{"id":2847,"date":"2022-04-01T17:17:03","date_gmt":"2022-04-01T08:17:03","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=2847"},"modified":"2023-03-14T16:54:11","modified_gmt":"2023-03-14T07:54:11","slug":"%e3%83%99%e3%82%af%e3%83%88%e3%83%ab%e3%81%ae%e3%82%b9%e3%82%ab%e3%83%a9%e3%83%bc%e4%b8%89%e9%87%8d%e7%a9%8d%e3%81%a8%e8%a1%8c%e5%88%97%e5%bc%8f","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/2847\/","title":{"rendered":"\u30d9\u30af\u30c8\u30eb\u306e\u30b9\u30ab\u30e9\u30fc\u4e09\u91cd\u7a4d\u3068\u884c\u5217\u5f0f"},"content":{"rendered":"

\u30d9\u30af\u30c8\u30eb\u306e\u30b9\u30ab\u30e9\u30fc\u4e09\u91cd\u7a4d\u306f\uff0c3\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206\u3092\u4e26\u3079\u305f $3\\times 3$ \u884c\u5217\u306e\u884c\u5217\u5f0f\u3068\u7b49\u3057\u3044\u3053\u3068\u3092 Maxima-Jupyter \u3067\u78ba\u8a8d\u3002\u5fae\u5c0f\u4f53\u7a4d\u8981\u7d20\u3068\u30e4\u30b3\u30d3\u30a2\u30f3\u306e\u8aac\u660e\u306e\u524d\u6e96\u5099\u7528\u306b\u3002<\/p>\n

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\u30d9\u30af\u30c8\u30eb\u306e\u30b9\u30ab\u30e9\u30fc\u4e09\u91cd\u7a4d<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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\u30d9\u30af\u30c8\u30eb\u306e\u5916\u7a4d<\/h4>\n

\u30d9\u30af\u30c8\u30eb\u306e\u5916\u7a4d\u3092\u8a08\u7b97\u3059\u308b\u95a2\u6570 cross()<\/code> \u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\uff0c\u81ea\u5206\u3067\u5b9a\u7fa9\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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cross<\/span>(<\/span>u<\/span>, v<\/span>)<\/span>:=<\/span>\r\n           [<\/span>u<\/span>[<\/span>2]<\/span>*<\/span>v<\/span>[<\/span>3]<\/span> -<\/span> u<\/span>[<\/span>3]<\/span>*<\/span>v<\/span>[<\/span>2]<\/span>,\r\n            u<\/span>[<\/span>3]<\/span>*<\/span>v<\/span>[<\/span>1]<\/span> -<\/span> u<\/span>[<\/span>1]<\/span>*<\/span>v<\/span>[<\/span>3]<\/span>,\r\n            u<\/span>[<\/span>1]<\/span>*<\/span>v<\/span>[<\/span>2]<\/span> -<\/span> u<\/span>[<\/span>2]<\/span>*<\/span>v<\/span>[<\/span>1]]<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[1]:<\/div>\n
\\[\\tag{${\\it \\%o}_{1}$}{\\it cross}\\left(u , v\\right):=\\left[ u_{2}\\,v_{3}-u_{3}\\,v_{2} , u_{3}\\,v_{1}-u_{1}\\,v_{3} , u_{1}\\,v_{2}-u_{2}\\,v_{1} \\right] \\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30b9\u30ab\u30e9\u30fc\u4e09\u91cd\u7a4d<\/h4>\n
$$\\boldsymbol{a} \\cdot (\\boldsymbol{b}\\times\\boldsymbol{c})$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[2]:<\/div>\n
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a<\/span>:<\/span> [<\/span>a1<\/span>, a2<\/span>, a3<\/span>]<\/span>;\r\nb<\/span>:<\/span> [<\/span>b1<\/span>, b2<\/span>, b3<\/span>]<\/span>;\r\nc<\/span>:<\/span> [<\/span>c1<\/span>, c2<\/span>, c3<\/span>]<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[2]:<\/div>\n
\\[\\tag{${\\it \\%o}_{2}$}\\left[ a_{1} , a_{2} , a_{3} \\right] \\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{3}$}\\left[ b_{1} , b_{2} , b_{3} \\right] \\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{4}$}\\left[ c_{1} , c_{2} , c_{3} \\right] \\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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s3juseki<\/span>:<\/span> a<\/span> .<\/span> cross<\/span>(<\/span>b<\/span>, c<\/span>)<\/span>, expand<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[3]:<\/div>\n
\\[\\tag{${\\it \\%o}_{5}$}a_{1}\\,b_{2}\\,c_{3}-a_{2}\\,b_{1}\\,c_{3}-a_{1}\\,b_{3}\\,c_{2}+a_{3}\\,b_{1}\\,c_{2}+a_{2}\\,b_{3}\\,c_{1}-a_{3}\\,b_{2}\\,c_{1}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u884c\u5217\u5f0f<\/h3>\n
3\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206\u3092\u4e26\u3079\u305f\u884c\u5217 $V$ \u306e\u884c\u5217\u5f0f<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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V<\/span>:<\/span> matrix<\/span>(<\/span>a<\/span>, b<\/span>, c<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[4]:<\/div>\n
\\[\\tag{${\\it \\%o}_{6}$}\\begin{pmatrix}a_{1} & a_{2} & a_{3} \\\\ b_{1} & b_{2} & b_{3} \\\\ c_{1} & c_{2} & c_{3} \\\\ \\end{pmatrix}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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det<\/span>:<\/span> determinant<\/span>(<\/span>V<\/span>)<\/span>, expand<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[5]:<\/div>\n
\\[\\tag{${\\it \\%o}_{7}$}a_{1}\\,b_{2}\\,c_{3}-a_{2}\\,b_{1}\\,c_{3}-a_{1}\\,b_{3}\\,c_{2}+a_{3}\\,b_{1}\\,c_{2}+a_{2}\\,b_{3}\\,c_{1}-a_{3}\\,b_{2}\\,c_{1}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30b9\u30ab\u30e9\u30fc\u4e09\u91cd\u7a4d\u3068\u884c\u5217\u5f0f\u304c\u7b49\u3057\u3044\u3053\u3068<\/h3>\n
$\\boldsymbol{a} \\cdot (\\boldsymbol{b}\\times\\boldsymbol{c}) = \\det A$ \u3067\u3042\u308b\u3053\u3068\u306e\u78ba\u8a8d\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[6]:<\/div>\n
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is<\/span>(<\/span>equal<\/span>(<\/span>s3juseki<\/span>, det<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[6]:<\/div>\n
\\[\\tag{${\\it \\%o}_{8}$}\\mathbf{true}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u8ee2\u7f6e\u884c\u5217\u306e\u884c\u5217\u5f0f<\/h3>\n
$\\det V = \\det {}^{t}V $ \uff08$V$ \u306e\u884c\u5217\u5f0f\u3068 $V$ \u306e\u8ee2\u7f6e\u884c\u5217 ${}^{t} V$ \u306e\u884c\u5217\u5f0f\u306f\u7b49\u3057\u3044\u3053\u3068\uff09\u306e\u78ba\u8a8d\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[7]:<\/div>\n
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tV<\/span>:<\/span> transpose<\/span>(<\/span>V<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[7]:<\/div>\n
\\[\\tag{${\\it \\%o}_{9}$}\\begin{pmatrix}a_{1} & b_{1} & c_{1} \\\\ a_{2} & b_{2} & c_{2} \\\\ a_{3} & b_{3} & c_{3} \\\\ \\end{pmatrix}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[8]:<\/div>\n
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is<\/span>(<\/span>equal<\/span>(<\/span>determinant<\/span>(<\/span>V<\/span>)<\/span>, determinant<\/span>(<\/span>tV<\/span>)))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[8]:<\/div>\n
\\[\\tag{${\\it \\%o}_{10}$}\\mathbf{true}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
\u30d9\u30af\u30c8\u30eb\u306e\u30b9\u30ab\u30e9\u30fc\u4e09\u91cd\u7a4d\u306f\uff0c3\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6210\u5206\u3092\u4e26\u3079\u305f $3\\times 3$ \u884c\u5217\u306e\u884c\u5217\u5f0f\u3068\u7b49\u3057\u3044\u3053\u3068\u3092 Maxima-Jupyter \u3067\u78ba\u8a8d\u3002\u5fae\u5c0f\u4f53\u7a4d\u8981\u7d20\u3068\u30e4\u30b3\u30d3\u30a2\u30f3\u306e\u8aac\u660e\u306e\u524d\u6e96\u5099\u7528\u306b\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":[14,21],"tags":[],"class_list":["post-2847","post","type-post","status-publish","format-standard","hentry","category-maxima","category-21","nodate","item-wrap"],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\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