{"id":2749,"date":"2022-03-29T17:28:48","date_gmt":"2022-03-29T08:28:48","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2749"},"modified":"2024-02-22T16:28:50","modified_gmt":"2024-02-22T07:28:50","slug":"%e5%8f%82%e8%80%83%ef%bc%9a%e9%9d%99%e7%a3%81%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e9%9a%9b%e3%81%ab%e4%bd%bf%e3%81%a3%e3%81%9f%e7%a9%8d%e5%88%86%e3%82%92-maxima-jupyter-%e3%81%a7%e7%a2%ba","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e9%9b%bb%e7%a3%81%e6%b0%97%e5%ad%a6-i\/%e9%9d%99%e7%a3%81%e5%a0%b4%ef%bc%9a%e9%9b%bb%e6%b5%81%e5%af%86%e5%ba%a6%e3%81%8b%e3%82%89%e7%9b%b4%e6%8e%a5%e9%9d%99%e7%a3%81%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b\/%e5%8f%82%e8%80%83%ef%bc%9a%e9%9d%99%e7%a3%81%e5%a0%b4%e3%82%92%e6%b1%82%e3%82%81%e3%82%8b%e9%9a%9b%e3%81%ab%e4%bd%bf%e3%81%a3%e3%81%9f%e7%a9%8d%e5%88%86%e3%82%92-maxima-jupyter-%e3%81%a7%e7%a2%ba\/","title":{"rendered":"\u53c2\u8003\uff1a\u9759\u78c1\u5834\u3092\u6c42\u3081\u308b\u969b\u306b\u4f7f\u3063\u305f\u7a4d\u5206\u3092 Maxima-Jupyter \u3067\u78ba\u8a8d\u3059\u308b"},"content":{"rendered":"

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\u7a4d\u5206\u3092 Maxima-Jupyter \u3067\u78ba\u8a8d\u3059\u308b<\/span><\/h3>\n

1<\/h4>\n

$$\\int_{-\\infty}^{\\infty}
\n\\frac{1}{\\left(x^2 + y^2 + (z-z’)^2\\right)^{3\/2}} dz’ =\u00a0 \\frac{2}{x^2 + y^2}$$<\/p>\n

\u306e\u78ba\u8a8d\u3002\uff08\u96fb\u5834\u3092\u6c42\u3081\u308b\u3068\u304d\u306b\u3082\u51fa\u307e\u3057\u305f\u3002\uff09<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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In\u00a0[1]:<\/div>\n
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\/* \u5206\u6bcd\u304c\u30bc\u30ed\u306b\u306a\u3089\u306a\u3044\u3088\u3046\u306b\u4eee\u5b9a\u3057\u307e\u3059\u3002*\/<\/span>\r\nassume<\/span>(<\/span>x<\/span> ><\/span> 0<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[2]:<\/div>\n
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'<\/span>integrate<\/span>(<\/span>1\/<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span> +<\/span> (<\/span>z<\/span>-<\/span>z1<\/span>)<\/span>**<\/span>2<\/span>)<\/span>**<\/span>(<\/span>3\/<\/span>2<\/span>)<\/span>, z1<\/span>, -<\/span>inf<\/span>, inf<\/span>)<\/span> =<\/span> \r\n integrate<\/span>(<\/span>1\/<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span> +<\/span> (<\/span>z<\/span>-<\/span>z1<\/span>)<\/span>**<\/span>2<\/span>)<\/span>**<\/span>(<\/span>3\/<\/span>2<\/span>)<\/span>, z1<\/span>, -<\/span>inf<\/span>, inf<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[2]:<\/div>\n
\\[\\tag{${\\it \\%o}_{2}$}\\int_{-\\infty }^{\\infty }{\\frac{1}{\\left(\\left(z-z_{1}\\right)^2+y^2+x^2\\right)^{\\frac{3}{2}}}\\;dz_{1}}=\\frac{2}{y^2+x^2}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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2<\/h4>\n
$$\\int_{-\\infty}^{\\infty}
\n\\frac{z – z’}{\\left((x-x’)^2 + (y-y’)^2 + (z-z’)^2\\right)^{3\/2}} dz’ =0$$<\/p>\n
\u306e\u78ba\u8a8d\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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'<\/span>integrate<\/span>(<\/span>\r\n   (<\/span>z<\/span>-<\/span>z1<\/span>)<\/span>\/<\/span>((<\/span>x<\/span>-<\/span>x1<\/span>)<\/span>**<\/span>2<\/span> +<\/span> (<\/span>y<\/span>-<\/span>y1<\/span>)<\/span>**<\/span>2<\/span> +<\/span> (<\/span>z<\/span>-<\/span>z1<\/span>)<\/span>**<\/span>2<\/span>)<\/span>**<\/span>(<\/span>3\/<\/span>2<\/span>)<\/span>, \r\n   z1<\/span>, -<\/span>inf<\/span>, inf<\/span>)<\/span> =<\/span>\r\n integrate<\/span>(<\/span>\r\n   (<\/span>z<\/span>-<\/span>z1<\/span>)<\/span>\/<\/span>((<\/span>x<\/span>-<\/span>x1<\/span>)<\/span>**<\/span>2<\/span> +<\/span> (<\/span>y<\/span>-<\/span>y1<\/span>)<\/span>**<\/span>2<\/span> +<\/span> (<\/span>z<\/span>-<\/span>z1<\/span>)<\/span>**<\/span>2<\/span>)<\/span>**<\/span>(<\/span>3\/<\/span>2<\/span>)<\/span>, \r\n   z1<\/span>, -<\/span>inf<\/span>, inf<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u001bX     2             2     2             2\r\nIs y1  - 2 y y1 + y  + x1  - 2 x x1 + x  zero or nonzero?\r\n\u001b\\     2             2     2             2\r\nIs y1  - 2 y y1 + y  + x1  - 2 x x1 + x  zero or nonzero?\r\nnonzero;\r\n\r\n<\/pre>\n<\/div>\n<\/div>\n
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Out[3]:<\/div>\n
\\[\\tag{${\\it \\%o}_{3}$}\\int_{-\\infty }^{\\infty }{\\frac{z-z_{1}}{\\left(\\left(z-z_{1}\\right)^2+\\left(y-y_{1}\\right)^2+\\left(x-x_{1}\\right)^2\\right)^{\\frac{3}{2}}}\\;dz_{1}}=0\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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3<\/h4>\n
\\begin{eqnarray}
\n\\int_0^{2\\pi}\u00a0 \\,d\\phi’\u00a0 \\frac{ a^2\u00a0 – a\u00a0 y\\sin\\phi’ – a x\\cos\\phi’\u00a0 }{x^2 + y^2 + a^2 – 2 a x \\cos\\phi’ – 2 a y \\sin\\phi’ } && \\\\
\n= \\left\\{
\n\\begin{array}{ll}
\n2\\pi\u00a0 & (a > \\sqrt{x^2 + y^2})\\\\
\n0 & (a < \\sqrt{x^2 + y^2})
\n\\end{array}
\n\\right.
\n\\end{eqnarray}<\/p>\n
\u306e\u78ba\u8a8d\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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\/* \u5909\u6570\u306b\u3064\u3044\u3066 assume() \u3057\u305f\u3053\u3068\u3092\u7121\u304b\u3063\u305f\u3053\u3068\u306b\u3057\u307e\u3059\u3002*\/<\/span>\r\nfacts<\/span>(<\/span>a<\/span>)<\/span>$\r\nforget<\/span>(<\/span>%<\/span>)<\/span>$\r\nfacts<\/span>(<\/span>x<\/span>)<\/span>$\r\nforget<\/span>(<\/span>%<\/span>)<\/span>$\r\n\r\n\/* \u30bd\u30ec\u30ce\u30a4\u30c9\u306e\u5185\u5074 *\/<\/span>\r\nassume<\/span>(<\/span>a<\/span> ><\/span> 0<\/span>)<\/span>$\r\nassume<\/span>(<\/span>a<\/span> ><\/span> sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>))<\/span>$\r\n\r\n'<\/span>integrate<\/span>(<\/span>\r\n    (<\/span>a<\/span>**<\/span>2<\/span> -<\/span> a<\/span>*<\/span>x<\/span>*<\/span>cos<\/span>(<\/span>phi1<\/span>)<\/span> -<\/span> a<\/span>*<\/span>y<\/span>*<\/span>sin<\/span>(<\/span>phi1<\/span>))<\/span>\r\n    \/<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span> +<\/span> a<\/span>**<\/span>2<\/span> -<\/span> 2*<\/span>a<\/span>*<\/span>x<\/span>*<\/span>cos<\/span>(<\/span>phi1<\/span>)<\/span>-<\/span>2*<\/span>a<\/span>*<\/span>y<\/span>*<\/span>sin<\/span>(<\/span>phi1<\/span>))<\/span>, \r\n    phi1<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>)<\/span> =<\/span>\r\n integrate<\/span>(<\/span>\r\n    (<\/span>a<\/span>**<\/span>2<\/span> -<\/span> a<\/span>*<\/span>x<\/span>*<\/span>cos<\/span>(<\/span>phi1<\/span>)<\/span> -<\/span> a<\/span>*<\/span>y<\/span>*<\/span>sin<\/span>(<\/span>phi1<\/span>))<\/span>\r\n    \/<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span> +<\/span> a<\/span>**<\/span>2<\/span> -<\/span> 2*<\/span>a<\/span>*<\/span>x<\/span>*<\/span>cos<\/span>(<\/span>phi1<\/span>)<\/span>-<\/span>2*<\/span>a<\/span>*<\/span>y<\/span>*<\/span>sin<\/span>(<\/span>phi1<\/span>))<\/span>, \r\n    phi1<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u001bX          2    2\r\n         y  + x\r\nIs ------------------- - 1 positive, negative or zero?\r\n         2  2    2  2\r\n   sqrt(a  y  + a  x )\r\n\u001b\\          2    2\r\n         y  + x\r\nIs ------------------- - 1 positive, negative or zero?\r\n         2  2    2  2\r\n   sqrt(a  y  + a  x )\r\nnegative;\r\n\r\n<\/pre>\n<\/div>\n<\/div>\n
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Out[4]:<\/div>\n
\\[\\tag{${\\it \\%o}_{10}$}\\int_{0}^{2\\,\\pi}{\\frac{-a\\,\\sin \\varphi_{1}\\,y-a\\,\\cos \\varphi_{1}\\,x+a^2}{y^2-2\\,a\\,\\sin \\varphi_{1}\\,y+x^2-2\\,a\\,\\cos \\varphi_{1}\\,x+a^2}\\;d\\varphi_{1}}=2\\,\\pi\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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\/* \u5909\u6570\u306b\u3064\u3044\u3066 assume() \u3057\u305f\u3053\u3068\u3092\u7121\u304b\u3063\u305f\u3053\u3068\u306b\u3057\u307e\u3059\u3002*\/<\/span>\r\nfacts<\/span>(<\/span>a<\/span>)<\/span>$\r\nforget<\/span>(<\/span>%<\/span>)<\/span>$\r\nfacts<\/span>(<\/span>x<\/span>)<\/span>$\r\nforget<\/span>(<\/span>%<\/span>)<\/span>$\r\n\r\n\/* \u30bd\u30ec\u30ce\u30a4\u30c9\u306e\u5916\u5074 *\/<\/span>\r\nassume<\/span>(<\/span>a<\/span> ><\/span> 0<\/span>)<\/span>$\r\nassume<\/span>(<\/span>a<\/span> <<\/span> sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>))<\/span>$\r\n\r\n'<\/span>integrate<\/span>(<\/span>\r\n    (<\/span>a<\/span>**<\/span>2<\/span> -<\/span> a<\/span>*<\/span>x<\/span>*<\/span>cos<\/span>(<\/span>phi1<\/span>)<\/span> -<\/span> a<\/span>*<\/span>y<\/span>*<\/span>sin<\/span>(<\/span>phi1<\/span>))<\/span>\r\n    \/<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span> +<\/span> a<\/span>**<\/span>2<\/span> -<\/span> 2*<\/span>a<\/span>*<\/span>x<\/span>*<\/span>cos<\/span>(<\/span>phi1<\/span>)<\/span>-<\/span>2*<\/span>a<\/span>*<\/span>y<\/span>*<\/span>sin<\/span>(<\/span>phi1<\/span>))<\/span>, \r\n    phi1<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>)<\/span> =<\/span>\r\n integrate<\/span>(<\/span>\r\n    (<\/span>a<\/span>**<\/span>2<\/span> -<\/span> a<\/span>*<\/span>x<\/span>*<\/span>cos<\/span>(<\/span>phi1<\/span>)<\/span> -<\/span> a<\/span>*<\/span>y<\/span>*<\/span>sin<\/span>(<\/span>phi1<\/span>))<\/span>\r\n    \/<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span> +<\/span> a<\/span>**<\/span>2<\/span> -<\/span> 2*<\/span>a<\/span>*<\/span>x<\/span>*<\/span>cos<\/span>(<\/span>phi1<\/span>)<\/span>-<\/span>2*<\/span>a<\/span>*<\/span>y<\/span>*<\/span>sin<\/span>(<\/span>phi1<\/span>))<\/span>, \r\n    phi1<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u001bX          2    2\r\n         y  + x\r\nIs ------------------- - 1 positive, negative or zero?\r\n         2  2    2  2\r\n   sqrt(a  y  + a  x )\r\n\u001b\\          2    2\r\n         y  + x\r\nIs ------------------- - 1 positive, negative or zero?\r\n         2  2    2  2\r\n   sqrt(a  y  + a  x )\r\npositive;\r\n\r\n<\/pre>\n<\/div>\n<\/div>\n
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Out[5]:<\/div>\n
\\[\\tag{${\\it \\%o}_{17}$}\\int_{0}^{2\\,\\pi}{\\frac{-a\\,\\sin \\varphi_{1}\\,y-a\\,\\cos \\varphi_{1}\\,x+a^2}{y^2-2\\,a\\,\\sin \\varphi_{1}\\,y+x^2-2\\,a\\,\\cos \\varphi_{1}\\,x+a^2}\\;d\\varphi_{1}}=0\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":33,"featured_media":0,"parent":2687,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-2749","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t