{"id":4199,"date":"2022-11-17T12:48:56","date_gmt":"2022-11-17T03:48:56","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=4199"},"modified":"2023-03-14T16:22:55","modified_gmt":"2023-03-14T07:22:55","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%ae%e8%bf%bd%e8%a8%98","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/4199\/","title":{"rendered":"Maxima \u3067\u9818\u57df\u306e\u5857\u308a\u3064\u3076\u3057\u306e\u8ffd\u8a18"},"content":{"rendered":"
\n
<\/div>\n
\n
\n

Maxima \u3067\u9818\u57df\u306e\u5857\u308a\u3064\u3076\u3057\u3068\u56de\u8ee2\u4f53\u306e\u8868\u793a<\/a> \u306b\u66f8\u3044\u305f Maxima \u3067\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3059\u4f8b\u306e\u8ffd\u8a18\u3002<\/p>\n

\u5f53\u6642\u306f\uff0c\u5857\u308a\u3064\u3076\u3057\u305f\u5f8c\u306b explicit(f(x), x, x0, x1)<\/code> \u304c\u3067\u304d\u306a\u304f\u3066\uff0c\u8ffd\u52a0\u306e\u7dda\u306f parametric \u3067\u63cf\u304f<\/code> \u306a\u3069\u3068\u562f\u3044\u3066\u3044\u305f\u304c\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b filled_func = false<\/code> \u3068\u3059\u308c\u3070\u5857\u308a\u3064\u3076\u3057\u7d42\u4e86\u3067\u305d\u306e\u5f8c\u306f explicit(f(x), x, x0, x1)<\/code> \u3067\u304d\u307e\u3059\u3002
\n<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n
<\/div>\n
\n
\n

\u967d\u95a2\u6570\u3067\u8868\u3055\u308c\u308b\u66f2\u7dda\u3067\u56f2\u307e\u308c\u305f\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3059\u4f8b<\/h3>\n

$\\ \\ $\u653e\u7269\u7dda $y = (x-2)^2$ \u3068\uff0c$x$ \u8ef8 ($y = 0$)\uff0c$y$ \u8ef8\u3068\u3067\u56f2\u307e\u308c\u305f\u9818\u57df\u3092 Maxima \u306e draw2d()<\/code> \u3067\u5857\u308a\u3064\u3076\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n
<\/div>\n
\n
\n

\u307e\u305a\uff0c\u9818\u57df\u306e\u4e0a\u9650\u3068\u4e0b\u9650\u3092\u8868\u3059\u967d\u95a2\u6570\u3092\u5b9a\u7fa9\u3059\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n
\n
In\u00a0[1]:<\/div>\n
\n
\n
\n
f<\/span>(<\/span>x<\/span>)<\/span>:=<\/span> (<\/span>x<\/span> -<\/span> 2<\/span>)<\/span>**<\/span>2$\r\ng<\/span>(<\/span>x<\/span>)<\/span>:=<\/span> 0$\r\n\r\ndraw2d<\/span>(<\/span>\r\n  font<\/span> =<\/span> \"Arial\"<\/span>, font_size<\/span> =<\/span> 18<\/span>,\r\n  \/* \u967d\u95a2\u6570\u306e\u66f2\u7dda\u3092\u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u306f\u3053\u306e\u6570\u5024\u3092\u5927\u304d\u3081\u306b *\/<\/span>\r\n  nticks<\/span> =<\/span> 30<\/span>, \r\n  \/* 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  \/* \u5857\u308a\u3064\u3076\u3057\u7d42\u4e86 *\/<\/span>\r\n  filled_func<\/span> =<\/span> false<\/span>, \r\n  \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>, \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  explicit<\/span>(<\/span>f<\/span>(<\/span>x<\/span>)<\/span>, x<\/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  explicit<\/span>(<\/span>g<\/span>(<\/span>x<\/span>)<\/span>, x<\/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  \r\n  file_name<\/span> =<\/span> region<\/span>-<\/span>fig1<\/span>, \r\n  dimensions<\/span> =<\/span> [<\/span>1280<\/span>,960]<\/span>,\r\n  terminal<\/span> =<\/span> '<\/span>png<\/span> \r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n
<\/div>\n
\"\"<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
\n
\n
region<\/code> \u3092\u6307\u5b9a\u3057\u3066\u5857\u308a\u3064\u3076\u3059\u4f8b\uff08\u967d\u95a2\u6570\u3092\u4f7f\u3063\u3066\uff09<\/h3>\n
region()<\/code> \u3092\u4f7f\u3046\u3068\uff0c\u967d\u95a2\u6570\u3060\u3051\u3067\u306a\u304f\u9670\u95a2\u6570\u3082\u4f7f\u3063\u305f\u4e0d\u7b49\u5f0f\u3067\u9818\u57df\u3092\u6307\u5b9a\u3057\u3066\u5857\u308a\u3064\u3076\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n
\u305f\u3068\u3048\u3070\uff0c\u4e0a\u306e\u4f8b\u306e\u9ec4\u8272\u3067\u5857\u308a\u3064\u3076\u3055\u308c\u305f\u9818\u57df\u306f\uff0c$ 0 < x < 2$\uff08\u5f93\u3063\u3066 $g(0) < y < f(0)$\uff09\u306e\u7bc4\u56f2\u3067 $y < f(x)$ \u306e\u9818\u57df\u3067\u3042\u308b\u3068\u3042\u3089\u308f\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3092\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u30aa\u30d6\u30b8\u30a7\u30af\u30c8 region()<\/code> \u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3057\u307e\u3059\u3002<\/p>\n
\n
region<\/span>(<\/span>y<\/span> <<\/span> f<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>, 0<\/span>, 2<\/span>, y<\/span>, g<\/span>(<\/span>0<\/span>)<\/span>, f<\/span>(<\/span>0<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
In\u00a0[2]:<\/div>\n
\n
\n
\n
f<\/span>(<\/span>x<\/span>)<\/span>:=<\/span> (<\/span>x<\/span> -<\/span> 2<\/span>)<\/span>**<\/span>2$\r\ng<\/span>(<\/span>x<\/span>)<\/span>:=<\/span> 0$\r\n\r\ndraw2d<\/span>(<\/span>\r\n  font<\/span> =<\/span> \"Arial\"<\/span>, font_size<\/span> =<\/span> 18<\/span>,\r\n  \/* \u967d\u95a2\u6570\u306e\u66f2\u7dda\u3092\u6ed1\u3089\u304b\u306b\u3059\u308b\u305f\u3081\u306b\u306f\u3053\u306e\u6570\u5024\u3092\u5927\u304d\u3081\u306b *\/<\/span>\r\n  nticks<\/span> =<\/span> 30<\/span>, \r\n  \/* 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\u6b8b\u3057\u304c\u3042\u308b\u3088\u3046\u306a\u3089\u5024\u3092\u5927\u304d\u304f\u3059\u308b *\/<\/span>\r\n  x_voxel<\/span> =<\/span> 30<\/span>, y_voxel<\/span> =<\/span> 30<\/span>,  \r\n\r\n  \/* \u5857\u308a\u3064\u3076\u3059\u8272\u306e\u6307\u5b9a *\/<\/span>\r\n  fill_color<\/span> =<\/span> yellow<\/span>,    \r\n\r\n  \/* \u5857\u308a\u3064\u3076\u3059\u9818\u57df\u306e\u6307\u5b9a *\/<\/span>\r\n  region<\/span>(<\/span>y<\/span> <<\/span> f<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>, 0<\/span>, 2<\/span>, y<\/span>, g<\/span>(<\/span>0<\/span>)<\/span>, f<\/span>(<\/span>0<\/span>))<\/span>, \r\n  \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>, \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  explicit<\/span>(<\/span>f<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>, 0<\/span>, 2<\/span>)<\/span>, \r\n\r\n  file_name<\/span> =<\/span> region<\/span>-<\/span>fig2<\/span>, \r\n  dimensions<\/span> =<\/span> [<\/span>1280<\/span>,960]<\/span>,\r\n  terminal<\/span> =<\/span> '<\/span>png<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
\n
\n
<\/div>\n
\"\"<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
\n
\n
region<\/code> \u3092\u6307\u5b9a\u3057\u3066\u5857\u308a\u3064\u3076\u3059\u4f8b\uff08\u9670\u95a2\u6570\u3082\u4f7f\u3063\u3066\uff09<\/h3>\n
$y < f(x) \\equiv -x + 1$ \u304b\u3064 $g(x, y) \\equiv x^2 + y^2 > 4$\uff0c\u307e\u305f\u306f $y > f(x)$ \u304b\u3064 $g(x, y) < 4$ \u306e\u9818\u57df\u3092\u5857\u308a\u3064\u3076\u3059\u4f8b\u3002<\/p>\n