{"id":9510,"date":"2024-11-13T22:00:31","date_gmt":"2024-11-13T13:00:31","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=9510"},"modified":"2024-11-14T10:08:24","modified_gmt":"2024-11-14T01:08:24","slug":"%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e8%a7%a3%e3%81%8f","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e3%82%b3%e3%83%b3%e3%83%94%e3%83%a5%e3%83%bc%e3%82%bf%e6%bc%94%e7%bf%92\/sympy-%e6%bc%94%e7%bf%92\/%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%82%92%e8%a7%a3%e3%81%8f\/","title":{"rendered":"2. SymPy \u3067\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f"},"content":{"rendered":"
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SymPy \u3067\u65b9\u7a0b\u5f0f\uff08\u7b49\u5f0f\uff09\u3092\u5b9a\u7fa9\u3057\uff0c\uff08\u4e3b\u306b\u4ee3\u6570\uff09\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3002\u95a2\u9023\u3057\u3066\uff0cPython \u306e\u30c7\u30fc\u30bf\u578b\u3067\u3042\u308b\u30bf\u30d7\u30eb (tuple)<\/strong> \u3068\u8f9e\u66f8 (dict)<\/strong> \u306b\u3064\u3044\u3066\u7c21\u5358\u306b\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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SymPy \u306e import<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[1]:<\/div>\n
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from<\/span> sympy.abc<\/span> import<\/span> *<\/span>\r\nfrom<\/span> sympy<\/span> import<\/span> *<\/span>\r\n\r\ninit_printing<\/span>()<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u65b9\u7a0b\u5f0f<\/h3>\n
SymPy \u306f\uff0c\u5f0f\u306e\u8a08\u7b97\u3060\u3051\u3067\u306a\u304f\uff0c\u4ee3\u6570\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4f8b\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n
$x^2 + 2 x – 2 = 0$ \u3092 $x$ \u306b\u3064\u3044\u3066\u89e3\u304d\u307e\u3059\u3002<\/p>\n
\u65b9\u7a0b\u5f0f\u306e\u5b9a\u7fa9 Eq()<\/code><\/h4>\n
\u65b9\u7a0b\u5f0f\u3068\u306f\uff0c\u672a\u77e5\u5909\u6570\u3092\u542b\u3080\u7b49\u5f0f\u306e\u3053\u3068\u3067\u3059\u3002<\/p>\n
\u65b9\u7a0b\u5f0f\u306f\u7b49\u5f0f\u3068\u540c\u3058\u304f Eq(\u5de6\u8fba, \u53f3\u8fba)<\/code> \u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\u3002\uff08=<\/code> \u306f SymPy \u3067\u306f\u4ee3\u5165\u3092\u8868\u3057\u307e\u3059\u3002\uff09<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[2]:<\/div>\n
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eq<\/span> =<\/span> Eq<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> 2<\/span>*<\/span>x<\/span> -<\/span> 2<\/span>,<\/span> 0<\/span>)<\/span>\r\neq<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[2]:<\/div>\n
$\\displaystyle x^{2} + 2 x – 2 = 0$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u65b9\u7a0b\u5f0f\u306e\u5de6\u8fba .lhs<\/code>\uff0c\u53f3\u8fba .rhs<\/code><\/h5>\n
\u65b9\u7a0b\u5f0f eq<\/code> \u306e\u5de6\u8fba\u306f eq.lhs<\/code> (left-hans-side)\uff0c\u53f3\u8fba\u306f eq.rhs<\/code> (right-hand-side) \u306e\u3088\u3046\u306b\u3057\u3066\u53d6\u308a\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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eq<\/span>.<\/span>lhs<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[3]:<\/div>\n
$\\displaystyle x^{2} + 2 x – 2$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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eq<\/span>.<\/span>rhs<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[4]:<\/div>\n
$\\displaystyle 0$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f solve()<\/code><\/h4>\n
\u65b9\u7a0b\u5f0f\u3092\u672a\u77e5\u5909\u6570\u306b\u3064\u3044\u3066\u89e3\u304f\u66f8\u5f0f\u306f solve(\u65b9\u7a0b\u5f0f, \u672a\u77e5\u5909\u6570)<\/code> \u3067\u3059\u3002<\/p>\n
\u305f\u3068\u3048\u3070\uff0c\u65b9\u7a0b\u5f0f eq<\/code> \u3092 x<\/code> \u306b\u3064\u3044\u3066\u89e3\u304f\u5834\u5408\u306f solve(eq, x)<\/code>\uff1a<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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solve<\/span>(<\/span>eq<\/span>,<\/span> x<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[5]:<\/div>\n
$\\displaystyle \\left[ -1 + \\sqrt{3}, \\ – \\sqrt{3} – 1\\right]$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u65b9\u7a0b\u5f0f\u304c \u5de6\u8fba = 0<\/code> \u306e\u5f62\uff08\u3064\u307e\u308a\u53f3\u8fba\u304c\u30bc\u30ed\uff09\u306b\u306a\u3063\u3066\u3044\u308b\u5834\u5408\u306f\uff0csolve(\u65b9\u7a0b\u5f0f\u306e\u5de6\u8fba, \u672a\u77e5\u5909\u6570)<\/code> \u3068\u3057\u3066\u3082\u540c\u3058\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[6]:<\/div>\n
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solve<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> 2<\/span>*<\/span>x<\/span> -<\/span> 2<\/span>,<\/span> x<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[6]:<\/div>\n
$\\displaystyle \\left[ -1 + \\sqrt{3}, \\ – \\sqrt{3} – 1\\right]$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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3 \u6b21\u65b9\u7a0b\u5f0f $x^3 – 8 = 0$ \u3092\u89e3\u304d\u307e\u3059\u3002solve(eq, x)<\/code> \u306e\u5834\u5408\u306e x<\/code> \u306f\u7701\u7565\u3057\u3066 solve(eq)<\/code> \u3068\u66f8\u304f\u3053\u3068\u3082\u3067\u304d\u308b\u3088\u3046\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[7]:<\/div>\n
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sols<\/span> =<\/span> solve<\/span>(<\/span>x<\/span>**<\/span>3<\/span> -<\/span> 8<\/span>)<\/span>\r\nsols<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[7]:<\/div>\n
$\\displaystyle \\left[ 2, \\ -1 – \\sqrt{3} i, \\ -1 + \\sqrt{3} i\\right]$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u89e3\u304c\u8907\u6570\u500b\u3042\u308b\u5834\u5408\u306f\uff0csolve()<\/code> \u306f\u89e3\u306e\u30ea\u30b9\u30c8\u3092\u8fd4\u3057\u307e\u3059\u3002<\/p>\n
\u5ff5\u306e\u305f\u3081\uff0c3\u756a\u76ee\u306e\u7b54\u3048\uff08Python \u306f\u30bc\u30ed\u304b\u3089\u306f\u3058\u307e\u308b\u3053\u3068\u306b\u6ce8\u610f\uff09\u30923\u4e57\u3057\u3066\u5c55\u958b\u3059\u308b\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[8]:<\/div>\n
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sols<\/span>[<\/span>2<\/span>]<\/span>**<\/span>3<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[8]:<\/div>\n
$\\displaystyle \\left(-1 + \\sqrt{3} i\\right)^{3}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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expand()<\/code> \u3067\u304b\u3063\u3053\u3092\u5c55\u958b\u3057\u3066\u8a08\u7b97\u3055\u305b\u308b\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[9]:<\/div>\n
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expand<\/span>(<\/span>_<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[9]:<\/div>\n
$\\displaystyle 8$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u9023\u7acb\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f solve([], [])<\/code><\/h4>\n
\u9023\u7acb\u65b9\u7a0b\u5f0f\u3092\u89e3\u304f\u969b\u306f\uff0c\u65b9\u7a0b\u5f0f\u3068\u5909\u6570\u3092\u30ea\u30b9\u30c8\u306b\u3057\u3066 solve()<\/code> \u306b\u5165\u308c\u307e\u3059\u3002<\/p>\n
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solve<\/span>([<\/span>eq1<\/span>,<\/span> eq2<\/span>,<\/span> ...<\/span>,<\/span> eqn<\/span>],<\/span> [<\/span>x1<\/span>,<\/span> x2<\/span>,<\/span> ...<\/span>,<\/span> xn<\/span>])<\/span>\r\n<\/pre>\n<\/div>\n
\u4f8b\u3068\u3057\u3066
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\nx^2 + y^2 &=& 5 \\\\
\nx + y &=& 1
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\u3092 $x, y$ \u306b\u3064\u3044\u3066\u89e3\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[10]:<\/div>\n
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eq1<\/span> =<\/span> Eq<\/span>(<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span>,<\/span> 5<\/span>)<\/span>\r\neq2<\/span> =<\/span> Eq<\/span>(<\/span>x<\/span> +<\/span> y<\/span>,<\/span> 1<\/span>)<\/span>\r\n\r\ndisplay<\/span>(<\/span>eq1<\/span>,<\/span> eq2<\/span>)<\/span>\r\nsolve<\/span>([<\/span>eq1<\/span>,<\/span> eq2<\/span>],<\/span> [<\/span>x<\/span>,<\/span> y<\/span>])<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$\\displaystyle x^{2} + y^{2} = 5$<\/div>\n<\/div>\n
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$\\displaystyle x + y = 1$<\/div>\n<\/div>\n
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Out[10]:<\/div>\n
$\\displaystyle \\left[ \\left( -1, \\ 2\\right), \\ \\left( 2, \\ -1\\right)\\right]$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u65b9\u7a0b\u5f0f\u306e\u53f3\u8fba\u3092\u79fb\u9805\u3057\u3066<\/p>\n
\\begin{eqnarray}
\nx^2 + y^2 -5 &=&0 \\\\
\nx + y -1 &=&0
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\u306e\u5f62\u306b\u3059\u308c\u3070\uff0c\u5404\u65b9\u7a0b\u5f0f\u306e\u5de6\u8fba\u306e\u307f\u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3044\u3066\u3082\u3088\u3044\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[11]:<\/div>\n
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sols12<\/span> =<\/span> solve<\/span>([<\/span>x<\/span>**<\/span>2<\/span> +<\/span> y<\/span>**<\/span>2<\/span> -<\/span> 5<\/span>,<\/span> x<\/span> +<\/span> y<\/span> -<\/span> 1<\/span>],<\/span> [<\/span>x<\/span>,<\/span> y<\/span>])<\/span>\r\nsols12<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[11]:<\/div>\n
$\\displaystyle \\left[ \\left( -1, \\ 2\\right), \\ \\left( 2, \\ -1\\right)\\right]$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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2\u7d44\u306e\u89e3\u304c\u3042\u308b\u5834\u5408\uff0csolve()<\/code> \u306f\u89e3 $(x, y)$ \u306e\u7d44\u3092\u30ea\u30b9\u30c8\u3067\u8fd4\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[12]:<\/div>\n
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type<\/span>(<\/span>sols12<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[12]:<\/div>\n
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list<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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display()<\/code> \u306b\u3088\u308b\u8868\u793a<\/h4>\n
\u4e0a\u306e\u30b3\u30fc\u30c9\u3067\u306f\u78ba\u8a8d\u306e\u610f\u5473\u3092\u8fbc\u3081\u3066 display()<\/code> \u3067\u65b9\u7a0b\u5f0f\u3092\u8868\u793a\u3055\u305b\u3066\u3044\u307e\u3059\u3002<\/p>\n
print()<\/code> \u306b\u3088\u308b\u8868\u793a\u3068 display()<\/code> \u306b\u3088\u308b\u8868\u793a\u3092\u6bd4\u8f03\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002display()<\/code> \u3067\u8868\u793a\u3055\u305b\u305f\u307b\u3046\u304c\uff0c\u7dba\u9e97\u306b\u5f62\u304c\u6574\u3048\u3089\u308c\u3066\u8868\u793a\u3055\u308c\u308b\u306e\u3067\uff0c\u78ba\u8a8d\u3057\u3084\u3059\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[13]:<\/div>\n
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print<\/span>(<\/span>eq1<\/span>)<\/span>\r\ndisplay<\/span>(<\/span>eq1<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Eq(x**2 + y**2, 5)\r\n<\/pre>\n<\/div>\n<\/div>\n
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$\\displaystyle x^{2} + y^{2} = 5$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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display()<\/code> \u3092\u4f7f\u308f\u306a\u304f\u3066\u3082\uff0ceq1<\/code> \u3068\u66f8\u3051\u3070\u8868\u793a\u3055\u308c\u307e\u3059\u304c\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b1\u3064\u306e\u30bb\u30eb\u5185\u306b\u8907\u6570\u884c\u66f8\u304f\u3068\uff0c\u6700\u5f8c\u306e\u884c\u3057\u304b\u8868\u793a\u3055\u308c\u307e\u305b\u3093\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[14]:<\/div>\n
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eq1<\/span>\r\neq2<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[14]:<\/div>\n
$\\displaystyle x + y = 1$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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display()<\/code> \u3092\u4f7f\u3046\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[15]:<\/div>\n
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display<\/span>(<\/span>eq1<\/span>)<\/span>\r\ndisplay<\/span>(<\/span>eq2<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$\\displaystyle x^{2} + y^{2} = 5$<\/div>\n<\/div>\n
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$\\displaystyle x + y = 1$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30bf\u30d7\u30eb (tuple)\uff1aPython \u306e\u30c7\u30fc\u30bf\u578b<\/h4>\n
\u89e3\u306e\u30ea\u30b9\u30c8 sols12<\/code> \u306e\u5404\u8981\u7d20\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b ( )<\/code> \u306e\u4e2d\u306b\u8907\u6570\u306e\uff08\u4eca\u306e\u5834\u5408\u306f2\u500b\u306e\uff09\u8981\u7d20\u304c\u30ab\u30f3\u30de (,<\/code>) \u3067\u533a\u5207\u3089\u308c\u3066\u4e26\u3093\u3067\u3044\u307e\u3059\u3002<\/p>\n
\u30ea\u30b9\u30c8\u3068\u4f3c\u3066\u3044\u307e\u3059\u304c\uff0c[ ]<\/code> \u306e\u4e2d\u306b\u8981\u7d20\u304c\u4e26\u3076\u30ea\u30b9\u30c8\u3068\u9055\u3044\uff0c( )<\/code> \u306e\u4e2d\u306b\u8981\u7d20\u304c\u4e26\u3076\u30c7\u30fc\u30bf\u578b\u3092\u300c\u30bf\u30d7\u30eb<\/strong> (tuple<\/strong>)\u300d\u3068\u547c\u3073\u307e\u3059\u3002\uff08( )<\/code> \u306a\u3057\u3067\u3082\u30bf\u30d7\u30eb\u3002\uff09<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[16]:<\/div>\n
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for<\/span> sol<\/span> in<\/span> sols12<\/span>:<\/span>\r\n    print<\/span>(<\/span>sol<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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(-1, 2)\r\n(2, -1)\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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type()<\/code> \u3067\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[17]:<\/div>\n
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type<\/span>(<\/span>sols12<\/span>[<\/span>0<\/span>]),<\/span> type<\/span>(<\/span>sols12<\/span>[<\/span>1<\/span>])<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[17]:<\/div>\n
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(tuple, tuple)<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u53c2\u8003\uff1a\u30bf\u30d7\u30eb (tuple) \u3068 \u30ea\u30b9\u30c8 (list) \u306e\u9055\u3044<\/h5>\n
\u30ea\u30b9\u30c8\u3068\u306f\u7570\u306a\u308a\uff0c\u30bf\u30d7\u30eb\u306f\u5909\u66f4\u304c\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n
\u30ea\u30b9\u30c8\u306e\u5834\u5408\u306f\uff0c\u4f8b\u3048\u3070 lista<\/code> \u306e2\u756a\u76ee\u306e\u8981\u7d20 lista[1]<\/code> \u306e\u5024\u3092\u5225\u306e\u5024\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[18]:<\/div>\n
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# \u30ea\u30b9\u30c8\u306e\u5b9a\u7fa9<\/span>\r\n\r\nlista<\/span> =<\/span> [<\/span>1<\/span>,<\/span> 2<\/span>,<\/span> 3<\/span>]<\/span>\r\ntype<\/span>(<\/span>lista<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[18]:<\/div>\n
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list<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[19]:<\/div>\n
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# lista \u306e2\u756a\u76ee\u306e\u8981\u7d20\u3002Python \u306f\u30bc\u30ed\u59cb\u307e\u308a\u3060\u304b\u3089...<\/span>\r\n\r\nlista<\/span>[<\/span>1<\/span>]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[19]:<\/div>\n
$\\displaystyle 2$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[20]:<\/div>\n
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# lista \u306e2\u756a\u76ee\u306e\u8981\u7d20\u306e\u5024\u3092 20 \u306b\u5909\u66f4<\/span>\r\n\r\nlista<\/span>[<\/span>1<\/span>]<\/span> =<\/span> 20<\/span>\r\nlista<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[20]:<\/div>\n
$\\displaystyle \\left[ 1, \\ 20, \\ 3\\right]$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u3057\u304b\u3057\uff0c\u30bf\u30d7\u30eb\u306e\u5834\u5408\u306f\uff0c\u4f8b\u3048\u3070 tupleb<\/code> \u306e2\u756a\u76ee\u306e\u8981\u7d20 tupleb[1]<\/code> \u306e\u5024\u3092\u5225\u306e\u5024\u306b\u7f6e\u304d\u63db\u3048\u3088\u3046\u3068\u3059\u308b\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[21]:<\/div>\n
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# \u30bf\u30d7\u30eb\u306e\u5b9a\u7fa9<\/span>\r\n\r\ntupleb<\/span> =<\/span> 1<\/span>,<\/span> 2<\/span>,<\/span> 3<\/span>\r\ntype<\/span>(<\/span>tupleb<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[21]:<\/div>\n
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tuple<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[22]:<\/div>\n
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# tupleb \u306e2\u756a\u76ee\u306e\u8981\u7d20\u3002<\/span>\r\n# \u30ea\u30b9\u30c8\u306e\u5834\u5408\u3068\u540c\u3058\u3088\u3046\u306b\u53c2\u7167\u3067\u304d\u308b\u3002<\/span>\r\n\r\ntupleb<\/span>[<\/span>1<\/span>]<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[22]:<\/div>\n
$\\displaystyle 2$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[23]:<\/div>\n
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# tupleb \u306e2\u756a\u76ee\u306e\u8981\u7d20\u306e\u5024\u3092\u5909\u66f4\u3057\u3088\u3046\u3068\u3059\u308b\u3068...<\/span>\r\n\r\ntupleb<\/span>[<\/span>1<\/span>]<\/span> =<\/span> 20<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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---------------------------------------------------------------------------<\/span>\r\nTypeError<\/span>                                 Traceback (most recent call last)\r\n<ipython-input-23-6574e716f335><\/span> in <module><\/span>\r\n      1<\/span> # tupleb \u306e2\u756a\u76ee\u306e\u8981\u7d20\u306e\u5024\u3092\u5909\u66f4\u3057\u3088\u3046\u3068\u3059\u308b\u3068...<\/span>\r\n      2<\/span> \r\n----> 3<\/span> tupleb[<\/span>1<\/span>]<\/span> =<\/span> 20<\/span>\r\n\r\nTypeError<\/span>: 'tuple' object does not support item assignment<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30a8\u30e9\u30fc\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\u8907\u6570\u5909\u6570\u3078\u306e\u4e00\u6642\u7684\u4ee3\u5165<\/h4>\n
.subs()<\/code><\/h5>\n
\u5ff5\u306e\u305f\u3081\uff0csolve()<\/code> \u3067\u5f97\u3089\u308c\u305f\u7b54\u3048\u3092 eq1<\/code> \u306e\u5de6\u8fba eq1.lhs<\/code> \u306b\u4ee3\u5165\u3057\u3066\u78ba\u304b\u306b\u7b54\u3048\u304c $5$ \u306b\u306a\u3063\u3066\u3044\u308b\u304b\uff0c\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n
.subs()<\/code> \u306b\u3088\u308b\u4e00\u6642\u7684\u4ee3\u5165\u306f\u65e2\u306b\u8aac\u660e\u6e08\u307f\u3067\u3059\u304c\uff0c\u8907\u6570\u306e\u5909\u6570\uff08\u4eca\u306e\u5834\u5408\u306f x<\/code> \u3068 y<\/code>\uff09\u306b\u5024 x1, y1<\/code> \u3092\u4e00\u6642\u7684\u306b\u4ee3\u5165\u3059\u308b\u306b\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b<\/p>\n
.subs({x:x1, y:y1})<\/code><\/p>\n
\u307e\u305f\u306f\uff0c<\/p>\n
.subs([(x, x1), (y, y1)])<\/code><\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[24]:<\/div>\n
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print<\/span>(<\/span>'(x, y) ='<\/span>,<\/span> sols12<\/span>[<\/span>0<\/span>])<\/span>\r\n(<\/span>x1<\/span>,<\/span> y1<\/span>)<\/span> =<\/span> sols12<\/span>[<\/span>0<\/span>]<\/span>\r\nprint<\/span>(<\/span>'eq1 \u306e\u5de6\u8fba ='<\/span>,<\/span> eq1<\/span>.<\/span>lhs<\/span>.<\/span>subs<\/span>({<\/span>x<\/span>:<\/span>x1<\/span>,<\/span> y<\/span>:<\/span>y1<\/span>}))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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(x, y) = (-1, 2)\r\neq1 \u306e\u5de6\u8fba = 5\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[25]:<\/div>\n
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print<\/span>(<\/span>'(x, y) ='<\/span>,<\/span> sols12<\/span>[<\/span>0<\/span>])<\/span>\r\n(<\/span>x1<\/span>,<\/span> y1<\/span>)<\/span> =<\/span> sols12<\/span>[<\/span>0<\/span>]<\/span>\r\nprint<\/span>(<\/span>'eq1 \u306e\u5de6\u8fba ='<\/span>,<\/span> eq1<\/span>.<\/span>lhs<\/span>.<\/span>subs<\/span>([(<\/span>x<\/span>,<\/span> x1<\/span>),<\/span> (<\/span>y<\/span>,<\/span> y1<\/span>)]))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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(x, y) = (-1, 2)\r\neq1 \u306e\u5de6\u8fba = 5\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u3082\u30461\u7d44\u306e\u89e3 (2, -1)<\/code> \u306b\u3064\u3044\u3066\u3082\u78ba\u8a8d\u3057\u3066\u307f\u3066\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[\u00a0]:<\/div>\n
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 \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Subs()<\/code><\/h5>\n
\u4e00\u6642\u7684\u306a\u4ee3\u5165\u3092 Subs(expr, variables, values).doit()<\/code> \u3067\u3084\u3063\u3066\u307f\u307e\u3059\u3002<\/p>\n
Subs()<\/code> \u3092\u4f7f\u3046\u5834\u5408\u306f\u5909\u6570\u3092 tuple \u306b\u3067\u304d\u3066<\/p>\n
Subs(expr, (x, y), (x1, y1)).doit()<\/code> \u306e\u3088\u3046\u306b\u66f8\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[26]:<\/div>\n
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print<\/span>(<\/span>'(x, y) ='<\/span>,<\/span> sols12<\/span>[<\/span>0<\/span>])<\/span>\r\nprint<\/span>(<\/span>'eq1 \u306e\u5de6\u8fba ='<\/span>,<\/span> Subs<\/span>(<\/span>eq1<\/span>.<\/span>lhs<\/span>,<\/span> (<\/span>x<\/span>,<\/span> y<\/span>),<\/span> sols12<\/span>[<\/span>0<\/span>])<\/span>.<\/span>doit<\/span>())<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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(x, y) = (-1, 2)\r\neq1 \u306e\u5de6\u8fba = 5\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u3082\u30461\u7d44\u306e\u89e3 (2, -1)<\/code> \u306b\u3064\u3044\u3066\u3082\u78ba\u8a8d\u3057\u3066\u307f\u3066\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[\u00a0]:<\/div>\n
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<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4f8b\u984c\uff1a\u9db4\u4e80\u7b97<\/h4>\n