{"id":6723,"date":"2023-09-28T14:04:10","date_gmt":"2023-09-28T05:04:10","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=6723"},"modified":"2024-09-26T15:21:09","modified_gmt":"2024-09-26T06:21:09","slug":"sympy-%e3%81%a7%e5%be%ae%e5%88%86%e7%a9%8d%e5%88%86%e3%83%bb%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%ae%e8%a7%a3","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\/python-%e3%81%a7%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-%e3%81%a7%e5%be%ae%e5%88%86%e7%a9%8d%e5%88%86%e3%83%bb%e6%96%b9%e7%a8%8b%e5%bc%8f%e3%81%ae%e8%a7%a3\/","title":{"rendered":"SymPy \u3067\u5fae\u5206\u7a4d\u5206\u30fb\u65b9\u7a0b\u5f0f\u306e\u89e3"},"content":{"rendered":"
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<\/div>\n
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Python \u304a\u3088\u3073 SymPy \u306e\u57fa\u672c\u304b\u3089\uff0c\u95a2\u6570\uff0c\u5fae\u5206\u30fb\u7a4d\u5206\uff0c\u65b9\u7a0b\u5f0f\u306e\u89e3\u307e\u3067\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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<\/div>\n
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\u5f18\u5927 JupyterHub \u3067\u306e Python \u306e\u8d77\u52d5<\/h3>\n

\u65b0\u3057\u304f Python \u3067\u8a08\u7b97\u3092\u306f\u3058\u3081\u308b\u3068\u304d\u306f\uff0c\u5f18\u5927 JupyterHub \u306b\u30ed\u30b0\u30a4\u30f3\u5f8c\uff0c\u30e1\u30cb\u30e5\u30fc\u53f3\u7aef\u306e\u300c\u65b0\u898f\u300d\u304b\u3089\u300cPython 3\u300d\u3092\u9078\u629e\u3057\u307e\u3059<\/p>\n

JupyterHub \u3067\u306e\u8a08\u7b97\u306e\u5b9f\u884c\u3068\u884c\u672b\u8a18\u53f7<\/h3>\n
    \n
  1. Python \u3067\u306f\uff0c\u30bb\u30eb\u306b\u5b9f\u884c\u6587\u3092\u66f8\u304d\uff0c<\/li>\n
  2. Shift \u30ad\u30fc\u3092\u62bc\u3057\u306a\u304c\u3089 Enter \u30ad\u30fc\uff08Return \u30ad\u30fc\uff09\u3092\u62bc\u3059\u3068\u5b9f\u884c\u3057\u307e\u3059\u3002<\/li>\n
  3. Shift + Enter \u306e\u304b\u308f\u308a\u306b\uff0c\u30e1\u30cb\u30e5\u30fc\u306e\u300c\u25b6\ufe0e Run\u300d\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u3082\u3088\u3044\u3067\u3059\u3002<\/li>\n
  4. \u884c\u672b\u306b\u30bb\u30df\u30b3\u30ed\u30f3 ;<\/code> \u3092\u5165\u529b\u5f8c\uff0c\u5b9f\u884c\u3059\u308b\u3068\uff0c\u7d50\u679c\u304c\u8868\u793a\u3055\u308c\u307e\u305b\u3093\u3002<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n

    <\/p>\n

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

    \u307e\u305a\u306f\u7c21\u5358\u306a\u304b\u3051\u7b97 123\u00d7456 \u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n

    \n
    \n
    In\u00a0[1]:<\/div>\n
    \n
    \n
    \n
    123<\/span> *<\/span> 456<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[1]:<\/div>\n
    \n
    56088<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    2 \u306e 100 \u4e57 ($2^{100}$) \u306e\u3088\u3046\u306a\u5927\u304d\u3044\u6570\u3067\u3082\uff0c\u53b3\u5bc6\u306a\u7d50\u679c\u3092\u51fa\u529b\u3057\u307e\u3059\u3002\uff08**<\/code> \u306f\u7d2f\u4e57\u3092\u8868\u3057\u307e\u3059\u3002\uff09<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[2]:<\/div>\n
    \n
    \n
    \n
    2<\/span>**<\/span>100<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[2]:<\/div>\n
    \n
    1267650600228229401496703205376<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    float<\/code> \u95a2\u6570\u3092\u4f7f\u3063\u3066\u6d6e\u52d5\u5c0f\u6570\u70b9\u8868\u793a\u3067\u8fd1\u4f3c\u5024\u3092\u51fa\u529b\u3055\u305b\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[3]:<\/div>\n
    \n
    \n
    \n
    float<\/span>(<\/span>2<\/span>**<\/span>100<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[3]:<\/div>\n
    \n
    1.2676506002282294e+30<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    SymPy \u306e import<\/h3>\n
    Python \u672c\u4f53\u306e\u307f\u3067\u3067\u304d\u308b\u3053\u3068\u306f\u9650\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u304b\u3089\u306f\uff0c\u5fae\u5206\u30fb\u7a4d\u5206\u306a\u3069\u306e\u8a18\u53f7\u8a08\u7b97\u3092\u884c\u3046\u305f\u3081\u306e\u30e9\u30a4\u30d6\u30e9\u30ea SymPy \u304c\u5fc5\u8981\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066 import \u3057\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[4]:<\/div>\n
    \n
    \n
    \n
    from<\/span> sympy.abc<\/span> import<\/span> *<\/span>\r\nfrom<\/span> sympy<\/span> import<\/span> *<\/span><\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u8868\u8a18\u306a\u3068\u3099\u306e\u7d04\u675f\u4e8b<\/h3>\n
    Python \u306e\u5b9f\u884c\u306b\u969b\u3057\u3066\uff0c\u3044\u304f\u3064\u304b\u8868\u8a18\u306b\u3064\u3044\u3066\u306e\u7d04\u675f\u4e8b\u304b\u3099\u3042\u308a\u307e\u3059\u3002\u4ee3\u8868\u7684\u306a\u3082\u306e\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n
    \u30b3\u30e1\u30f3\u30c8 (\u5b9f\u884c\u306b\u5f71\u97ff\u3057\u306a\u3044\u6ce8\u91c8) \u3092\u5165\u308c\u305f\u3044\u3068\u304d\u306f\uff0c#<\/code> \u3092\u66f8\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[5]:<\/div>\n
    \n
    \n
    \n
    1<\/span> +<\/span> 2<\/span> +<\/span> 3<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[5]:<\/div>\n
    \n
    6<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[6]:<\/div>\n
    \n
    \n
    \n
    1<\/span> +<\/span> 2<\/span> # + 3<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[6]:<\/div>\n
    \n
    3<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u52a0\u6cd5 +<\/code>\uff0c\u6e1b\u6cd5 -<\/code>\uff0c\u4e57\u6cd5 *<\/code>\uff0c\u9664\u6cd5 \/<\/code> \u306b\u304a\u3051\u308b\u512a\u5148\u9806\u4f4d\u306f\u6570\u5b66\u3068\u540c\u3057\u3099\u3066\u3099\u3059\u3002\u512a\u5148\u3057\u3066\u8a08\u7b97\u3057\u305f\u3044\u7b87\u6240\u306f ( )<\/code> \u3066\u3099 \u56f2\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[7]:<\/div>\n
    \n
    \n
    \n
    1<\/span> +<\/span> 2<\/span> *<\/span> 3<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[7]:<\/div>\n
    \n
    7<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[8]:<\/div>\n
    \n
    \n
    \n
    (<\/span>1<\/span> +<\/span> 2<\/span>)<\/span> *<\/span> 3<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[8]:<\/div>\n
    \n
    9<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u4ee3\u5165<\/h4>\n
    \u5909\u6570\u306b\u5f0f\u3084\u5024\u3092\u4ee3\u5165\u3059\u308b\u3068\u304d\u306f\uff0c\u7b49\u53f7 =<\/code> \u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n
    \u5909\u6570 a<\/code> \u306b $100+3\/21$
    \n\u3092\u4ee3\u5165\u3057\uff0ca<\/code> \u306e\u5024\u3092\u8868\u793a\u3055\u305b\u308b\u4f8b\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[9]:<\/div>\n
    \n
    \n
    \n
    a<\/span> =<\/span> 100<\/span> +<\/span> 3<\/span>\/<\/span>21<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[10]:<\/div>\n
    \n
    \n
    \n
    (<\/span>a<\/span> -<\/span> 100<\/span>)<\/span> *<\/span> 7<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[10]:<\/div>\n
    \n
    0.9999999999999716<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u4e0a\u8a18\u306e\u8a08\u7b97\u3067\u306f\uff0c\u5272\u308a\u7b97 \/<\/code> \u306f\u5b9f\u6570\u306b\u306a\u308a\u307e\u3059\u3002\u6709\u7406\u6570\u3068\u3057\u3066\u5206\u6570\u3092\u3042\u3064\u304b\u3046\u969b\u306f\uff0cSymPy \u306e Rational()<\/code> \u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[11]:<\/div>\n
    \n
    \n
    \n
    a<\/span> =<\/span> 100<\/span> +<\/span> Rational<\/span>(<\/span>3<\/span>,<\/span>21<\/span>)<\/span>\r\na<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[11]:<\/div>\n
    $\\displaystyle \\frac{701}{7}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[12]:<\/div>\n
    \n
    \n
    \n
    (<\/span>a<\/span> -<\/span> 100<\/span>)<\/span> *<\/span> 7<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[12]:<\/div>\n
    $\\displaystyle 1$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u95a2\u6570\u306e\u5b9a\u7fa9<\/h4>\n
    Python \u306e\u8a18\u6cd5\u3067\u95a2\u6570\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002$ f(x) = x^2$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[13]:<\/div>\n
    \n
    \n
    \n
    def<\/span> f<\/span>(<\/span>x<\/span>):<\/span>\r\n    return<\/span> x<\/span>**<\/span>2<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[14]:<\/div>\n
    \n
    \n
    \n
    f<\/span>(<\/span>x<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[14]:<\/div>\n
    $\\displaystyle x^{2}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    $f(4) = 4^2 = 16$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[15]:<\/div>\n
    \n
    \n
    \n
    f<\/span>(<\/span>4<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[15]:<\/div>\n
    \n
    16<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u5b9f\u884c\u7d50\u679c\u306e\u8868\u793a\u30fb\u975e\u8868\u793a<\/h4>\n
    \u4e0a\u306e\u4f8b\u3067\u308f\u304b\u308b\u3088\u3046\u306b\uff0c\u4ee3\u5165\u3084\u95a2\u6570\u306e\u5b9a\u7fa9\u306e\u3068\u304d\u306f\uff0c\u5f0f\u3084\u5909\u6570\u306e\u5024\u304c\u8868\u793a\u3055\u308c\u307e\u305b\u3093\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[16]:<\/div>\n
    \n
    \n
    \n
    eq<\/span> =<\/span> x<\/span>**<\/span>2<\/span> +<\/span> 3<\/span>*<\/span>x<\/span> +<\/span> 2<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u660e\u793a\u7684\u306b\u5909\u6570\u3092 Shift + Enter \u3059\u308c\u3070\u8868\u793a\u3055\u308c\u307e\u3059\u304c\uff0c\u6587\u672b\u306b ;<\/code> \u3092\u3064\u3051\u308b\u3068\u7d50\u679c\u304c\u51fa\u529b\u3055\u308c\u307e\u305b\u3093\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[17]:<\/div>\n
    \n
    \n
    \n
    eq<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[17]:<\/div>\n
    $\\displaystyle x^{2} + 3 x + 2$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[18]:<\/div>\n
    \n
    \n
    \n
    eq<\/span>;<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u524d\u306e\u51fa\u529b\u7d50\u679c\u306e\u53c2\u7167<\/h4>\n
    \u76f4\u524d\u306e\u51fa\u529b\u7d50\u679c\u306f _<\/code> \u3067\u53c2\u7167\u3067\u304d\u307e\u3059\u3002expand()<\/code> \u306f\u5c55\u958b\u3059\u308b\u95a2\u6570\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[19]:<\/div>\n
    \n
    \n
    \n
    expand<\/span>((<\/span>x<\/span> -<\/span> 2<\/span>)<\/span>**<\/span>4<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[19]:<\/div>\n
    $\\displaystyle x^{4} – 8 x^{3} + 24 x^{2} – 32 x + 16$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u76f4\u524d\u306e\u7d50\u679c\u3092 factor()<\/code> \u3067\u56e0\u6570\u5206\u89e3\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[20]:<\/div>\n
    \n
    \n
    \n
    factor<\/span>(<\/span>_<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[20]:<\/div>\n
    $\\displaystyle \\left(x – 2\\right)^{4}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u6570\u306e\u8a08\u7b97\u30fb\u57fa\u672c\u7684\u306a\u95a2\u6570<\/h3>\n
    \u57fa\u672c\u7684\u306a\u56db\u5247\u6f14\u7b97 (+ - * \/<\/code>) \u4ee5\u5916\u306b\u3088\u304f\u4f7f\u308f\u308c\u308b\u6f14\u7b97\u3092\u793a\u3057\u307e\u3059\u3002\u7d2f\u4e57\u306f **<\/code> \u3067\u3057\u305f\u3002<\/p>\n
    $4$ \u306e\u968e\u4e57\u306e\u8a08\u7b97\u3092\u3057\u307e\u3059\u3002$4!=4\u00d73\u00d72\u00d71=24$ \u3067\u3059\u3002SymPy \u3067\u306f\uff0c\u968e\u4e57\u306f factorial()<\/code> \u95a2\u6570\u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[21]:<\/div>\n
    \n
    \n
    \n
    factorial<\/span>(<\/span>4<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[21]:<\/div>\n
    $\\displaystyle 24$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    factorial2()<\/code> \u95a2\u6570\u306f\uff0c\u4e00\u3064\u304a\u304d\u306e\u968e\u4e57\u306e\u8a08\u7b97\u3092\u3057\u307e\u3059\u3002$5!!=5\u00d73\u00d71=15$ \u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[22]:<\/div>\n
    \n
    \n
    \n
    factorial2<\/span>(<\/span>5<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[22]:<\/div>\n
    $\\displaystyle 15$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u7df4\u7fd2 1-1<\/h4>\n
    (\u7df4\u7fd2) 3, 2, 1 \u3067\u3064\u304f\u308b\u6700\u5927\u306e\u6570<\/strong><\/span><\/p>\n
    \u6570\u5b57\u306e 3 \u3068 2 \u3068 1 \u3092 1 \u500b\u305a\u3064\u4f7f\u3063\u305f\u6f14\u7b97\u3067\u3064\u304f\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u6700\u5927\u306e\u6574\u6570\u306f?<\/p>\n
    \u30d2\u30f3\u30c8:<\/strong><\/p>\n
    (1 + 2) \u00d7 3 = 9<\/code> \u3058\u3083\u5168\u7136\u3060\u3081\u3002\u305d\u306e\u307e\u307e\u4e26\u3079\u308b\u3068 321<\/code> \u3067\u3059\u304c\uff0c\u7d2f\u4e57\u3092\u4f7f\u3046\u3068\u3082\u3063\u3068\u5927\u304d\u3044\u6570\u3092\u3064\u304f\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002
    \n$21^3$ \u3068\u304b\uff0c$31^2$ \u3068\u304b\uff0c$2^{31}$ \u3068\u304b…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[\u00a0]:<\/div>\n
    \n
    \n
    \n
     \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[\u00a0]:<\/div>\n
    \n
    \n
    \n
     \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[\u00a0]:<\/div>\n
    \n
    \n
    \n
     \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[\u00a0]:<\/div>\n
    \n
    \n
    \n
     \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u57fa\u672c\u7684\u306a\u5b9a\u6570<\/h4>\n
    SymPy \u306e\u57fa\u672c\u7684\u5b9a\u6570\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066 import \u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n
    \n
    from<\/span> sympy<\/span> import<\/span> I<\/span>,<\/span> pi<\/span>,<\/span> E<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n\n\n\n\n\n\n
    <\/th>\n<\/th>\n<\/th>\n<\/th>\n<\/th>\n<\/tr>\n<\/thead>\n
    \u3000\u5186\u5468\u7387 $\\pi$<\/td>\n\u3000\u7121\u9650\u5927 $\\infty$<\/td>\n\u3000\u81ea\u7136\u5bfe\u6570\u306e\u5e95 $e$<\/td>\n\u3000\u865a\u6570\u5358\u4f4d $i$<\/td>\n<\/tr>\n
    pi<\/code><\/td>\noo<\/code><\/td>\nE<\/code><\/td>\nI<\/code><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
    \u7121\u9650\u5927\u306f\u5c0f\u6587\u5b57\u306e o<\/code>\uff08\u30aa\u30fc\uff09\u30922\u3064\u4e26\u3079\u3066\u66f8\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u7121\u7406\u6570 $e$\uff0c$\\pi$ \u3068\u865a\u6570\u5358\u4f4d $i$ \u3068\u6574\u6570 $\u22121$ \u306e\u9593\u306e\u3059\u3066\u304d\u306a\u95a2\u4fc2\uff0c\u30aa\u30a4\u30e9\u30fc\u306e\u7b49\u5f0f $$e^{i\\pi} +1 = 0$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[23]:<\/div>\n
    \n
    \n
    \n
    E<\/span>**<\/span>(<\/span>I<\/span> *<\/span> pi<\/span>)<\/span> +<\/span> 1<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[23]:<\/div>\n
    $\\displaystyle 0$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u6d6e\u52d5\u5c0f\u6570\u70b9\u3067\u8fd1\u4f3c\u5024\u3092\u8868\u793a\u3059\u308b\u306b\u306f float()<\/code> \u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[24]:<\/div>\n
    \n
    \n
    \n
    pi<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[24]:<\/div>\n
    $\\displaystyle \\pi$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[25]:<\/div>\n
    \n
    \n
    \n
    float<\/span>(<\/span>pi<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[25]:<\/div>\n
    \n
    3.141592653589793<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u57fa\u672c\u7684\u306a\u95a2\u6570<\/h4>\n\n\n\n\n\n\n
    <\/th>\n<\/th>\n<\/th>\n<\/th>\n<\/th>\n<\/th>\n<\/th>\n<\/tr>\n<\/thead>\n
    \u3000\u5e73\u65b9\u6839<\/td>\n\u3000\u6307\u6570\u95a2\u6570<\/td>\n\u3000\u81ea\u7136\u5bfe\u6570<\/td>\n\u3000\u7d76\u5bfe\u5024<\/td>\n\u3000\u4e09\u89d2\u95a2\u6570<\/td>\n\u3000\u9006\u95a2\u6570<\/td>\n\u3000\u53cc\u66f2\u7dda\u95a2\u6570<\/td>\n<\/tr>\n
    sqrt<\/code><\/td>\nexp<\/code><\/td>\nlog<\/code><\/td>\nabs<\/code><\/td>\nsin<\/code>
    \ncos<\/code>
    \ntan<\/code><\/td>\n    		asin<\/code>
    \nacos<\/code>
    \natan<\/code><\/td>\n    		sinh<\/code>
    \ncosh<\/code>
    \ntanh<\/code><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u3046\u3063\u304b\u308a $\\sqrt{x^2} = x$ \u3068\u3057\u306a\u3044\u3088\u3046\u306b\u3002SymPy \u306f\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u306f…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[26]:<\/div>\n
    \n
    \n
    \n
    sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[26]:<\/div>\n
    $\\displaystyle \\sqrt{x^{2}}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    $x$ \u3092\u5b9f\u6570\u3068\u3057\u3066\u3084\u308b\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[27]:<\/div>\n
    \n
    \n
    \n
    x<\/span> =<\/span> Symbol<\/span>(<\/span>'x'<\/span>,<\/span> real<\/span>=<\/span>True<\/span>)<\/span>\r\n\r\nsqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[27]:<\/div>\n
    $\\displaystyle \\left|{x}\\right|$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[28]:<\/div>\n
    \n
    \n
    \n
    # \u5b9f\u6570\u306e\u8a2d\u5b9a\u3092\u521d\u671f\u5316\u3059\u308b<\/span>\r\n\r\nx<\/span> =<\/span> Symbol<\/span>(<\/span>'x'<\/span>)<\/span>\r\n\r\nsqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[28]:<\/div>\n
    $\\displaystyle \\sqrt{x^{2}}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u30d4\u30bf\u30b4\u30e9\u30b9\u306e\u5b9a\u7406\u3092\u307f\u305f\u3059\u6574\u6570\u306e\u4f8b\u3002
    \n$\\sqrt{3^2 + 4^2} = 5$ \u3067\u3059\u306d\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[29]:<\/div>\n
    \n
    \n
    \n
    sqrt<\/span>(<\/span>3<\/span>**<\/span>2<\/span> +<\/span> 4<\/span>**<\/span>2<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[29]:<\/div>\n
    $\\displaystyle 5$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    $e^{\\log x}$ \u3084 $\\log(e^2)$ \u306e\u8a08\u7b97\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[30]:<\/div>\n
    \n
    \n
    \n
    exp<\/span>(<\/span>log<\/span>(<\/span>x<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[30]:<\/div>\n
    $\\displaystyle x$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[31]:<\/div>\n
    \n
    \n
    \n
    log<\/span>(<\/span>E<\/span>**<\/span>2<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[31]:<\/div>\n
    $\\displaystyle 2$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u4e09\u89d2\u95a2\u6570\u306e\u5024\u30fb\u5f15\u6570\u306e\u5358\u4f4d<\/h4>\n
    \u4e09\u89d2\u95a2\u6570\u306e\u5024\u3092\u6570\u5024\u3067\u6c42\u3081\u305f\u3044\u3068\u304d\u306b\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u307e\u3059\u3002<\/p>\n
    $\\displaystyle \\sin \\frac{\\pi}{3}$ \u306e\u5024\u306f…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[32]:<\/div>\n
    \n
    \n
    \n
    sin<\/span>(<\/span>pi<\/span>\/<\/span>3<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[32]:<\/div>\n
    $\\displaystyle \\frac{\\sqrt{3}}{2}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    float()<\/code> \u95a2\u6570\u3092\u4f7f\u3063\u3066\uff0c\u76f4\u524d\u306e\u7d50\u679c\u3092\u6d6e\u52d5\u5c0f\u6570\u70b9\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[33]:<\/div>\n
    \n
    \n
    \n
    float<\/span>(<\/span>_<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[33]:<\/div>\n
    \n
    0.8660254037844386<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u5909\u6570 Pi<\/code> \u306b\u6d6e\u52d5\u5c0f\u6570\u70b9\u8868\u793a\u306e $\\pi$ \u306e\u5024\u3092\u4ee3\u5165\u3057\u307e\u3059\u3002 \u6d6e\u52d5\u5c0f\u6570\u70b9\u8868\u793a\u3067\u6570\u5024\u3092\u5165\u308c\u308b\u3068\uff0c sin()<\/code> \u3082\u6d6e\u52d5\u5c0f\u6570\u70b9\u8868\u793a\u3067\u7b54\u3048\u3092\u8fd4\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[34]:<\/div>\n
    \n
    \n
    \n
    Pi<\/span> =<\/span> float<\/span>(<\/span>pi<\/span>)<\/span>\r\nsin<\/span>(<\/span>Pi<\/span>\/<\/span>3<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[34]:<\/div>\n
    $\\displaystyle 0.866025403784439$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u4e09\u89d2\u95a2\u6570\u306e\u5f15\u6570\u306f\u30e9\u30b8\u30a2\u30f3\u3067\u3059\u3002\u5ea6\u3092\u4f7f\u3063\u3066\u6c42\u3081\u305f\u3044\u3068\u304d\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u307e\u3059\u3002<\/p>\n
    \u5ea6\u3092\u30e9\u30b8\u30a2\u30f3\u306b\u5909\u63db\u3059\u308b\u95a2\u6570 degrad<\/code> \u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[35]:<\/div>\n
    \n
    \n
    \n
    def<\/span> degrad<\/span>(<\/span>x<\/span>):<\/span>\r\n    return<\/span> Rational<\/span>(<\/span>x<\/span>,<\/span> 180<\/span>)<\/span>*<\/span>pi<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    $\\sin 60^{\\circ}$ \u3092\u6c42\u3081\u308b\u5834\u5408\u306f degrad(60)<\/code> \u3092\u5f15\u6570\u306b\u3057\u3066 sin<\/code> \u306e\u5024\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[36]:<\/div>\n
    \n
    \n
    \n
    sin<\/span>(<\/span>degrad<\/span>(<\/span>60<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[36]:<\/div>\n
    $\\displaystyle \\frac{\\sqrt{3}}{2}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u7df4\u7fd2 1-2<\/h4>\n
    \uff08\u7df4\u7fd2\uff09\u5c4b\u6839\u52fe\u914d<\/strong><\/span><\/p>\n
    \u5bb6\u306e\u5c4b\u6839\u306e\u52fe\u914d\u306f\u89d2\u5ea6\u3067\u306f\u306a\u304f\uff0c\u4f1d\u7d71\u7684\u306b 3 \u5bf8\u52fe\u914d\uff0c4 \u5bf8\u52fe\u914d\u306e\u3088\u3046\u306b\u6c34\u5e73\u65b9\u5411\u306b 1 \u5c3a(10 \u5bf8)\u306b\u5bfe\u3057\u3066\u5782\u76f4\u65b9\u5411\u306b\u4f55\u5bf8\u7acb\u3061\u4e0a\u304c\u308b\u304b\u3067\u793a\u3057\u307e\u3059\u3002<\/p>\n
    \u56f3\u306e\u30ed\u30b0\u30cf\u30a6\u30b9\u306e\u5c4b\u6839\u306f 8 \u5bf8\u52fe\u914d\u3067\u3059\u3002
    \n\u50be\u659c\u89d2\u5ea6\u306b\u3059\u308b\u3068\u4f55\u5ea6\u3067\u3059\u304b?<\/p>\n
    <\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u30e9\u30b8\u30a2\u30f3\u3092\u5ea6\u306b\u5909\u63db\u3059\u308b\u95a2\u6570\u3092\u4f5c\u3063\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[37]:<\/div>\n
    \n
    \n
    \n
    def<\/span> raddeg<\/span>(<\/span>x<\/span>):<\/span>\r\n    return<\/span> float<\/span>(<\/span>x<\/span> *<\/span> 180<\/span>\/<\/span>pi<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[38]:<\/div>\n
    \n
    \n
    \n
    # 8\u5bf8\u52fe\u914d\u3068\u306a\u308b\u89d2\u5ea6\u3092\u6c42\u3081\u308b<\/span>\r\n\r\natan<\/span>(<\/span>0.8<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[38]:<\/div>\n
    $\\displaystyle 0.674740942223553$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[39]:<\/div>\n
    \n
    \n
    \n
    # \u5ea6\u306b\u306a\u304a\u3059<\/span>\r\n\r\nraddeg<\/span>(<\/span>_<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[39]:<\/div>\n
    \n
    38.659808254090095<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u4ee5\u4e0b\u306b\u5404\u5bf8\u52fe\u914d\u306e\u89d2\u5ea6\u306e\u8868\u304c\u3042\u308a\u307e\u3059\u300210 \u5bf8\u52fe\u914d\uff08\u77e9\u52fe\u914d\u3000\u304b\u306d\u3053\u3046\u3070\u3044\uff09\u307e\u3067\u8868
    \n\u3092\u5b8c\u6210\u3055\u305b\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n\n\n\n\n
    \u52fe\u914d<\/th>\n1\u5bf8\u52fe\u914d<\/th>\n2\u5bf8\u52fe\u914d<\/th>\n3\u5bf8\u52fe\u914d<\/th>\n…<\/th>\n<\/tr>\n<\/thead>\n
    <\/td>\natan(0.1)<\/code><\/td>\natan(0.2)<\/code><\/td>\natan(0.3)<\/code><\/td>\n…<\/td>\n<\/tr>\n
    rad<\/td>\n0.0997<\/td>\n0.1974<\/td>\n0.2915<\/td>\n…<\/td>\n<\/tr>\n
    \u5ea6<\/td>\n5.7106\u00b0<\/td>\n11.3099\u00b0<\/td>\n16.6992\u00b0<\/td>\n…<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u7df4\u7fd2 1-3<\/h4>\n
    (\u7df4\u7fd2)\u52a0\u6cd5\u5b9a\u7406\u30fb\u4e09\u500d\u89d2\u306e\u516c\u5f0f<\/strong><\/span><\/p>\n
      \n
    1. \u4e09\u89d2\u95a2\u6570\u53ca\u3072\u3099\u53cc\u66f2\u7dda\u95a2\u6570\u306e\u52a0\u6cd5\u5b9a\u7406\u3092\u78ba\u8a8d\u3057\u306a\u3055\u3044\u3002<\/li>\n
    2. $\\sin 3x$ \u3092 $\\sin x$ \u305f\u3099\u3051\u3092\u4f7f\u3063\u3066\u8868\u3057\u306a\u3055\u3044\u3002<\/li>\n
    3. $\\tan 3x$ \u3092 $\\tan x$ \u305f\u3099\u3051\u3092\u4f7f\u3063\u3066\u8868\u3057\u306a\u3055\u3044.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[40]:<\/div>\n
      \n
      \n
      \n
      # \u30d2\u30f3\u30c8\u3002<\/span>\r\n# trig=True \u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u3064\u3051\u3066 expand() \u3067\u5c55\u958b\u3059\u308b\u3002<\/span>\r\n\r\nexpand<\/span>(<\/span>sin<\/span>(<\/span>x<\/span> +<\/span> y<\/span>),<\/span> trig<\/span>=<\/span>True<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      Out[40]:<\/div>\n
      $\\displaystyle \\sin{\\left(x \\right)} \\cos{\\left(y \\right)} + \\sin{\\left(y \\right)} \\cos{\\left(x \\right)}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[\u00a0]:<\/div>\n
      \n
      \n
      \n
       \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[\u00a0]:<\/div>\n
      \n
      \n
      \n
       \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[\u00a0]:<\/div>\n
      \n
      \n
      \n
       \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[\u00a0]:<\/div>\n
      \n
      \n
      \n
       \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[\u00a0]:<\/div>\n
      \n
      \n
      \n
       \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[\u00a0]:<\/div>\n
      \n
      \n
      \n
       \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      \u5fae\u5206\u30fb\u7a4d\u5206\u30fb\u6570\u5024\u7a4d\u5206<\/h3>\n
      \u5fae\u5206\u30fb\u7a4d\u5206\u3092\u884c\u3046\u95a2\u6570\u306e\u8868\u8a18\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n\n\n\n\n\n\n
      \u64cd\u4f5c<\/th>\n<\/th>\n\u8868\u8a18\u4f8b<\/th>\n<\/tr>\n<\/thead>\n
      \u5fae\u5206<\/td>\n<\/td>\ndiff(f(x), x)<\/code><\/td>\n<\/tr>\n
      n \u968e\u5fae\u5206<\/td>\n<\/td>\ndiff(f(x), x, n)<\/code><\/td>\n<\/tr>\n
      \u4e0d\u5b9a\u7a4d\u5206<\/td>\n<\/td>\nintegrate(f(x), x)<\/code><\/td>\n<\/tr>\n
      \u5b9a\u7a4d\u5206<\/td>\n<\/td>\nintegrate(f(x), (x, a, b))<\/code><\/td>\n<\/tr>\n
      \u6570\u5024\u7a4d\u5206<\/td>\n<\/td>\nintegrate(f(x), (x, a, b)).evalf()<\/code><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      \u5fae\u5206\u30fb\u7a4d\u5206<\/h4>\n
      $x^3 + 5 x + 2$ \u3092 $x$ \u3067\u5fae\u5206\u3057\u307e\u3059\u3002\u3068\u3063\u3068\u3068\u7b54\u3048\u3060\u3051\u3092\u8868\u793a\u3055\u305b\u308b\u306b\u306f…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[41]:<\/div>\n
      \n
      \n
      \n
      diff<\/span>(<\/span>x<\/span>**<\/span>3<\/span> +<\/span> 5<\/span>*<\/span>x<\/span> +<\/span> 2<\/span>,<\/span> x<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      Out[41]:<\/div>\n
      $\\displaystyle 3 x^{2} + 5$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      \u4f55\u3092\u8a08\u7b97\u3055\u305b\u308b\u306e\u304b\u3092\u8868\u793a\u3055\u305b\u3066\u304b\u3089\u7b54\u3048\u3092\u8868\u793a\u3055\u305b\u308b\u306b\u306f…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[42]:<\/div>\n
      \n
      \n
      \n
      Eq<\/span>(<\/span>\r\n    diff<\/span>(<\/span>x<\/span>**<\/span>3<\/span> +<\/span> 5<\/span>*<\/span>x<\/span> +<\/span> 2<\/span>,<\/span> x<\/span>,<\/span> evaluate<\/span>=<\/span>False<\/span>),<\/span> \r\n    diff<\/span>(<\/span>x<\/span>**<\/span>3<\/span> +<\/span> 5<\/span>*<\/span>x<\/span> +<\/span> 2<\/span>,<\/span> x<\/span>)<\/span>\r\n)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      Out[42]:<\/div>\n
      $\\displaystyle \\frac{d}{d x} \\left(x^{3} + 5 x + 2\\right) = 3 x^{2} + 5$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      \u307e\u305f\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u3044\u3066\u3082\u3088\u3044\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[43]:<\/div>\n
      \n
      \n
      \n
      Eq<\/span>(<\/span>\r\n    Derivative<\/span>(<\/span>x<\/span>**<\/span>3<\/span> +<\/span> 5<\/span>*<\/span>x<\/span> +<\/span> 2<\/span>,<\/span> x<\/span>),<\/span> \r\n    Derivative<\/span>(<\/span>x<\/span>**<\/span>3<\/span> +<\/span> 5<\/span>*<\/span>x<\/span> +<\/span> 2<\/span>,<\/span> x<\/span>)<\/span>.<\/span>doit<\/span>()<\/span>\r\n)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      Out[43]:<\/div>\n
      $\\displaystyle \\frac{d}{d x} \\left(x^{3} + 5 x + 2\\right) = 3 x^{2} + 5$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      \u4e0d\u5b9a\u7a4d\u5206\u306e\u4f8b\uff1a<\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[44]:<\/div>\n
      \n
      \n
      \n
      Eq<\/span>(<\/span>\r\n    Integral<\/span>(<\/span>x<\/span>**<\/span>2<\/span> *<\/span> cos<\/span>(<\/span>x<\/span>)<\/span> +<\/span> 2<\/span>*<\/span>x<\/span>*<\/span>sin<\/span>(<\/span>x<\/span>),<\/span> x<\/span>),<\/span> \r\n    integrate<\/span>(<\/span>x<\/span>**<\/span>2<\/span> *<\/span> cos<\/span>(<\/span>x<\/span>)<\/span> +<\/span> 2<\/span>*<\/span>x<\/span>*<\/span>sin<\/span>(<\/span>x<\/span>),<\/span> x<\/span>)<\/span>\r\n)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      Out[44]:<\/div>\n
      $\\displaystyle \\int \\left(x^{2} \\cos{\\left(x \\right)} + 2 x \\sin{\\left(x \\right)}\\right)\\, dx = x^{2} \\sin{\\left(x \\right)}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      \u5b9a\u7a4d\u5206\u306e\u4f8b\uff1a<\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[45]:<\/div>\n
      \n
      \n
      \n
      Eq<\/span>(<\/span>\r\n    Integral<\/span>(<\/span>sin<\/span>(<\/span>x<\/span>),<\/span> (<\/span>x<\/span>,<\/span> 0<\/span>,<\/span> pi<\/span>\/<\/span>2<\/span>)),<\/span>\r\n    Integral<\/span>(<\/span>sin<\/span>(<\/span>x<\/span>),<\/span> (<\/span>x<\/span>,<\/span> 0<\/span>,<\/span> pi<\/span>\/<\/span>2<\/span>))<\/span>.<\/span>doit<\/span>()<\/span>\r\n)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      Out[45]:<\/div>\n
      $\\displaystyle \\int\\limits_{0}^{\\frac{\\pi}{2}} \\sin{\\left(x \\right)}\\, dx = 1$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      \u6570\u5024\u7a4d\u5206<\/h4>\n
      \u3067\u306f\uff0c\u89e3\u6790\u7684\u306b\u7a4d\u5206\u3067\u304d\u306a\u3044\u5834\u5408\u306f\u3069\u3046\u3059\u308b\u304b\uff1f<\/p>\n
      \u5b9f\u969b\uff0c\u5927\u5b66\u3067\u7fd2\u3046\u300c\u521d\u7b49\u95a2\u6570\u300d\u304a\u3088\u3073\u305d\u306e\u5408\u6210\u95a2\u6570\u306f\u5168\u3066\u5fae\u5206\u3067\u304d\u307e\u3059\u304c\uff0c\u3067\u306f\u521d\u7b49\u95a2\u6570\u304a\u3088\u3073\u305d\u306e\u5408\u6210\u95a2\u6570\uff08\u521d\u7b49\u95a2\u6570\u3092\u4f7f\u3063\u3066\u66f8\u304b\u308c\u308b\u95a2\u6570\uff09\u306f\u5168\u3066\u7a4d\u5206\u3067\u304d\u308b\u304b\u3068\u3044\u3046\u3068\uff0c\u305d\u3046\u3067\u306f\u306a\u3044\u3002<\/p>\n
      \u5927\u5b66\u306e\u6388\u696d\uff0c\u305f\u3068\u3048\u3070\u7406\u5de5\u7cfb\u306e\u6570\u5b66B\u306a\u3069\u3067\u306f\uff0c\u89e3\u6790\u7684\u306b\u7a4d\u5206\u3067\u304d\u308b\u3088\u3046\u306a\u4f8b\u984c\u3060\u3051\u3092\u6271\u3044\u307e\u3059\u304c\uff0c\u5b9f\u969b\u306b\u306f\uff0c\u4ee5\u4e0b\u306e\u4f8b\u306e\u3088\u3046\u306b $\\sin(\\sin x)$ \u306a\u3069\u306e\u3088\u3046\u306a\u5358\u7d14\u306a\u4f8b\u3067\u3082\uff0c\u89e3\u6790\u7684\u306b\u306f\u7a4d\u5206\u3067\u304d\u307e\u305b\u3093\u3002<\/p>\n
      \u89e3\u6790\u7684\u306b\u7a4d\u5206\u3066\u3099\u304d\u306a\u3044\u5834\u5408\u306f\uff0c\u6570\u5024\u7a4d\u5206\u306b\u3088\u3063\u3066\u8fd1\u4f3c\u5024\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      $\\displaystyle \\int_0^{\\pi} \\sin(\\sin x)\\ dx$ \u306e\u8a08\u7b97\u3092\u3057\u307e\u3059\u3002\u89e3\u6790\u7684\u306b\u89e3\u3051\u306a\u3044\u3068\u305d\u306e\u307e\u307e\u8fd4\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[46]:<\/div>\n
      \n
      \n
      \n
      integrate<\/span>(<\/span>sin<\/span>(<\/span>sin<\/span>(<\/span>x<\/span>)),<\/span> (<\/span>x<\/span>,<\/span> 0<\/span>,<\/span> pi<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      Out[46]:<\/div>\n
      $\\displaystyle \\int\\limits_{0}^{\\pi} \\sin{\\left(\\sin{\\left(x \\right)} \\right)}\\, dx$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      \u4ee5\u4e0b\u306e\u3088\u3046\u306b .evalf()<\/code> \u3092\u3064\u3051\u308b\u3068\u6570\u5024\u7a4d\u5206\u3057\u3066\u304f\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[47]:<\/div>\n
      \n
      \n
      \n
      integrate<\/span>(<\/span>sin<\/span>(<\/span>sin<\/span>(<\/span>x<\/span>)),<\/span> (<\/span>x<\/span>,<\/span> 0<\/span>,<\/span> pi<\/span>))<\/span>.<\/span>evalf<\/span>()<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      Out[47]:<\/div>\n
      $\\displaystyle 1.78648748195005$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      \u65b9\u7a0b\u5f0f<\/h3>\n
      \u591a\u9805\u5f0f\u65b9\u7a0b\u5f0f\u30fb\u9023\u7acb\u65b9\u7a0b\u5f0f<\/h4>\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<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[48]:<\/div>\n
      \n
      \n
      \n
      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
      \n
      \n
      \n
      Out[48]:<\/div>\n
      \n
      [-1 + sqrt(3), -sqrt(3) - 1]<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      \u9023\u7acb\u65b9\u7a0b\u5f0f $x^2 + y^2 = 5, \\ x + y = 1$ \u3092 $x, y$ \u306b\u3064\u3044\u3066\u89e3\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[49]:<\/div>\n
      \n
      \n
      \n
      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\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      Out[49]:<\/div>\n
      \n
      [(-1, 2), (2, -1)]<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      3 \u6b21\u65b9\u7a0b\u5f0f $x^3 – 8 = 0$ \u3092\u89e3\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[50]:<\/div>\n
      \n
      \n
      \n
      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
      \n
      \n
      \n
      Out[50]:<\/div>\n
      \n
      [2, -1 - sqrt(3)*I, -1 + sqrt(3)*I]<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \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
      \n
      \n
      In\u00a0[51]:<\/div>\n
      \n
      \n
      \n
      sols<\/span>[<\/span>2<\/span>]<\/span>**<\/span>3<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      Out[51]:<\/div>\n
      $\\displaystyle \\left(-1 + \\sqrt{3} i\\right)^{3}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[52]:<\/div>\n
      \n
      \n
      \n
      expand<\/span>(<\/span>_<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      Out[52]:<\/div>\n
      $\\displaystyle 8$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      \u7df4\u7fd2 1-4<\/h4>\n
      \uff08\u7df4\u7fd2\uff09\u9db4\u3068\u4e80\u3068\u87fb<\/strong><\/span><\/p>\n
      \u9db4\u3068\u4e80\u3068\u87fb\uff0c\u500b\u4f53\u6570\u306e\u5408\u8a08\u306f 10\u3002\u8db3\u306e\u6570\u306f\u5168\u90e8\u3066\u3099 34 \u672c\u3002\u87fb\u306f\u4e80\u3088\u308a 1 \u5339\u5c11\u306a\u3044\u3002\u9db4\uff0c\u4e80\uff0c\u87fb\uff0c\u305d\u308c\u305d\u3099\u308c\u4f55\u7fbd\u30fb\u4f55\u5339?<\/p>\n
      \u9db4\u3068\u4e80\u3068\u87fb\u306e\u500b\u4f53\u6570\u3092\u305d\u308c\u305d\u3099\u308c $x, y, z$ \u3068\u3057\u3066\u9023\u7acb\u65b9\u7a0b\u5f0f\u3092\u305f\u3066\u3066 solve<\/code> \u3057\u307e\u3059\u3002\u87fb\u306e\u8db3\u306f\u4f55\u672c\u304b\u308f\u304b\u308a\u307e\u3059\u3088\u306d?<\/p>\n
      \u304b\u3064\u3066\u7dda\u5f62\u4ee3\u6570\u306e\u6388\u696d\u3067\u3053\u306e\u554f\u984c\u3092\u51fa\u3057\u305f\u3068\u304d\uff0c\u771f\u3063\u5148\u306b\u51fa\u305f\u8cea\u554f\u304c\u300c\u5148\u751f\uff0c\u87fb\u306e\u8db3\u306f\u4f55\u672c\u3067\u3059\u304b\uff1f\u300d\u3067\u3057\u305f… orz<\/p>\n