{"id":3279,"date":"2022-07-21T17:18:49","date_gmt":"2022-07-21T08:18:49","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=3279"},"modified":"2023-03-14T16:29:46","modified_gmt":"2023-03-14T07:29:46","slug":"maxima-%e3%81%a7%e9%a0%98%e5%9f%9f%e3%81%ae%e5%a1%97%e3%82%8a%e3%81%a4%e3%81%b6%e3%81%97%e3%81%a8%e5%9b%9e%e8%bb%a2%e4%bd%93%e3%81%ae%e8%a1%a8%e7%a4%ba","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/3279\/","title":{"rendered":"Maxima \u3067\u9818\u57df\u306e\u5857\u308a\u3064\u3076\u3057\u3068\u56de\u8ee2\u4f53\u306e\u8868\u793a"},"content":{"rendered":"

\u6388\u696d\u306e\u5b9a\u7a4d\u5206\u306e\u3068\u3053\u308d<\/a>\u3067\uff0c\u30b0\u30e9\u30d5\u3092\u63cf\u3044\u3066\u304b\u3089\u9762\u7a4d\u3084\u4f53\u7a4d\u3092\u6c42\u3081\u308b\u3088\u3046\u306b\u5b66\u751f\u3055\u3093\u306b\u8a00\u3063\u305f\u306e\u3067\u3002<\/p>\n

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\u66f2\u7dda\u3067\u56f2\u307e\u308c\u305f\u9818\u57df\u306e\u9762\u7a4d<\/h3>\n

\u6b21\u306e\u56f3\u5f62\u306e\u9762\u7a4d\u3092\u6c42\u3081\u306a\u3055\u3044\u3002<\/p>\n

$\\ \\ $\u653e\u7269\u7dda $y = (x-2)^2$ \u3068\uff0c$x$ \u8ef8 ($y = 0$)\uff0c$y$ \u8ef8\u3068\u3067\u56f2\u307e\u308c\u305f\u56f3\u5f62<\/p>\n

\u66f2\u7dda\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f<\/h4>\n

\u307e\u305a\u30b0\u30e9\u30d5\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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\u95a2\u6570 $y = f(x) = (x-2)^2$ \u3068 $x$ \u8ef8 $y = g(x) = 0$ \u3067\u56f2\u307e\u308c\u3066\u3044\u308b\u306e\u3067\uff0c\u4e0a\u4e0b\u306e\u7dda\u3092\u4e00\u7dd2\u306b\u56f3\u793a\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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In\u00a0[1]:<\/div>\n
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f<\/span>(<\/span>x<\/span>)<\/span>:=<\/span> (<\/span>x<\/span> -<\/span> 2<\/span>)<\/span>**<\/span>2<\/span>;\r\ng<\/span>(<\/span>x<\/span>)<\/span>:=<\/span> 0<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[1]:<\/div>\n
\\[\\tag{${\\it \\%o}_{1}$}f\\left(x\\right):=\\left(x-2\\right)^2\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{2}$}g\\left(x\\right):=0\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[2]:<\/div>\n
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plot2d<\/span>([<\/span>f<\/span>(<\/span>x<\/span>)<\/span>,  g<\/span>(<\/span>x<\/span>)]<\/span>, [<\/span>x<\/span>, -<\/span>0.2<\/span>, 2.<\/span>2]<\/span>, \r\n       [<\/span>legend<\/span>, \"(x-2)^2\"<\/span>, \"\"<\/span>])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u9818\u57df\u3092\u7e01\u53d6\u308b<\/h4>\n
\u30b0\u30e9\u30d5\u306e\u63cf\u753b\u7bc4\u56f2\u3068\uff0c\u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2\u3092\u5225\u3005\u306b\u8a2d\u5b9a\u3059\u308b\u305f\u3081\u306b\uff0c\u5a92\u4ecb\u5909\u6570\u8868\u793a\u3067\u30b0\u30e9\u30d5\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n
$x = x(t), y = y(t)$ \u3092 $a \\leq t \\leq b$ \u306e\u7bc4\u56f2\u3067\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u4f8b\uff1a<\/p>\n
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plot2d<\/span>([<\/span>parametric<\/span>, x<\/span>(<\/span>t<\/span>)<\/span>, y<\/span>(<\/span>t<\/span>)<\/span>, [<\/span>t<\/span>, a<\/span>, b<\/span>])<\/span>$\r\n<\/pre>\n<\/div>\n
\u4ee5\u4e0b\u306f\uff0c3\u672c\u306e\u30b0\u30e9\u30d5\u3092\u4e00\u7dd2\u306b\u63cf\u304f\u4f8b\u3002\u3044\u304f\u3064\u304b\u30aa\u30d7\u30b7\u30e7\u30f3\u3082\u8a2d\u5b9a\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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plot2d<\/span>([[<\/span>parametric<\/span>, t<\/span>, f<\/span>(<\/span>t<\/span>)<\/span>, [<\/span>t<\/span>, 0<\/span>, 2]]<\/span>, \/* y = f(x) *\/<\/span>\r\n        [<\/span>parametric<\/span>, t<\/span>, g<\/span>(<\/span>t<\/span>)<\/span>, [<\/span>t<\/span>, 0<\/span>, 2]]<\/span>, \/* x \u8ef8 y = g(x) *\/<\/span>\r\n        [<\/span>parametric<\/span>, 0<\/span>, t<\/span>, [<\/span>t<\/span>, 0<\/span>, 4]]<\/span>     \/* y \u8ef8 *\/<\/span>\r\n       ]<\/span>, \r\n        \r\n        \/* \u7dda\u306e\u8272\u3084\u592a\u3055\u306e\u8a2d\u5b9a *\/<\/span>\r\n        [<\/span>color<\/span>, blue<\/span>, black<\/span>, black<\/span>]<\/span>,\r\n        [<\/span>style<\/span>, [<\/span>lines<\/span>, 2]<\/span>, [<\/span>lines<\/span>, 2]<\/span>, [<\/span>lines<\/span>, 2]]<\/span>,\r\n        \r\n        \/* \u6a2a\u8ef8\u7e26\u8ef8\u306e\u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n        [<\/span>x<\/span>, -<\/span>0.5<\/span>, 2.<\/span>5]<\/span>, [<\/span>y<\/span>, -<\/span>0.5<\/span>, 4.<\/span>5]<\/span>, \r\n        \r\n        \/* \u51e1\u4f8b\u306e\u8a2d\u5b9a *\/<\/span>\r\n        [<\/span>legend<\/span>, \"(x-2)^2\"<\/span>, \"\"<\/span>, \"\"<\/span>])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u9762\u7a4d\u3092\u6c42\u3081\u308b<\/h4>\n
\u6c42\u3081\u308b\u9762\u7a4d\u306f…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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'<\/span>integrate<\/span>(<\/span>f<\/span>(<\/span>x<\/span>)<\/span> -<\/span> g<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>, 0<\/span>, 2<\/span>)<\/span> =<\/span>\r\n integrate<\/span>(<\/span>f<\/span>(<\/span>x<\/span>)<\/span> -<\/span> g<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>, 0<\/span>, 2<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[4]:<\/div>\n
\\[\\tag{${\\it \\%o}_{5}$}\\int_{0}^{2}{\\left(x-2\\right)^2\\;dx}=\\frac{8}{3}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3059<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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$0 < x < 2$ \u306e\u7bc4\u56f2\u3067\uff0c$y = (x-2)^2$ \u3068 $y = 0$ \u3067\u56f2\u307e\u308c\u305f\u90e8\u5206\u3092\u9ec4\u8272\u3067\u5857\u308a\u3064\u3076\u3059\u4f8b\u3002Maxima \u3067\u306f plot2d()<\/code> \u3067\u306f\u306a\u304f\uff0cdraw2d()<\/code> \u95a2\u6570\u3092\u4f7f\u3044\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u4f8b\u3092\u53c2\u7167\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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\/* \u56f2\u307e\u308c\u305f\u90e8\u5206\u3092\u5857\u308a\u3064\u3076\u3057\u3066\u8868\u793a\u3002*\/<\/span>\r\n\r\ndraw2d<\/span>(<\/span>\/* \u5857\u308a\u3064\u3076\u3059\u8272\u306e\u6307\u5b9a\u3002*\/<\/span>\r\n       fill_color<\/span> =<\/span> yellow<\/span>, \r\n       \r\n       \/* \u4e0a\u306e\u7dda\u3002y = f(x) \u3092 filled_func \u306b\u4ee3\u5165\u3002*\/<\/span>\r\n       filled_func<\/span> =<\/span> f<\/span>(<\/span>x<\/span>)<\/span>, \r\n       \r\n       \/* \u4e0b\u306e\u7dda\u3002y = g(x) \u3092 0 < x < 2 \u306e\u7bc4\u56f2\u3067\u63cf\u304f\u3002*\/<\/span>\r\n       explicit<\/span>(<\/span>g<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>, 0<\/span>, 2<\/span>))<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[6]:<\/div>\n
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\/* \u3082\u3046\u5c11\u3057\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u4ed8\u3051\u3066\u3002*\/<\/span>\r\n\/* \u7e26\u306e\u7dda x = 0 \u3082\u63cf\u3044\u3066\u307f\u308b\u3002 *\/<\/span>\r\n\r\ndraw2d<\/span>(<\/span>\/* x \u8ef8 y \u8ef8\u306e\u8868\u793a\u7bc4\u56f2\u306e\u8a2d\u5b9a\u3002*\/<\/span> \r\n       xrange<\/span> =<\/span> [<\/span>-<\/span>0.5<\/span>, 2.<\/span>5]<\/span>, xaxis<\/span>=<\/span>true<\/span>,\r\n       yrange<\/span> =<\/span> [<\/span>-<\/span>0.5<\/span>, 4.<\/span>5]<\/span>, yaxis<\/span>=<\/span>true<\/span>,\r\n       \r\n       \/* \u5857\u308a\u3064\u3076\u3059\u8272\u306e\u6307\u5b9a\u3002*\/<\/span>\r\n       fill_color<\/span> =<\/span> yellow<\/span>, \r\n       \r\n       \/* \u4e0a\u306e\u7dda\u3002y = f(x) \u3092 filled_func \u306b\u4ee3\u5165\u3002*\/<\/span>\r\n       filled_func<\/span> =<\/span> f<\/span>(<\/span>x<\/span>)<\/span>, \r\n       \r\n       \/* \u4e0b\u306e\u7dda\u3002y = g(x) \u3092 0 < x < 2 \u306e\u7bc4\u56f2\u3067\u63cf\u304f\u3002*\/<\/span>\r\n       explicit<\/span>(<\/span>g<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>, 0<\/span>, 2<\/span>)<\/span>,  \r\n       \r\n       \/* \u8ffd\u52a0\u306e\u7dda\u306f parametric \u3067\u63cf\u304f\u3002           *\/<\/span>\r\n       \/* x = x(t), y = y(t), a < t < b \u306e\u30b0\u30e9\u30d5\u306f *\/<\/span>\r\n       \/* parametric(x(t), y(t), t, a, b) \u3068\u66f8\u304f\u3002 *\/<\/span>\r\n       \/* \u7dda\u306e\u592a\u3055\u3092 2 \u306b\u3057\u3066\u30e1\u30ea\u30cf\u30ea\u3092\u3064\u3051\u3066      *\/<\/span>\r\n       line_width<\/span> =<\/span> 2<\/span>, nticks<\/span> =<\/span> 200<\/span>, \r\n       \r\n       \/* \u4e0a\u306e\u7dda\u3002y = f(x) *\/<\/span>\r\n       color<\/span> =<\/span> blue<\/span>, key<\/span> =<\/span> \"(x-2)^2\"<\/span>,\r\n       parametric<\/span>(<\/span>t<\/span>, f<\/span>(<\/span>t<\/span>)<\/span>, t<\/span>, 0<\/span>, 2<\/span>)<\/span>,\r\n\r\n       \/* \u4e0b\u306e\u7dda\u3002y = g(x) *\/<\/span>\r\n       color<\/span> =<\/span> black<\/span>, key<\/span> =<\/span> \"\"<\/span>,\r\n       parametric<\/span>(<\/span>t<\/span>, g<\/span>(<\/span>x<\/span>)<\/span>, t<\/span>, 0<\/span>, 2<\/span>)<\/span>, \r\n       \r\n       \/* x = 0 (y \u8ef8) *\/<\/span>\r\n       color<\/span> =<\/span> black<\/span>, key<\/span> =<\/span> \"\"<\/span>,\r\n       parametric<\/span>(<\/span>0<\/span>, t<\/span>, t<\/span>, 0<\/span>, 4<\/span>)<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u56de\u8ee2\u4f53\u306e\u4f53\u7a4d<\/h3>\n
\u6b21\u306e\u56f3\u5f62\u3092 $x$ \u8ef8\u306e\u307e\u308f\u308a\u306b1\u56de\u8ee2\u3055\u305b\u3066\u3067\u304d\u308b\u56de\u8ee2\u4f53\u306e\u4f53\u7a4d $V$ \u3092\u6c42\u3081\u306a\u3055\u3044\u3002<\/p>\n
\u66f2\u7dda $y = \\sqrt{x}$ \u3068 $x$ \u8ef8\uff0c\u76f4\u7dda $x = 1$ \u3067\u56f2\u307e\u308c\u305f\u56f3\u5f62<\/p>\n
\u66f2\u7dda\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f<\/h4>\n
\u307e\u305a\uff0c\u30b0\u30e9\u30d5\u3092\u63cf\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[7]:<\/div>\n
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f<\/span>(<\/span>x<\/span>)<\/span>:=<\/span> sqrt<\/span>(<\/span>x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[7]:<\/div>\n
\\[\\tag{${\\it \\%o}_{8}$}f\\left(x\\right):=\\sqrt{x}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[8]:<\/div>\n
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plot2d<\/span>(<\/span>f<\/span>(<\/span>x<\/span>)<\/span>, [<\/span>x<\/span>, 0<\/span>, 1])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u56de\u8ee2\u3055\u305b\u308b\u9818\u57df\u3092\u7e01\u53d6\u308b<\/h4>\n
\u30b0\u30e9\u30d5\u306e\u63cf\u753b\u7bc4\u56f2\u3068\uff0c\u7e26\u8ef8\u6a2a\u8ef8\u306e\u8868\u793a\u7bc4\u56f2\u3092\u5225\u9014\u8a2d\u5b9a\u3057\u305f\u3044\u5834\u5408\u306f\uff0c\u5a92\u4ecb\u5909\u6570\u8868\u793a parametric<\/code> \u3067\u8868\u793a\u3059\u308b\u3068\u3088\u3044\u3002
\n$x = x(t), y = y(t)$ \u3092 $a \\leq t \\leq b$ \u306e\u7bc4\u56f2\u3067\u63cf\u304f\u4f8b\uff1a<\/p>\n
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plot2d<\/span>([<\/span>parametric<\/span>, x<\/span>(<\/span>t<\/span>)<\/span>, y<\/span>(<\/span>t<\/span>)<\/span>, [<\/span>t<\/span>, a<\/span>, b<\/span>]])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[9]:<\/div>\n
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plot2d<\/span>([[<\/span>parametric<\/span>, t<\/span>, f<\/span>(<\/span>t<\/span>)<\/span>, [<\/span>t<\/span>, 0<\/span>, 1]]<\/span>, \/* y = f(x) *\/<\/span>\r\n        [<\/span>parametric<\/span>, t<\/span>, 0<\/span>, [<\/span>t<\/span>, 0<\/span>, 1]]<\/span>,    \/* x \u8ef8 y = 0 *\/<\/span>\r\n        [<\/span>parametric<\/span>, 1<\/span>, t<\/span>, [<\/span>t<\/span>, 0<\/span>, 1]]]<\/span>,   \/* x = 1*\/<\/span>\r\n\r\n        \/* \u7dda\u306e\u8272\u3084\u592a\u3055\u306e\u8a2d\u5b9a *\/<\/span>\r\n        [<\/span>color<\/span>, blue<\/span>, black<\/span>, black<\/span>]<\/span>,\r\n        [<\/span>style<\/span>, [<\/span>lines<\/span>, 2]<\/span>, [<\/span>lines<\/span>, 1]<\/span>, [<\/span>lines<\/span>, 1]]<\/span>,\r\n\r\n        [<\/span>x<\/span>, -<\/span>0.5<\/span>, 1.<\/span>5]<\/span>, [<\/span>y<\/span>, -<\/span>1.5<\/span>, 1.<\/span>5]<\/span>, \r\n        [<\/span>legend<\/span>, \"sqrt(x)\"<\/span>, \"\"<\/span>, \"\"<\/span>])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\"\"<\/p>\n
\u4f53\u7a4d\u3092\u6c42\u3081\u308b<\/h4>\n
\u56de\u8ee2\u4f53\u306e\u4f53\u7a4d\u306f $\\displaystyle V = \\int_a^b \\pi \\left\\{f(x)\\right\\}^2 \\, dx$ \u3067\u3042\u3063\u305f\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[10]:<\/div>\n
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V<\/span> =<\/span> integrate<\/span>(<\/span>%pi<\/span> *<\/span> f<\/span>(<\/span>x<\/span>)<\/span>**<\/span>2<\/span>, x<\/span>, 0<\/span>, 1<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[10]:<\/div>\n
\\[\\tag{${\\it \\%o}_{11}$}V=\\frac{\\pi}{2}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u56de\u8ee2\u3055\u305b\u308b\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3059<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[11]:<\/div>\n
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draw2d<\/span>(<\/span>\/* x \u8ef8 y \u8ef8\u306e\u8868\u793a\u7bc4\u56f2\u306e\u8a2d\u5b9a\u3002*\/<\/span> \r\n       xrange<\/span> =<\/span> [<\/span>-<\/span>0.2<\/span>, 1.<\/span>5]<\/span>,\r\n       yrange<\/span> =<\/span> [<\/span>-<\/span>1.5<\/span>, 1.<\/span>5]<\/span>, \r\n       \r\n       xaxis<\/span> =<\/span> true<\/span>, \r\n       \/* \u5857\u308a\u3064\u3076\u3059\u8272\u306e\u6307\u5b9a\u3002*\/<\/span>\r\n       fill_color<\/span> =<\/span> yellow<\/span>, \r\n       \/* \u4e0a\u306e\u7dda\u3002y = f(x) \u3092 filled_func \u306b\u4ee3\u5165\u3002*\/<\/span>\r\n       filled_func<\/span> =<\/span> f<\/span>(<\/span>x<\/span>)<\/span>, \r\n       \/* \u4e0b\u306e\u7dda\u3002y = 0 \uff08x\u8ef8\uff09\u3092 0<x<1 \u306e\u7bc4\u56f2\u3067\u63cf\u304f\u3002*\/<\/span>\r\n       explicit<\/span>(<\/span>0<\/span>, x<\/span>, 0<\/span>, 1<\/span>)<\/span>,   \r\n       \r\n       \/* \u8ffd\u52a0\u306e\u7dda\u306f parametric \u3067\u63cf\u304f\u3002 *\/<\/span>\r\n       \/* x = x(t), y = y(t), a < t < b \u306e\u30b0\u30e9\u30d5\u306f *\/<\/span>\r\n       \/* parametric(x(t), y(t), t, a, b) \u3068\u3059\u308b\u3002*\/<\/span>\r\n       \/* \u7dda\u306e\u592a\u3055\u3092 2 \u306b\u3057\u3066\u30e1\u30ea\u30cf\u30ea\u3092\u3064\u3051\u3066 *\/<\/span>\r\n       nticks<\/span> =<\/span> 500<\/span>, line_width<\/span> =<\/span> 2<\/span>,\r\n       \r\n       \/* y = f(x) *\/<\/span>\r\n       color<\/span> =<\/span> blue<\/span>, key<\/span> =<\/span> \"sqrt(x)\"<\/span>,\r\n       parametric<\/span>(<\/span>t<\/span>, f<\/span>(<\/span>t<\/span>)<\/span>, t<\/span>, 0<\/span>, 1<\/span>)<\/span>,\r\n       \r\n       \/* y = -f(x) *\/<\/span>\r\n       color<\/span> =<\/span> blue<\/span>, key<\/span> =<\/span> \"\"<\/span>,\r\n       parametric<\/span>(<\/span>t<\/span>, -<\/span>f<\/span>(<\/span>t<\/span>)<\/span>, t<\/span>, 0<\/span>, 1<\/span>)<\/span>, \r\n       \r\n       \/* \u56de\u8ee2\u4f53\u306e\u5e95\u9762\u3092\u6955\u5186\u3067\u63cf\u304f\u3002*\/<\/span>\r\n       color<\/span> =<\/span> blue<\/span>, key<\/span> =<\/span> \"\"<\/span>,\r\n       parametric<\/span>(<\/span>0.<\/span>1*<\/span>cos<\/span>(<\/span>t<\/span>)<\/span>+<\/span>1<\/span>, 1*<\/span>sin<\/span>(<\/span>t<\/span>)<\/span>, t<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>)<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u56de\u8ee2\u4f53\u3092\u305d\u308c\u3089\u3057\u304f3\u6b21\u5143\u7684\u306b\u63cf\u304f<\/h4>\n
\u3082\u3046\u5c11\u30573\u6b21\u5143\u7684\u306a\u30b0\u30e9\u30d5\u306b\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n
$y = f(x)$ \u3092 $x$ \u8ef8\u306e\u307e\u308f\u308a\u306b\u89d2\u5ea6 $\\theta$ \u3057\u305f\u3068\u304d\u306b\u3067\u304d\u308b\u66f2\u9762\u4e0a\u306e\u70b9 $P$ \u306e\u5ea7\u6a19\u306f<\/p>\n
\\begin{eqnarray}
\nx &=& x\\\\
\ny &=& f(x) \\cos\\theta \\\\
\nz &=& f(x) \\sin\\theta
\n\\end{eqnarray}<\/p>\n
\u3067\u3059\u3002\u3053\u306e\u66f2\u9762\u3092 plot3d()<\/code> \u95a2\u6570\u3067\u63cf\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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plot3d<\/span>(<\/span>\/* \u5a92\u4ecb\u5909\u6570\u8868\u793a\u306e\u66f2\u9762\u3092\u63cf\u304f\u3002*\/<\/span>\r\n       [<\/span>x<\/span>, f<\/span>(<\/span>x<\/span>)<\/span>*<\/span>cos<\/span>(<\/span>t<\/span>)<\/span>, f<\/span>(<\/span>x<\/span>)<\/span>*<\/span>sin<\/span>(<\/span>t<\/span>)]<\/span>, \r\n       [<\/span>x<\/span>, 0<\/span>, 1]<\/span>, [<\/span>t<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>]<\/span>, \r\n\r\n       \/* \u5404\u7a2e\u8a2d\u5b9a\u3002*\/<\/span>\r\n       [<\/span>xtics<\/span>, false<\/span>]<\/span>, [<\/span>ytics<\/span>, false<\/span>]<\/span>, [<\/span>ztics<\/span>, false<\/span>]<\/span>,\r\n       [<\/span>x<\/span>, -<\/span>0.2<\/span>, 1.<\/span>5]<\/span>, [<\/span>y<\/span>, -<\/span>1.2<\/span>, 1.<\/span>2]<\/span>, [<\/span>z<\/span>, -<\/span>1.2<\/span>, 1.<\/span>2]<\/span>, \r\n       [<\/span>elevation<\/span>,85]<\/span>, [<\/span>azimuth<\/span>,5]<\/span>, [<\/span>grid<\/span>, 60<\/span>,36]<\/span>, \r\n       [<\/span>legend<\/span>, \"\"<\/span>]<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u3053\u306e\u307e\u307e\u3060\u3068\u5e95\u9762\u304c\u63cf\u304b\u308c\u3066\u304a\u3089\u305a\uff0c\u306a\u3093\u3068\u306a\u304f\u5e95\u304c\u629c\u3051\u3066\u3044\u308b\u611f\u3058\u3067\u3059\u3002 plot3d()<\/code> \u3067\u306f\uff0c\u3069\u3046\u3059\u308c\u3070\u5a92\u4ecb\u5909\u6570\u8868\u793a\u306e\u66f2\u9762\u3092\u8907\u6570\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u304b\uff0c\u4eca\u306e\u3068\u3053\u308d\u4e0d\u660e\u3067\u3059\u3002<\/p>\n
draw3d()<\/code> \u3092\u4f7f\u3046\u3068\uff0c\u3082\u3046\u5c11\u3057\u67d4\u8edf\u306b\u63cf\u3051\u305d\u3046\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u4f8b\u3092\u53c2\u7167\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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draw3d<\/span>(<\/span>\r\n       xrange<\/span> =<\/span> [<\/span>-<\/span>0.2<\/span>, 1.<\/span>5]<\/span>,\r\n       yrange<\/span> =<\/span> [<\/span>-<\/span>1.5<\/span>, 1.<\/span>5]<\/span>, \r\n       zrange<\/span> =<\/span> [<\/span>-<\/span>1.1<\/span>, 1.<\/span>1]<\/span>, \r\n       \r\n  \/* \u5074\u9762 *\/<\/span>\r\n  line_width<\/span>=<\/span>0.2<\/span>, xu_grid<\/span> =<\/span> 60<\/span>, yv_grid<\/span> =<\/span> 36<\/span>,\r\n  parametric_surface<\/span>(<\/span>x<\/span>, f<\/span>(<\/span>x<\/span>)<\/span>*<\/span>cos<\/span>(<\/span>t<\/span>)<\/span>, f<\/span>(<\/span>x<\/span>)<\/span>*<\/span>sin<\/span>(<\/span>t<\/span>)<\/span>, \r\n                     x<\/span>, 0<\/span>, 1<\/span>, t<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>)<\/span>,\r\n  \/* \u5e95\u9762 *\/<\/span>\r\n  xu_grid<\/span> =<\/span> 6<\/span>, yv_grid<\/span> =<\/span> 36<\/span>,\r\n  parametric_surface<\/span>(<\/span>f<\/span>(<\/span>1<\/span>)<\/span>, x<\/span>*<\/span>cos<\/span>(<\/span>t<\/span>)<\/span>, x<\/span>*<\/span>sin<\/span>(<\/span>t<\/span>)<\/span>, \r\n                     x<\/span>, 0<\/span>, 1<\/span>, t<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>)<\/span>,\r\n  \/* \u8af8\u8a2d\u5b9a*\/<\/span>\r\n  surface_hide<\/span> =<\/span>true<\/span>, view=[90, 9], \r\n  axis_3d = false, \r\n  \r\n  \/* x \u8ef8 *\/<\/span>\r\n  color<\/span>=<\/span>black<\/span>, line_width<\/span> =<\/span> 1<\/span>,\r\n  parametric<\/span>(<\/span>x<\/span>, 0<\/span>, 0<\/span>, x<\/span>, -<\/span>0.2<\/span>, 1.5<\/span>)<\/span>, \r\n  \r\n  \/* z = f(x) \u3092\u96a0\u308c\u306a\u3044\u3088\u3046\u306b\u5c11\u3057\u305a\u3089\u3057\u3066 *\/<\/span>\r\n  nticks<\/span>=<\/span>1000<\/span>, color<\/span>=<\/span>red<\/span>, line_width<\/span> =<\/span> 2<\/span>,\r\n  parametric<\/span>(<\/span>x<\/span>, 0<\/span>, sqrt<\/span>(<\/span>x<\/span>)<\/span>+<\/span>0.01<\/span>, x<\/span>, 0<\/span>, 1<\/span>)<\/span>, \r\n  parametric<\/span>(<\/span>1<\/span>, 0.01<\/span>, x<\/span>, x<\/span>, 0<\/span>, 1+<\/span>0.01<\/span>)<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u56de\u8ee2\u4f53\u306e\u300c\u5207\u308a\u53e3\u300d\u3092\u898b\u305b\u308b\u4f8b<\/h4>\n
Maxima \u306e draw3d() \u3060\u3051\u3067\u4f5c\u3063\u3066\u307f\u307e\u3057\u305f\u3002\uff08svg \u30d5\u30a1\u30a4\u30eb\u304c\u5de8\u5927\u306b\u306a\u3063\u305f\u306e\u3067 png \u306b\u5909\u63db\u3002\uff09<\/p>\n
\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
\u6388\u696d\u306e\u5b9a\u7a4d\u5206\u306e\u3068\u3053\u308d\u3067\uff0c\u30b0\u30e9\u30d5\u3092\u63cf\u3044\u3066\u304b\u3089\u9762\u7a4d\u3084\u4f53\u7a4d\u3092\u6c42\u3081\u308b\u3088\u3046\u306b\u5b66\u751f\u3055\u3093\u306b\u8a00\u3063\u305f\u306e\u3067\u3002<\/p>
\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[14],"tags":[],"class_list":["post-3279","post","type-post","status-publish","format-standard","hentry","category-maxima","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/3279","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/post"}],"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=3279"}],"version-history":[{"count":17,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/3279\/revisions"}],"predecessor-version":[{"id":3315,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/3279\/revisions\/3315"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=3279"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=3279"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=3279"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}