{"id":5596,"date":"2023-03-08T11:30:18","date_gmt":"2023-03-08T02:30:18","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=5596"},"modified":"2023-03-08T11:30:18","modified_gmt":"2023-03-08T02:30:18","slug":"%e5%8f%82%e8%80%83%ef%bc%9amaxima-%e3%81%a7-sin-x-%e3%81%a8-x-%e3%81%ae%e3%82%b0%e3%83%a9%e3%83%95%e3%82%92%e6%8f%8f%e3%81%8f","status":"publish","type":"page","link":"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\/%e4%b8%89%e8%a7%92%e9%96%a2%e6%95%b0%e3%81%ae%e5%be%ae%e5%88%86\/%e5%8f%82%e8%80%83%ef%bc%9amaxima-%e3%81%a7-sin-x-%e3%81%a8-x-%e3%81%ae%e3%82%b0%e3%83%a9%e3%83%95%e3%82%92%e6%8f%8f%e3%81%8f\/","title":{"rendered":"\u53c2\u8003\uff1aMaxima \u3067 sin x \u3068 x \u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f"},"content":{"rendered":"
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\u53c2\u8003\uff1agnuplot \u3067 sin x \u3068 x \u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f<\/a> \u306e Maxima \u7248\u3002Maxima \u3067 $y = \\sin x $ \u3068 $y = x$ \u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3002<\/p>\n

$ |x| \\ll 1 $ \u3067\u306f2\u3064\u306e\u30b0\u30e9\u30d5\u306f\u307b\u3068\u3093\u3069\u91cd\u306a\u3063\u3066\u3044\u3066 $ \\sin x \\simeq x $ \u3059\u306a\u308f\u3061 $\\displaystyle \\frac{\\sin x}{x} \\simeq 1$ \u3067\u3042\u308b\u3053\u3068\u3092\u898b\u3066\u78ba\u304b\u3081\u308b\u3002<\/p>\n

Maxima \u3067\u306f plot2d()<\/code> \uff08\u3044\u308f\u3086\u308b plot \u7cfb\uff09\u3068 draw2d()<\/code> \uff08\u3044\u308f\u3086\u308b draw \u7cfb\uff09\u304c\u3042\u308b\u3002\u6700\u8fd1\u306f\u500b\u4eba\u7684\u306b\u306f\u6388\u696d\u7b49\u3067\u306f draw \u7cfb\u3092\u4f7f\u3046\u3088\u3046\u306b\u306a\u3063\u3066\u304d\u3066\u3044\u308b\u304c\uff0c\u53c2\u8003\u307e\u3067\u306b\u4e21\u65b9\u306e\u4f7f\u7528\u4f8b\u3092\u66f8\u3044\u3066\u304a\u304f\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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plot2d()<\/code> \u7de8<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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$ – \\pi \\leq x \\leq \\pi$ \u306e\u7bc4\u56f2\u3067 $y = \\sin x$ \u3068 $ y = x$ \u3092 plot2d()<\/code>\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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\/* \u6b21\u306b\u62e1\u5927\u8868\u793a\u3059\u308b\u90e8\u5206\u306e\u77e9\u5f62 *\/<\/span>\r\npoints4<\/span>:<\/span> [[<\/span>-<\/span>1<\/span>,-<\/span>1]<\/span>,[<\/span>1<\/span>,-<\/span>1]<\/span>,[<\/span>1<\/span>,1]<\/span>,[<\/span>-<\/span>1<\/span>,1]<\/span>,[<\/span>-<\/span>1<\/span>,-<\/span>1]]<\/span>$\r\n\r\nplot2d<\/span>(<\/span>\r\n  [[<\/span>discrete<\/span>, points4<\/span>]<\/span>, sin<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>]<\/span>, [<\/span>x<\/span>, -<\/span>%pi<\/span>, %pi<\/span>]<\/span>, \r\n  [<\/span>color<\/span>, orange<\/span>, red<\/span>, blue<\/span>]<\/span>,\r\n  [<\/span>style<\/span>, [<\/span>lines<\/span>, 2]<\/span>, [<\/span>lines<\/span>, 3]<\/span>, [<\/span>lines<\/span>, 1.<\/span>5]]<\/span>, \r\n  [<\/span>legend<\/span>, \"\"<\/span>, \"sin x\"<\/span>, \"x\"<\/span>]<\/span>,\r\n  \r\n  [<\/span>x<\/span>, -<\/span>%pi<\/span>, %pi<\/span>]<\/span>, [<\/span>y<\/span>, -<\/span>%pi<\/span>, %pi<\/span>]<\/span>, [<\/span>same_xy<\/span>]<\/span>, grid2d<\/span>,\r\n  \/* \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba\u3068\u30d5\u30a9\u30f3\u30c8\u306e\u8a2d\u5b9a *\/<\/span>\r\n  [<\/span>gnuplot_svg_term_command<\/span>, \"set term svg size 600,600 font 'Times,18'\"<\/span>]<\/span>,\r\n  \/* \u51e1\u4f8b\u306e\u4f4d\u7f6e *\/<\/span>\r\n  [<\/span>gnuplot_preamble<\/span>, \"set key top left;\"<\/span>]<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$ – 1 \\leq x \\leq 1$ \u306e\u7bc4\u56f2\u3067 $y = \\sin x$ \u3068 $ y = x$ \u3092 plot2d()<\/code>\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\/* \u6b21\u306b\u62e1\u5927\u8868\u793a\u3059\u308b\u90e8\u5206\u306e\u77e9\u5f62 *\/<\/span>\r\npoints4s<\/span>:<\/span> [[<\/span>-<\/span>0.1<\/span>,-<\/span>0.<\/span>1]<\/span>,[<\/span>0.1<\/span>,-<\/span>0.<\/span>1]<\/span>,[<\/span>0.1<\/span>,0.<\/span>1]<\/span>,[<\/span>-<\/span>0.1<\/span>,0.<\/span>1]<\/span>,[<\/span>-<\/span>0.1<\/span>,-<\/span>0.<\/span>1]]<\/span>$\r\n\r\nplot2d<\/span>(<\/span>\r\n  [[<\/span>discrete<\/span>, points4s<\/span>]<\/span>, sin<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>]<\/span>, [<\/span>x<\/span>, -<\/span>1<\/span>, 1]<\/span>, \r\n  [<\/span>color<\/span>, orange<\/span>, red<\/span>, blue<\/span>]<\/span>,\r\n  [<\/span>style<\/span>, [<\/span>lines<\/span>, 2]<\/span>, [<\/span>lines<\/span>, 3]<\/span>, [<\/span>lines<\/span>, 1.<\/span>5]]<\/span>, \r\n  [<\/span>legend<\/span>, \"\"<\/span>, \"sin x\"<\/span>, \"x\"<\/span>]<\/span>,\r\n  \r\n  [<\/span>x<\/span>, -<\/span>1<\/span>, 1]<\/span>, [<\/span>y<\/span>, -<\/span>1<\/span>, 1]<\/span>, [<\/span>same_xy<\/span>]<\/span>, grid2d<\/span>,\r\n  [<\/span>gnuplot_svg_term_command<\/span>, \"set term svg size 600,600 font 'Times,18'\"<\/span>]<\/span>,\r\n  [<\/span>gnuplot_preamble<\/span>, \"set key top left;\"<\/span>]<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$ – 0.1 \\leq x \\leq 0.1$ \u306e\u7bc4\u56f2\u3067 $y = \\sin x$ \u3068 $ y = x$ \u3092 plot2d()<\/code>\u3002\u307b\u3068\u3093\u3069\u91cd\u306a\u3063\u3066\u3044\u3066\uff0c\u533a\u5225\u304c\u3064\u304d\u306b\u304f\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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plot2d<\/span>(<\/span>\r\n  [<\/span>sin<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>]<\/span>, [<\/span>x<\/span>, -<\/span>0.1<\/span>, 0.<\/span>1]<\/span>, \r\n  [<\/span>color<\/span>, red<\/span>, blue<\/span>]<\/span>,\r\n  [<\/span>style<\/span>, [<\/span>lines<\/span>, 3]<\/span>, [<\/span>lines<\/span>, 1.<\/span>5]]<\/span>, \r\n  [<\/span>legend<\/span>, \"sin x\"<\/span>, \"x\"<\/span>]<\/span>,\r\n  \r\n  [<\/span>x<\/span>, -<\/span>0.1<\/span>, 0.<\/span>1]<\/span>, [<\/span>y<\/span>, -<\/span>0.1<\/span>, 0.<\/span>1]<\/span>, [<\/span>same_xy<\/span>]<\/span>, grid2d<\/span>,\r\n  [<\/span>gnuplot_svg_term_command<\/span>, \"set term svg size 600,600 font 'Times,18'\"<\/span>]<\/span>,\r\n  [<\/span>gnuplot_preamble<\/span>, \"set key top left;\"<\/span>]<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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draw2d()<\/code> \u7de8<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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$ – \\pi \\leq x \\leq \\pi$ \u306e\u7bc4\u56f2\u3067 $y = \\sin x$ \u3068 $ y = x$ \u3092 draw2d()<\/code>\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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draw2d<\/span>(<\/span>\r\n  \/* \u6b21\u306b\u62e1\u5927\u8868\u793a\u3059\u308b\u90e8\u5206\u3092\u77e9\u5f62\u3067\u56f2\u3080 *\/<\/span>\r\n  color<\/span> =<\/span> orange<\/span>, line_width<\/span> =<\/span> 2<\/span>, key<\/span> =<\/span> \"\"<\/span>, \r\n  transparent<\/span> =<\/span> true<\/span>,\r\n  rectangle<\/span>([<\/span>-<\/span>1<\/span>,-<\/span>1]<\/span>, [<\/span>1<\/span>, 1])<\/span>,\r\n\r\n  color<\/span> =<\/span> red<\/span>, line_width<\/span> =<\/span> 3<\/span>, key<\/span> =<\/span> \"sin x\"<\/span>,\r\n  explicit<\/span>(<\/span>sin<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>, -<\/span>%pi<\/span>, %pi<\/span>)<\/span>, \r\n  color<\/span> =<\/span> blue<\/span>, line_width<\/span> =<\/span> 1.5<\/span>, key<\/span> =<\/span> \"x\"<\/span>,\r\n  explicit<\/span>(<\/span>x<\/span>, x<\/span>, -<\/span>%pi<\/span>, %pi<\/span>)<\/span>,   \r\n  \r\n  xrange<\/span> =<\/span> [<\/span>-<\/span>%pi<\/span>, %pi<\/span>]<\/span>, yrange<\/span> =<\/span> [<\/span>-<\/span>%pi<\/span>, %pi<\/span>]<\/span>, \r\n  proportional_axes<\/span> =<\/span> xy<\/span>, \r\n  xaxis<\/span> =<\/span> true<\/span>, yaxis<\/span> =<\/span> true<\/span>, grid<\/span> =<\/span> true<\/span>,\r\n  \/* \u30b0\u30e9\u30d5\u306e\u30b5\u30a4\u30ba\u3068\u30d5\u30a9\u30f3\u30c8\u306e\u8a2d\u5b9a *\/<\/span>\r\n  dimensions<\/span> =<\/span> [<\/span>600<\/span>,600]<\/span>, font<\/span> =<\/span> \"Times\"<\/span>, font_size<\/span> =<\/span> 18<\/span>, \r\n  \/* \u51e1\u4f8b\u306e\u4f4d\u7f6e *\/<\/span>\r\n  user_preamble<\/span> =<\/span> [<\/span>\"set key top left;\"<\/span>]<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$ – 1 \\leq x \\leq 1$ \u306e\u7bc4\u56f2\u3067 $y = \\sin x$ \u3068 $ y = x$ \u3092 draw2d()<\/code>\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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draw2d<\/span>(<\/span>\r\n  \/* \u6b21\u306b\u62e1\u5927\u8868\u793a\u3059\u308b\u90e8\u5206\u3092\u77e9\u5f62\u3067\u56f2\u3080 *\/<\/span>\r\n  color<\/span> =<\/span> orange<\/span>, line_width<\/span> =<\/span> 2<\/span>, key<\/span> =<\/span> \"\"<\/span>, \r\n  transparent<\/span> =<\/span> true<\/span>,\r\n  rectangle<\/span>([<\/span>-<\/span>0.1<\/span>,-<\/span>0.<\/span>1]<\/span>, [<\/span>0.1<\/span>, 0.<\/span>1])<\/span>,\r\n\r\n  color<\/span> =<\/span> red<\/span>, line_width<\/span> =<\/span> 3<\/span>, key<\/span> =<\/span> \"sin x\"<\/span>,\r\n  explicit<\/span>(<\/span>sin<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>, -<\/span>1<\/span>, 1<\/span>)<\/span>, \r\n  color<\/span> =<\/span> blue<\/span>, line_width<\/span> =<\/span> 1.5<\/span>, key<\/span> =<\/span> \"x\"<\/span>,\r\n  explicit<\/span>(<\/span>x<\/span>, x<\/span>, -<\/span>1<\/span>, 1<\/span>)<\/span>,   \r\n  \r\n  xrange<\/span> =<\/span> [<\/span>-<\/span>1<\/span>, 1]<\/span>, yrange<\/span> =<\/span> [<\/span>-<\/span>1<\/span>, 1]<\/span>, \r\n  proportional_axes<\/span> =<\/span> xy<\/span>, \r\n  xaxis<\/span> =<\/span> true<\/span>, yaxis<\/span> =<\/span> true<\/span>, grid<\/span> =<\/span> true<\/span>,\r\n  dimensions<\/span> =<\/span> [<\/span>600<\/span>,600]<\/span>, font<\/span> =<\/span> \"Times\"<\/span>, font_size<\/span> =<\/span> 18<\/span>, \r\n  user_preamble<\/span> =<\/span> [<\/span>\"set key top left;\"<\/span>]<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$ – 0.1 \\leq x \\leq 0.1$ \u306e\u7bc4\u56f2\u3067 $y = \\sin x$ \u3068 $ y = x$ \u3092 draw2d()<\/code>\u3002\u307b\u3068\u3093\u3069\u91cd\u306a\u3063\u3066\u3044\u3066\uff0c\u533a\u5225\u304c\u3064\u304d\u306b\u304f\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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draw2d<\/span>(<\/span>\r\n  color<\/span> =<\/span> red<\/span>, line_width<\/span> =<\/span> 3<\/span>, key<\/span> =<\/span> \"sin x\"<\/span>,\r\n  explicit<\/span>(<\/span>sin<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>, -<\/span>0.1<\/span>, 0.1<\/span>)<\/span>, \r\n  color<\/span> =<\/span> blue<\/span>, line_width<\/span> =<\/span> 1.5<\/span>, key<\/span> =<\/span> \"x\"<\/span>,\r\n  explicit<\/span>(<\/span>x<\/span>, x<\/span>, -<\/span>0.1<\/span>, 0.1<\/span>)<\/span>,   \r\n  \r\n  xrange<\/span> =<\/span> [<\/span>-<\/span>0.1<\/span>, 0.<\/span>1]<\/span>, yrange<\/span> =<\/span> [<\/span>-<\/span>0.1<\/span>, 0.<\/span>1]<\/span>, \r\n  proportional_axes<\/span> =<\/span> xy<\/span>, \r\n  xaxis<\/span> =<\/span> true<\/span>, yaxis<\/span> =<\/span> true<\/span>, grid<\/span> =<\/span> true<\/span>,\r\n  dimensions<\/span> =<\/span> [<\/span>600<\/span>,600]<\/span>, font<\/span> =<\/span> \"Times\"<\/span>, font_size<\/span> =<\/span> 18<\/span>, \r\n  user_preamble<\/span> =<\/span> [<\/span>\"set key top left;\"<\/span>]<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u53c2\u8003\uff1agnuplot \u3067 sin x \u3068 x \u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f \u306e Maxima \u7248\u3002Maxima \u3067 $y = \\sin x $ \u3068 $y = x$ \u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3002<\/p>\n
$ |x| \\ll 1 $ \u3067\u306f2\u3064\u306e\u30b0\u30e9\u30d5\u306f\u307b\u3068\u3093\u3069\u91cd\u306a\u3063\u3066\u3044\u3066 $ \\sin x \\simeq x $ \u3059\u306a\u308f\u3061 $\\displaystyle \\frac{\\sin x}{x} \\simeq 1$ \u3067\u3042\u308b\u3053\u3068\u3092\u898b\u3066\u78ba\u304b\u3081\u308b\u3002<\/p>\n
Maxima \u3067\u306f plot2d() \uff08\u3044\u308f\u3086\u308b plot \u7cfb\uff09\u3068 draw2d() \uff08\u3044\u308f\u3086\u308b draw \u7cfb\uff09\u304c\u3042\u308b\u3002\u6700\u8fd1\u306f\u500b\u4eba\u7684\u306b\u306f\u6388\u696d\u7b49\u3067\u306f draw \u7cfb\u3092\u4f7f\u3046\u3088\u3046\u306b\u306a\u3063\u3066\u304d\u3066\u3044\u308b\u304c\uff0c\u53c2\u8003\u307e\u3067\u306b\u4e21\u65b9\u306e\u4f7f\u7528\u4f8b\u3092\u66f8\u3044\u3066\u304a\u304f\u3002<\/p>
\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":2096,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-5596","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\/5596","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=5596"}],"version-history":[{"count":1,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/5596\/revisions"}],"predecessor-version":[{"id":5603,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/5596\/revisions\/5603"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2096"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=5596"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}