u672c\u3067\u3059\u304b\uff1f\u300d\u3067\u3057\u305f&#8230; orz<\/p>\n<ul>\n<li><a href=\"https:\/\/www.google.com\/search?q=%E8%9F%BB&amp;client=firefox-b-d&amp;channel=nrow5&amp;sxsrf=AOaemvI1Cf_GqRu-D6pjmISmE2CYjINcSw:1634007019423&amp;source=lnms&amp;tbm=isch&amp;sa=X&amp;ved=2ahUKEwi9vc-_7sPzAhWtwosBHUmsD7EQ_AUoAXoECAEQAw&amp;biw=1186&amp;bih=904&amp;dpr=1.09\">Google \u3067\u30a2\u30ea\u306e\u753b\u50cf\u3092\u691c\u7d22&#8230;<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[\u00a0]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\">\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u591a\u9805\u5f0f\u65b9\u7a0b\u5f0f\u3066\u3099\u306a\u3044\u5834\u5408\u306b\u306f <code>find_root<\/code> \u95a2\u6570\u3092\u4f7f\u3063\u3066\uff0c\u7bc4\u56f2\u3092\u6307\u5b9a\u3057\u3066\u89e3\u3092\u63a2\u3057\u307e\u3059\u3002<\/p>\n<p>\u95a2\u6570 $g(x):= (x \u2212 1)\\,e^x$ \u306e\u5b9a\u7fa9\u3002<\/p>\n<p>$g(x):= (x \u2212 1)\\,e^x = 1$ \u306e\u89e3\u306f <code>solve<\/code> \u306a\u3068\u3099\u3066\u3099\u306f\u6c42\u3081\u308b\u3053\u3068\u304b\u3099\u3066\u3099\u304d\u307e\u305b\u3093\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[48]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">g<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"p\">(<\/span><span class=\"nv\">x<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span><span class=\"o\">*<\/span><span class=\"nf\">exp<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>;\r\n<span class=\"nf\">solve<\/span><span class=\"p\">(<\/span><span class=\"nf\">g<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>, <span class=\"nv\">x<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[48]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{56}$}g\\left(x\\right):=\\left(x-1\\right)\\,\\exp x\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[48]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{57}$}\\left[ x=e^ {- x }\\,\\left(e^{x}+1\\right) \\right] \\]<\/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><code>find_root<\/code> \u3092\u4f7f\u3063\u3066 $0 \\leq x \\leq 2$ \u306e \u7bc4\u56f2\u3066\u3099\u89e3\u3092\u63a2\u3057\u3066\u307f\u307e\u3059\u3002 \uff08\u306a\u305c\u3053\u306e\u7bc4\u56f2\u306b\u89e3\u304c\u3042\u308b\u3068\u308f\u304b\u308b\u306e\u304b\uff0c\u306f\u4ee5\u4e0b\u3067\u3002\uff09<\/p>\n<p>\u51fa\u305f\u7b54\u3048\u3092\u4ee3\u5165\u3057\u3066\u78ba\u304b\u3081\u308b\u3068&#8230;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[49]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">find_root<\/span><span class=\"p\">(<\/span><span class=\"nf\">g<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, <span class=\"mi\">2<\/span><span class=\"p\">)<\/span>;\r\n<span class=\"nf\">g<\/span><span class=\"p\">(<\/span><span class=\"nv\">%<\/span><span class=\"p\">)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[49]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{58}$}1.278464542761074\\]<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[49]:<\/div>\n<div class=\"output_latex output_subarea output_execute_result\">\\[\\tag{${\\it \\%o}_{59}$}1.0\\]<\/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>$g(x)$ \u304c\u3069\u306e\u3078\u3093\u3067 $1$ \u306b\u306a\u308b\u304b\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u30b0\u30e9\u30d5\u3092\u63cf\u3044\u3066\u307f\u308c\u3070\u308f\u304b\u308a\u307e\u3059\u3002Maxima \u306b\u3088\u308b\u30b0\u30e9\u30d5\u4f5c\u6210\u306b\u3064\u3044\u3066\u306f\uff0c\u5225\u9014\u89e3\u8aac\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[50]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"nf\">plot2d<\/span><span class=\"p\">(<\/span><span class=\"nf\">g<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">x<\/span>, <span class=\"mi\">0<\/span>, 5<span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">y<\/span>, <span class=\"o\">-<\/span><span class=\"mi\">1<\/span>, 1<span class=\"p\">]<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">ylabel<\/span>, <span class=\"s\">\"g(x)\"<\/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-4595\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxcon101.svg\" alt=\"\" width=\"640\" height=\"512\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4 id=\"\u7df4\u7fd2-1-5\">\u7df4\u7fd2 1-5<\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p><strong>\uff08\u7df4\u7fd2\uff09\u95a2\u6570\u306e\u6975\u5927\u5024<\/strong><\/p>\n<p>\u6b21\u306e\u95a2\u6570\u304b\u3099\u6975\u5927\u5024\u3092\u3068\u308b $x$ \u306e\u5024\u304a\u3088\u3072\u3099\u305d\u306e\u6975\u5927\u5024\u3092\u6c42\u3081\u3088\u3002<\/p>\n<p>$$ 1. \\ \\ f(x) = \\frac{x^3}{e^x &#8211; 1}, \\qquad 2. \\ \\ g(x) = \\frac{x^5}{e^x -1}$$<\/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[52]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* 1. \u306e\u30d2\u30f3\u30c8 *\/<\/span>\r\n<span class=\"cm\">\/* f(x) \u3092\u5b9a\u7fa9\u3057\u3066... *\/<\/span>\r\n<span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span><span class=\"o\">:=<\/span> <span class=\"nv\">x<\/span><span class=\"o\">**<\/span>3<span class=\"o\">\/<\/span><span class=\"p\">(<\/span><span class=\"nf\">exp<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span> <span class=\"o\">-<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* f(x) \u3092\u5fae\u5206\u3057\u3066... *\/<\/span>\r\n<span class=\"nf\">diff<\/span><span class=\"p\">(<\/span><span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">x<\/span><span class=\"p\">)<\/span>$\r\n\r\n<span class=\"cm\">\/* \u5fae\u5206\u3057\u305f\u76f4\u524d\u306e\u7d50\u679c\u3092\u95a2\u6570 df(x) \u3068\u5b9a\u7fa9\u3002*\/<\/span>\r\n<span class=\"nf\">define<\/span><span class=\"p\">(<\/span><span class=\"nf\">df<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"nv\">%<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[53]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5c0e\u95a2\u6570 df(x) \u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304d\uff0c\u3042\u305f\u308a\u3092\u3064\u3051\u308b\u3002*\/<\/span>\r\n<span class=\"nf\">plot2d<\/span><span class=\"p\">(<\/span><span class=\"nf\">df<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span>, <span class=\"p\">[<\/span><span class=\"nv\">x<\/span>, <span class=\"mf\">0.1<\/span>, 10<span class=\"p\">])<\/span>$\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-4596\" src=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-content\/uploads\/sites\/76\/maxcon102.svg\" alt=\"\" width=\"640\" height=\"512\" \/><\/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[55]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u5c0e\u95a2\u6570 df(x) \u304c\u30bc\u30ed\u306b\u306a\u308b x \u3092 0 &lt; x &lt; 4 \u306e\u9593\u3067\u63a2\u3059\uff1e*\/<\/span>\r\n<span class=\"nf\">find_root<\/span><span class=\"p\">(<\/span><span class=\"nf\">df<\/span><span class=\"p\">(<\/span><span class=\"nv\">x<\/span><span class=\"p\">)<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>, <span class=\"nv\">x<\/span>, <span class=\"mi\">2<\/span>, <span class=\"mi\">4<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[56]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* \u6975\u5024\u3092\u3068\u308b x \u306e\u5024\u304c\u6c42\u307e\u3063\u305f\u306e\u3067\uff0c\u6975\u5024\u306f... *\/<\/span>\r\n<span class=\"nf\">f<\/span><span class=\"p\">(<\/span><span class=\"nv\">%<\/span><span class=\"p\">)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"prompt input_prompt\">In\u00a0[57]:<\/div>\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\" highlight hl-maxima\">\n<pre><span class=\"cm\">\/* 2. \u3082\u540c\u69d8\u306b\u3084\u3063\u3066\u304a\u304f\u3002*\/<\/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=\"\u53c2\u8003\uff1a\u30d7\u30e9\u30f3\u30af\u306e\u6cd5\u5247\">\u53c2\u8003\uff1a\u30d7\u30e9\u30f3\u30af\u306e\u6cd5\u5247<\/h4>\n<p>\u71b1\u529b\u5b66\uff0c\u6c17\u8c61\u5b66\uff0c\u5929\u6587\u5b66\uff0c\u5b87\u5b99\u7269\u7406\u5b66\u7b49\u3067\u73fe\u308c\u308b\u300c\u30d7\u30e9\u30f3\u30af\u306e\u6cd5\u5247\u300d\u3002<\/p>\n<ul>\n<li>\u53c2\u8003\uff1a<a href=\"https:\/\/ja.wikipedia.org\/wiki\/%E3%83%97%E3%83%A9%E3%83%B3%E3%82%AF%E3%81%AE%E6%B3%95%E5%89%87\">\u30d7\u30e9\u30f3\u30af\u306e\u6cd5\u5247 &#8211; Wikipedia<\/a><\/li>\n<\/ul>\n<p>\u6e29\u5ea6 $T$ \u306e\u9ed2\u4f53\u304b\u3089\u653e\u5c04\u3055\u308c\u308b\u96fb\u78c1\u6ce2\u306e\u653e\u5c04\u5f37\u5ea6\u306f\u5468\u6ce2\u6570\u3092 $\\nu$ \u3068\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u308b\u3002<\/p>\n<p>$$I(\\nu, T) = \\frac{2h\\nu^3}{c^2} \\frac{1}{e^{h\\nu\/kT} &#8211; 1}$$<\/p>\n<p>\u3053\u3053\u3067\uff0c$\\displaystyle x \\equiv \\frac{h\\nu}{kT}$ \u3068\u304a\u304f\u3068<\/p>\n<p>$$I(\\nu, T) = \\frac{2 (k T)^3}{h^2 c^2} \\frac{x^3}{e^{x} &#8211; 1} \\equiv C \\frac{x^3}{e^{x} &#8211; 1}$$<\/p>\n<p>\u3068\u306a\u308a\uff0c$f(x)$ \u306e\u6975\u5927\u5024\u3092\u8abf\u3079\u308b\u3053\u3068\u306f\uff0c\u30d7\u30e9\u30f3\u30af\u306e\u6cd5\u5247\u3067\u4e0e\u3048\u3089\u308c\u308b\u9ed2\u4f53\u304b\u3089\u306e\u653e\u5c04\u5f37\u5ea6\u306e\u6975\u5927\u5024\u3092\u8abf\u3079\u308b\u3053\u3068\u306b\u3064\u306a\u304c\u308b\u3093\u3067\u3059\u3088\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Maxima \u306e\u57fa\u672c\u304b\u3089\uff0c\u95a2\u6570\uff0c\u5fae\u5206\u30fb\u7a4d\u5206\uff0c\u65b9\u7a0b\u5f0f\u306e\u89e3\u307e\u3067\u3002<\/p><p><a class=\"more-link btn\" href=\"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/%e5%8f%82%e8%80%83%ef%bc%9amaxima-%e7%b7%a8\/maxima-%e3%81%ab%e3%82%88%e3%82%8b%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/maxima-%e3%81%a6%e3%82%99%e5%be%ae%e5%88%86%e7%a9%8d%e5%88%86%e3%83%bb%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%ae%e8%a7%a3\/\">\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":4506,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-4593","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4593","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=4593"}],"version-history":[{"count":14,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4593\/revisions"}],"predecessor-version":[{"id":6720,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4593\/revisions\/6720"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/4506"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=4593"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}