{"id":9504,"date":"2024-11-13T22:00:39","date_gmt":"2024-11-13T13:00:39","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=9504"},"modified":"2024-11-24T11:12:18","modified_gmt":"2024-11-24T02:12:18","slug":"%e5%9f%ba%e6%9c%ac%e4%ba%8b%e9%a0%85%e3%81%a8%e4%b8%bb%e3%81%aa%e5%ae%9a%e6%95%b0%e3%83%bb%e9%96%a2%e6%95%b0","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\/%e5%9f%ba%e6%9c%ac%e4%ba%8b%e9%a0%85%e3%81%a8%e4%b8%bb%e3%81%aa%e5%ae%9a%e6%95%b0%e3%83%bb%e9%96%a2%e6%95%b0\/","title":{"rendered":"1. SymPy \u306e\u57fa\u672c\u4e8b\u9805\u3068\u4e3b\u306a\u5b9a\u6570\u30fb\u95a2\u6570"},"content":{"rendered":"
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SymPy \u3067\u6570\u5b66\u7684\u8a08\u7b97\u3092\u884c\u3046\u305f\u3081\u306e\u57fa\u672c\u3068\uff0cSymPy \u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u4e3b\u306a\u5b9a\u6570\u3084\u95a2\u6570\u306b\u3064\u3044\u3066\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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<\/div>\n
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\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 #<\/code><\/h4>\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
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In\u00a0[2]:<\/div>\n
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1<\/span> +<\/span> 2<\/span> +<\/span> 3<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[2]:<\/div>\n
$\\displaystyle 6$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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1<\/span> +<\/span> 2<\/span> # + 3<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[3]:<\/div>\n
$\\displaystyle 3$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u56db\u5247\u6f14\u7b97\u3068\u304b\u3063\u3053 ()<\/code><\/h4>\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[ ]<\/code> \u3084 { }<\/code> \u306f\u512a\u5148\u9806\u4f4d\u306e\u6307\u5b9a\u306b\u306f\u4f7f\u3044\u307e\u305b\u3093\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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1<\/span> +<\/span> 2<\/span> *<\/span> 3<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[4]:<\/div>\n
$\\displaystyle 7$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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(<\/span>1<\/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[5]:<\/div>\n
$\\displaystyle 9$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u7d2f\u4e57\uff08\u3079\u304d\u4e57\uff09**<\/code><\/h4>\n
**<\/code> \u306f\u7d2f\u4e57\uff08\u3079\u304d\u4e57\uff09\u3092\u8868\u3057\u307e\u3059\u3002 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<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[6]:<\/div>\n
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2<\/span>**<\/span>100<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[6]:<\/div>\n
$\\displaystyle 1267650600228229401496703205376$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6d6e\u52d5\u5c0f\u6570\u70b9\u8868\u793a N()<\/code><\/h4>\n
SymPy \u306e N()<\/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
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In\u00a0[7]:<\/div>\n
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N<\/span>(<\/span>2<\/span>**<\/span>100<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[7]:<\/div>\n
$\\displaystyle 1.26765060022823 \\cdot 10^{30}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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N()<\/code> \u3067\u6841\u6570\u3092\u6307\u5b9a\u3059\u308b\u4f8b\uff1a\u4ee5\u4e0b\u3067\u306f\u6709\u52b9\u6841\u65705\u6841\u3067\u8868\u793a\u3055\u305b\u3066\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[8]:<\/div>\n
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N<\/span>(<\/span>2<\/span>**<\/span>100<\/span>,<\/span> 5<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[8]:<\/div>\n
$\\displaystyle 1.2677 \\cdot 10^{30}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u25cb\u7df4\u7fd2\uff1a3, 2, 1 \u3067\u3064\u304f\u308b\u6700\u5927\u6570<\/h4>\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
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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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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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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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\u5272\u308a\u7b97 \/<\/code>\uff0c\u5546 \/\/<\/code>\uff0c\u5270\u4f59 %<\/code><\/h4>\n
Python \u3067\u306f\u9664\u7b97 \/<\/code> \u306f\u5e38\u306b\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u578b\u306e\u5b9f\u6570\u3092\u8fd4\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[9]:<\/div>\n
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3<\/span>\/<\/span>21<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[9]:<\/div>\n
$\\displaystyle 0.142857142857143$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\/\/<\/code> \u6f14\u7b97\u5b50\u306f\u6574\u6570\u9664\u7b97\u3092\u884c\u3044\u3001\u5c0f\u6570\u90e8\u3092\u5207\u308a\u6368\u3066\u305f\u6574\u6570\u5024\uff08\u5546\uff09\u3092\u8fd4\u3057\u307e\u3059\u3002\u5270\u4f59\u306f\u3001%<\/code> \u3067\u6c42\u3081\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[10]:<\/div>\n
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17<\/span> \/\/<\/span> 3<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[10]:<\/div>\n
$\\displaystyle 5$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[11]:<\/div>\n
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17<\/span> %<\/span> 3<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[11]:<\/div>\n
$\\displaystyle 2$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[12]:<\/div>\n
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17<\/span> ==<\/span> 3<\/span> *<\/span> (<\/span>17<\/span>\/\/<\/span>3<\/span>)<\/span> +<\/span> (<\/span>17<\/span>%<\/span>3<\/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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True<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u6709\u7406\u6570 Rational()<\/code><\/h4>\n
\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
\u4ee5\u4e0b\u3067\u306f $\\displaystyle \\frac{3}{21} \\Rightarrow \\frac{1}{7}$ \u306b\u81ea\u52d5\u7684\u306b\u7d04\u5206\u3057\u3066\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[13]:<\/div>\n
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# 3\/21 = 1\/7<\/span>\r\n\r\nRational<\/span>(<\/span>3<\/span>,<\/span> 21<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[13]:<\/div>\n
$\\displaystyle \\frac{1}{7}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4ee3\u5165 =<\/code><\/h4>\n
\u5909\u6570\u306b\u5f0f\u3084\u5024\u3092\u4ee3\u5165\u3059\u308b\u3068\u304d\u306f\uff0c\u7b49\u53f7\u8a18\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
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In\u00a0[14]:<\/div>\n
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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
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Out[14]:<\/div>\n
$\\displaystyle \\frac{701}{7}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u5909\u6570 a<\/code> \u306b\u4ee3\u5165\u3055\u308c\u305f\u5024\u3092\u4f7f\u3063\u3066\uff0c\u3055\u3089\u306b\u8a08\u7b97\u3092\u7d9a\u3051\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[15]:<\/div>\n
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(<\/span>a<\/span> -<\/span> 100<\/span>)<\/span> *<\/span> 7<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[15]:<\/div>\n
$\\displaystyle 1$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$\\displaystyle a = a -\\frac{1}{7}$ \u306f\u7b49\u5f0f\u30fb\u65b9\u7a0b\u5f0f\u3068\u3057\u3066\u306f\u6210\u308a\u7acb\u3061\u307e\u305b\u3093\u304c\uff0cPython\uff08\u3084\u305d\u306e\u4ed6\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\uff09\u3067\u306f\uff0c\u5909\u6570 $a$ \u306b\u76f4\u524d\u307e\u3067\u306b\u4ee3\u5165\u3055\u308c\u3066\u3044\u308b\u5024\u304b\u3089 $\\displaystyle \\frac{1}{7}$ \u3092\u5f15\u3044\u305f\u53f3\u8fba\u306e\u7b54\u3048\u3092 \u3042\u305f\u3089\u3081\u3066<\/strong> \u5de6\u8fba\u306e\u5909\u6570 $a$ \u306b\u4ee3\u5165\u3059\u308b\uff0c\u3068\u3044\u3046\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3088\u306d\u3047\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[16]:<\/div>\n
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a<\/span> =<\/span> 100<\/span> +<\/span> Rational<\/span>(<\/span>3<\/span>,<\/span>21<\/span>)<\/span>\r\na<\/span> =<\/span> a<\/span> -<\/span> Rational<\/span>(<\/span>1<\/span>,<\/span> 7<\/span>)<\/span>\r\na<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[16]:<\/div>\n
$\\displaystyle 100$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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a = a - Rational(1, 7)<\/code> \u3068\u540c\u3058\u3053\u3068\u3092 Python \u3067\u306f\u30a4\u30f3\u30af\u30ea\u30e1\u30f3\u30c8 +=<\/code> \u3084\u30c7\u30af\u30ea\u30e1\u30f3\u30c8 -=<\/code> \u3092\u4f7f\u3063\u3066\u66f8\u304f\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[17]:<\/div>\n
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a<\/span> =<\/span> 100<\/span> +<\/span> Rational<\/span>(<\/span>3<\/span>,<\/span>21<\/span>)<\/span>\r\ndisplay<\/span>(<\/span>a<\/span>)<\/span>\r\na<\/span> -=<\/span> Rational<\/span>(<\/span>1<\/span>,<\/span> 7<\/span>)<\/span>\r\ndisplay<\/span>(<\/span>a<\/span>)<\/span>\r\na<\/span> +=<\/span> Rational<\/span>(<\/span>1<\/span>,<\/span> 7<\/span>)<\/span>\r\ndisplay<\/span>(<\/span>a<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
$\\displaystyle \\frac{701}{7}$<\/div>\n<\/div>\n
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<\/div>\n
$\\displaystyle 100$<\/div>\n<\/div>\n
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$\\displaystyle \\frac{701}{7}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4e00\u6642\u7684\u4ee3\u5165 .subs()<\/code><\/h4>\n
$b = 3 a$ \u3068\u5b9a\u7fa9\u3057\uff0c…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[18]:<\/div>\n
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# \u4e0a\u3067 a \u306b\u5024\u304c\u4ee3\u5165\u3055\u308c\u3066\u3044\u308b\u306e\u3067\u521d\u671f\u5316<\/span>\r\nvar<\/span>(<\/span>'a'<\/span>)<\/span>\r\n\r\nb<\/span> =<\/span> 3<\/span>*<\/span>a<\/span>\r\nb<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[18]:<\/div>\n
$\\displaystyle 3 a$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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b.subs(a, 2)<\/code> \u3067\u4e00\u6642\u7684\u306b $a$ \u306b\u5024 $2$ \u3092\u4ee3\u5165\u3059\u308b\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[19]:<\/div>\n
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# \u4e0a\u3067 a \u306b\u5024\u304c\u4ee3\u5165\u3055\u308c\u3066\u3044\u308b\u306e\u3067\u521d\u671f\u5316<\/span>\r\nvar<\/span>(<\/span>'a'<\/span>)<\/span>\r\n\r\nb<\/span> =<\/span> 3<\/span>*<\/span>a<\/span>\r\nb<\/span>.<\/span>subs<\/span>(<\/span>a<\/span>,<\/span> 2<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[19]:<\/div>\n
$\\displaystyle 6$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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b.subs(a, 2)<\/code> $\\displaystyle = 3 a \\bigr|_{a=2} = 3\\times 2 = 6$ \u3092\u51fa\u529b\u3057\u307e\u3059\u304c\uff0c<\/p>\n
$b$ \u306e\u5b9a\u7fa9\u305d\u306e\u3082\u306e\u306f\u5909\u308f\u308a\u307e\u305b\u3093\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[20]:<\/div>\n
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b<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[20]:<\/div>\n
$\\displaystyle 3 a$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u7b49\u5f0f Eq()<\/code><\/h4>\n
\u7b49\u5f0f\u306f Eq(\u5de6\u8fba, \u53f3\u8fba)<\/code> \u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\u3002=<\/code> \u306f Python \u3067\u306f\u4ee3\u5165\u3092\u8868\u3059\u305f\u3081\u306b\u4f7f\u308f\u308c\u3066\u308b\u306e\u3067\uff0c\u5de6\u8fba = \u53f3\u8fba<\/code> \u306e\u3088\u3046\u306b\u66f8\u304f\u3068\u53f3\u8fba\u306e\u91cf\u3092\u5de6\u8fba\u306e\u5909\u6570\u306b\u4ee3\u5165\u3059\u308b\uff0c\u3068\u3044\u3046\u610f\u5473\u306b\u306a\u308a\uff0c\u5de6\u8fba\u3068\u53f3\u8fba\u306f\u7b49\u3057\u3044\uff0c\u3068\u3044\u3046\u7b49\u5f0f\u306e\u610f\u5473\u306b\u306f\u306a\u308a\u307e\u305b\u3093\u3002<\/p>\n
Eq(\u5de6\u8fba, \u53f3\u8fba)<\/code> \u306b\u3064\u3044\u3066\u306f\u300c\u65b9\u7a0b\u5f0f\u300d\u306e\u9805\u3067\u3042\u3089\u305f\u3081\u3066\u8aac\u660e\u3059\u308b\u307b\u304b\uff0c\u4ee5\u4e0b\u3067\u306f\u5de6\u8fba\u3092 SymPy \u3067\u8a08\u7b97\u3059\u308b\u3068\u53f3\u8fba\u306e\u3088\u3046\u306a\u91cf\u306b\u306a\u308b\uff0c\u3068\u3044\u3046\u8868\u793a\u3092\u3055\u305b\u308b\u305f\u3081\u306b\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u5b9f\u884c\u7d50\u679c\u306e\u975e\u8868\u793a (;<\/code>)<\/h4>\n
\u4ee5\u4e0b\u306e\u4f8b\u3067\u306f\uff0c\u591a\u9805\u5f0f $x^2 + 3 x + 2$ \u3092\u5909\u6570 eq<\/code> \u306b\u4ee3\u5165\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[21]:<\/div>\n
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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
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<\/div>\n
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\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
eq<\/code> \u306e\u5185\u5bb9\u3092\u77e5\u308a\u305f\u3044\u3068\u304d\u306f\uff0cShift + Enter \u3059\u308c\u3070\u5b9f\u884c\u7d50\u679c\u304c\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
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In\u00a0[22]:<\/div>\n
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eq<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[22]:<\/div>\n
$\\displaystyle x^{2} + 3 x + 2$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[23]:<\/div>\n
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eq<\/span>;<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u56e0\u6570\u5206\u89e3 factor()<\/code><\/h4>\n
eq<\/code> \u306b\u4ee3\u5165\u3055\u308c\u305f\u591a\u9805\u5f0f\u3092 factor()<\/code> \u3067\u56e0\u6570\u5206\u89e3\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[24]:<\/div>\n
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factor<\/span>(<\/span>eq<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[24]:<\/div>\n
$\\displaystyle \\left(x + 1\\right) \\left(x + 2\\right)$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u5c55\u958b expand()<\/code><\/h4>\n
$(x-2)^4$ \u3092 expand()<\/code> \u3067\u5c55\u958b\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[25]:<\/div>\n
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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
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Out[25]:<\/div>\n
$\\displaystyle x^{4} -8 x^{3} + 24 x^{2} -32 x + 16$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u76f4\u524d\u306e\u51fa\u529b\u7d50\u679c\u306e\u53c2\u7167 _<\/code><\/h4>\n
\u76f4\u524d\u306e\u51fa\u529b\u7d50\u679c\u306f _<\/code> \u3067\u53c2\u7167\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\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
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In\u00a0[26]:<\/div>\n
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factor<\/span>(<\/span>_<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[26]:<\/div>\n
$\\displaystyle \\left(x -2\\right)^{4}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u4e3b\u306a\u5b9a\u6570<\/h3>\n
SymPy \u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u4e3b\u306a\u5b9a\u6570\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u5186\u5468\u7387 $\\pi =$ pi<\/code><\/h4>\n
SymPy \u3067\u306f\u5186\u5468\u7387 $\\pi$ \u306f pi<\/code> \u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[27]:<\/div>\n
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pi<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[27]:<\/div>\n
$\\displaystyle \\pi$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u6d6e\u52d5\u5c0f\u6570\u70b9\u3067\u8fd1\u4f3c\u5024\u3092\u8868\u793a\u3059\u308b\u306b\u306f N()<\/code> \u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[28]:<\/div>\n
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N<\/span>(<\/span>pi<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[28]:<\/div>\n
$\\displaystyle 3.14159265358979$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u53c2\u8003\u307e\u3067\u306b\uff0cN()<\/code> \u3092\u4f7f\u3063\u3066\u5186\u5468\u7387 $\\pi$ \u3092 30\u6841\u307e\u3067\u8868\u793a\u3055\u305b\u308b\u4f8b\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[29]:<\/div>\n
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N<\/span>(<\/span>pi<\/span>,<\/span> 30<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[29]:<\/div>\n
$\\displaystyle 3.14159265358979323846264338328$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30cd\u30a4\u30d4\u30a2\u6570\uff08\u81ea\u7136\u5bfe\u6570\u306e\u5e95\uff09$e =$ E<\/code><\/h4>\n
SymPy \u3067\u306f\u81ea\u7136\u5bfe\u6570\u306e\u5e95 $e$ \u306f E<\/code> \u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[30]:<\/div>\n
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E<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[30]:<\/div>\n
$\\displaystyle e$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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N()<\/code> \u3067\u5c0f\u6570\u70b9\u8868\u793a\u3055\u305b\u308b\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[31]:<\/div>\n
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N<\/span>(<\/span>E<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[31]:<\/div>\n
$\\displaystyle 2.71828182845905$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u30cd\u30a4\u30d4\u30a2\u6570 $e$ \u306f\u5143\u3005\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u5b9a\u7fa9\u3067\u5c0e\u5165\u3055\u308c\u307e\u3057\u305f\u3002<\/p>\n
\\begin{eqnarray}
\n\\lim_{h \\rightarrow 0} \\frac{e^{h} -1}{h} &=& 1\\\\
\n\\therefore\\ e &=& \\lim_{h \\rightarrow 0} \\left(1 + h\\right)^{\\frac{1}{h}}
\n\\end{eqnarray}<\/p>\n
\u3053\u306e\u6975\u9650\u3092 SymPy \u3067\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n
\u6975\u9650 limit()<\/code><\/h4>\n
SymPy \u3067\u306f\u6975\u9650\u306f limit()<\/code> \u307e\u305f\u306f Limit().doit()<\/code> \u3067\u3059\u3002Limit()<\/code> \u306f\u6975\u9650\u306e\u5f0f\u3092\u8868\u793a\u3059\u308b\u3060\u3051\u3067\u5b9f\u884c\u306f\u3057\u307e\u305b\u3093\u3002<\/p>\n
$\\displaystyle \\lim_{h \\rightarrow 0} \\frac{e^{h} -1}{h} = $ limit((E**h-1)\/h, h, 0)<\/code><\/p>\n
Eq(\u5de6\u8fba, \u53f3\u8fba)<\/code> \u306f\u7b49\u5f0f\u3092\u3042\u3089\u308f\u3057\uff0c\u5de6\u8fba\u306e\u5f0f\u3092 SymPy \u3067\u8a08\u7b97\u3059\u308b\u3068\u53f3\u8fba\u306e\u5f0f\u306b\u306a\u308b\uff0c\u3068\u8868\u793a\u3055\u305b\u308b\u305f\u3081\u306b\u4f7f\u3063\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[32]:<\/div>\n
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Eq<\/span>(<\/span>Limit<\/span>((<\/span>E<\/span>**<\/span>h<\/span>-<\/span>1<\/span>)<\/span>\/<\/span>h<\/span>,<\/span> h<\/span>,<\/span> 0<\/span>),<\/span>\r\n   limit<\/span>((<\/span>E<\/span>**<\/span>h<\/span>-<\/span>1<\/span>)<\/span>\/<\/span>h<\/span>,<\/span> h<\/span>,<\/span> 0<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[32]:<\/div>\n
$\\displaystyle \\lim_{h \\to 0^+}\\left(\\frac{e^{h} -1}{h}\\right) = 1$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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$\\displaystyle \\lim_{h\\rightarrow 0} \\left(1+h\\right)^{\\frac{1}{h}} = $ limit((1+h)**(1\/h), h, 0)<\/code> $= \\cdots$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[33]:<\/div>\n
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Eq<\/span>(<\/span>Limit<\/span>((<\/span>1<\/span>+<\/span>h<\/span>)<\/span>**<\/span>(<\/span>1<\/span>\/<\/span>h<\/span>),<\/span> h<\/span>,<\/span> 0<\/span>),<\/span> \r\n   limit<\/span>((<\/span>1<\/span>+<\/span>h<\/span>)<\/span>**<\/span>(<\/span>1<\/span>\/<\/span>h<\/span>),<\/span> h<\/span>,<\/span> 0<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[33]:<\/div>\n
$\\displaystyle \\lim_{h \\to 0^+} \\left(h + 1\\right)^{\\frac{1}{h}} = e$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u865a\u6570\u5358\u4f4d $i =$ I<\/code><\/h4>\n
SymPy \u3067\u306f\u865a\u6570\u5358\u4f4d $i$ \u306f I<\/code><\/p>\n
$\\displaystyle i^2 = -1$ \u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[34]:<\/div>\n
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I<\/span>**<\/span>2<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[34]:<\/div>\n
$\\displaystyle -1$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u30aa\u30a4\u30e9\u30fc\u306e\u7b49\u5f0f<\/h5>\n
\u7121\u7406\u6570 $e$\uff0c$\\pi$\uff0c\u865a\u6570\u5358\u4f4d $i$\uff0c\u6574\u6570 $1$ \u304a\u3088\u3073 $0$ \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
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In\u00a0[35]:<\/div>\n
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E<\/span>**<\/span>(<\/span>I<\/span> *<\/span> pi<\/span>)<\/span> +<\/span> 1<\/span> ==<\/span> 0<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[35]:<\/div>\n
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True<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u7121\u9650\u5927 $\\infty =$ oo<\/code><\/h4>\n
\u7121\u9650\u5927\u306f\u5b9a\u6570\u3067\u306f\u306a\u3044\u304c\uff0cSymPy \u3067\u306f $\\infty = $ oo<\/code> \u3068\u5c0f\u6587\u5b57\u306e o<\/code>\uff08\u30aa\u30fc\uff09\u30922\u3064\u4e26\u3079\u3066\u66f8\u304d\u307e\u3059\u3002\uff08\u3061\u3087\u3063\u3068\u304b\u308f\u3044\u3044\u3002\uff09<\/p>\n
$\\displaystyle \\lim_{x \\rightarrow \\infty} e^{-x}$ = limit(exp(-x), x, oo)<\/code> $= \\cdots$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[36]:<\/div>\n
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limit<\/span>(<\/span>exp<\/span>(<\/span>-<\/span>x<\/span>),<\/span> x<\/span>,<\/span> oo<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[36]:<\/div>\n
$\\displaystyle 0$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u4e3b\u306a\u95a2\u6570<\/h3>\n
SymPy \u3067\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u4e3b\u306a\u95a2\u6570\uff08\u521d\u7b49\u95a2\u6570\u306a\u3069\uff09\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
\n
\n
\u3079\u304d\u95a2\u6570 x**n<\/code><\/h4>\n
$\\displaystyle x^n = $ x**n<\/code><\/p>\n
\u5e73\u65b9\u6839 sqrt()<\/code><\/h4>\n<\/div>\n<\/div>\n<\/div>\n
\n
<\/div>\n
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$\\displaystyle \\sqrt{x} = x^{\\frac{1}{2}} =$ sqrt(x)<\/code><\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[37]:<\/div>\n
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print<\/span>(<\/span>'sqrt(64) ='<\/span>,<\/span> sqrt<\/span>(<\/span>64<\/span>))<\/span>\r\nprint<\/span>(<\/span>'64**(1\/2) ='<\/span>,<\/span> 64<\/span>**<\/span>(<\/span>Rational<\/span>(<\/span>1<\/span>,<\/span>2<\/span>)))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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sqrt(64) = 8\r\n64**(1\/2) = 8\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u5e73\u65b9\u6839\u306b\u3064\u3044\u3066\u88dc\u8db3<\/h5>\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
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In\u00a0[38]:<\/div>\n
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sqrt<\/span>(<\/span>x<\/span>**<\/span>2<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[38]:<\/div>\n
$\\displaystyle \\sqrt{x^{2}}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$x$ \u3092\u5b9f\u6570\u3068\u3057\u3066\u3084\u308b\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[39]:<\/div>\n
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var<\/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
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Out[39]:<\/div>\n
$\\displaystyle \\left|{x}\\right|$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$x$ \u3092\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[40]:<\/div>\n
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var<\/span>(<\/span>'x'<\/span>,<\/span> positive<\/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
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Out[40]:<\/div>\n
$\\displaystyle x$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[41]:<\/div>\n
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# \u5b9f\u6570\u306e\u8a2d\u5b9a\u3092\u521d\u671f\u5316\u3059\u308b<\/span>\r\nvar<\/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
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Out[41]:<\/div>\n
$\\displaystyle \\sqrt{x^{2}}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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<\/div>\n
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\u7d76\u5bfe\u5024 abs()<\/code><\/h5>\n
abs(x)<\/code> \u306f $x$ \u306e\u7d76\u5bfe\u5024 $|x|$ \u3067\u3059\u3002<\/p>\n
\u8907\u7d20\u6570 $x = a + b i$ \u306b\u3064\u3044\u3066\u306f\uff0c$|x| = \\sqrt{a^2 + b^2}$ \u3067\u3042\u308b\u305f\u3081\uff0c
\n$\\sqrt{x^2} \\neq |x|$ \u3067\u3059\u3002\u4f8b\u3068\u3057\u3066 $x = 1 + 3 i$ \u3068\u3059\u308b\u3068<\/p>\n
$\\sqrt{x} =$ sqrt((1 + 3*I)**2)<\/code> $= \\cdots$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[42]:<\/div>\n
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sqrt<\/span>((<\/span>1<\/span> +<\/span> 3<\/span>*<\/span>I<\/span>)<\/span>**<\/span>2<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[42]:<\/div>\n
$\\displaystyle 1 + 3 i$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4e00\u65b9\uff0c<\/p>\n
$|x| =$ abs(1 + 3*I)<\/code> $= \\cdots$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[43]:<\/div>\n
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abs<\/span>(<\/span>1<\/span> +<\/span> 3<\/span>*<\/span>I<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[43]:<\/div>\n
$\\displaystyle \\sqrt{10}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$\\sqrt{x^2} \\neq |x|$ \u3067\u3042\u308b\u3053\u3068\u306f\u660e\u3089\u304b\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\u6307\u6570\u95a2\u6570 exp()<\/code><\/h4>\n
$a$ \u3092\u5e95\u3068\u3059\u308b\u6307\u6570\u95a2\u6570 $a^x$ \u306e\u3046\u3061\uff0c\u3068\u304f\u306b\u30cd\u30a4\u30d4\u30a2\u6570 $e$ \u3092\u5e95\u3068\u3059\u308b\u6307\u6570\u95a2\u6570\u306f<\/p>\n
$e^x =$ exp(x)<\/code> $=$ E**x<\/code><\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\u6307\u6570\u6cd5\u5247<\/h5>\n
$1. \\ a^x\\,a^y = a^{x+y}$<\/p>\n
$\\displaystyle 2. \\ \\left(a^x\\right)^y = a^{xy}$<\/p>\n
$3. \\ (a b)^x = a^x\\, b^x$<\/p>\n
\u5ff5\u306e\u305f\u3081\uff0cSymPy \u3067\u78ba\u8a8d\u3057\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\u5909\u6570 $a, b, x, y$ \u3092\u5ff5\u306e\u305f\u3081\u521d\u671f\u5316\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[44]:<\/div>\n
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var<\/span>(<\/span>'a b x y'<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[44]:<\/div>\n
$\\displaystyle \\left( a, \\ b, \\ x, \\ y\\right)$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$1. \\ a^x\\,a^y = a^{x+y}$ \u306f simplify()<\/code> \u3067\u793a\u305b\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[45]:<\/div>\n
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f<\/span> =<\/span> a<\/span>**<\/span>x<\/span> *<\/span> a<\/span>**<\/span>y<\/span>\r\nEq<\/span>(<\/span>f<\/span>,<\/span> simplify<\/span>(<\/span>f<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[45]:<\/div>\n
$\\displaystyle a^{x} a^{y} = a^{x + y}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$3. \\ (a b)^x = a^x\\, b^x$ \u306f expand()<\/code> \u306b force=True<\/code> \u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u3064\u3051\u308c\u3070\u793a\u305b\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[46]:<\/div>\n
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g<\/span> =<\/span> (<\/span>a<\/span>*<\/span>b<\/span>)<\/span>**<\/span>x<\/span>\r\nEq<\/span>(<\/span>g<\/span>,<\/span> expand<\/span>(<\/span>g<\/span>,<\/span> force<\/span>=<\/span>True<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[46]:<\/div>\n
$\\displaystyle \\left(a b\\right)^{x} = a^{x} b^{x}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$\\displaystyle 2. \\ \\left(a^x\\right)^y = a^{xy}$ \u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092 SymPy \u3067\u78ba\u8a8d\u3059\u308b\u306b\u306f\u3069\u3046\u3057\u305f\u3089\u3044\u3044\u3093\u3067\u3057\u3087\u3046\u304b\u306d\u3047\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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\u5bfe\u6570\u95a2\u6570 log()<\/code><\/h4>\n
\u4e00\u822c\u306b $b$ \u3092\u5e95\u3068\u3059\u308b\u5bfe\u6570\u95a2\u6570\u306f $\\log_b x =$ log(x, b)<\/code><\/p>\n
\u81ea\u7136\u5bfe\u6570 $\\displaystyle \\log_e x = \\log x =$ log(x)<\/code><\/p>\n
\u81ea\u7136\u5bfe\u6570 $\\log x$ \u306f\u6307\u6570\u95a2\u6570 $e^x$ \u306e\u9006\u95a2\u6570\u3067\u3042\u308b\u304b\u3089\uff0c<\/p>\n
$\\displaystyle e^{\\log x} = x$ \u3084 $\\displaystyle \\log \\left(e^x\\right) = x$ \u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[47]:<\/div>\n
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exp<\/span>(<\/span>log<\/span>(<\/span>x<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[47]:<\/div>\n
$\\displaystyle x$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$\\displaystyle \\log \\left(e^x\\right) = x$ \u3092\u793a\u3059\u306b\u306f\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b expand_log()<\/code> \u306b force=True<\/code> \u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u3064\u3051\u3066\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[48]:<\/div>\n
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Eq<\/span>(<\/span>log<\/span>(<\/span>exp<\/span>(<\/span>x<\/span>)),<\/span> \r\n   expand_log<\/span>(<\/span>log<\/span>(<\/span>exp<\/span>(<\/span>x<\/span>)),<\/span> force<\/span>=<\/span>True<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[48]:<\/div>\n
$\\displaystyle \\log{\\left(e^{x} \\right)} = x$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u5e38\u7528\u5bfe\u6570 log( , 10)<\/code><\/h5>\n
$10$ \u3092\u5e95\u3068\u3059\u308b\u5e38\u7528\u5bfe\u6570 $\\log_{10}$ \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b…<\/p>\n
$\\displaystyle \\log_{10} 1000 = \\log_{10} 10^3 = 3$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[49]:<\/div>\n
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log<\/span>(<\/span>1000<\/span>,<\/span> 10<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[49]:<\/div>\n
$\\displaystyle 3$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u53c2\u8003\uff1alog10 \u306e import<\/h6>\n
\u4ee5\u4e0b\u306e\u3088\u3046\u306b log10()<\/code> \u3092 import \u3057\u3066\u4f7f\u3046\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[50]:<\/div>\n
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from<\/span> sympy.codegen.cfunctions<\/span> import<\/span> log10<\/span>\r\n\r\nlog10<\/span>(<\/span>1000<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[50]:<\/div>\n
$\\displaystyle 3$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u5bfe\u6570\u6cd5\u5247<\/h5>\n
$1.\\ \\log(x y) = \\log x + \\log y$<\/p>\n
$2. \\ \\log(x^y) = y \\log x$<\/p>\n
\u3053\u308c\u3089\u3092\u78ba\u8a8d\u3059\u308b\u306b\u3082\uff0c expand_log()<\/code> \u306b force=True<\/code> \u30aa\u30d7\u30b7\u30e7\u30f3\u304c\u5fc5\u8981\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[51]:<\/div>\n
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Eq<\/span>(<\/span>log<\/span>(<\/span>x<\/span>*<\/span>y<\/span>),<\/span> \r\n   expand_log<\/span>(<\/span>log<\/span>(<\/span>x<\/span>*<\/span>y<\/span>),<\/span> force<\/span>=<\/span>True<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[51]:<\/div>\n
$\\displaystyle \\log{\\left(x y \\right)} = \\log{\\left(x \\right)} + \\log{\\left(y \\right)}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[52]:<\/div>\n
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Eq<\/span>(<\/span>log<\/span>(<\/span>x<\/span>**<\/span>y<\/span>),<\/span> \r\n   expand_log<\/span>(<\/span>log<\/span>(<\/span>x<\/span>**<\/span>y<\/span>),<\/span> force<\/span>=<\/span>True<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[52]:<\/div>\n
$\\displaystyle \\log{\\left(x^{y} \\right)} = y \\log{\\left(x \\right)}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4e09\u89d2\u95a2\u6570 sin(x)<\/code>, cos(x)<\/code>, tan(x)<\/code><\/h4>\n
$\\sin x =$ sin(x)<\/code>, $\\cos x =$ cos(x)<\/code>, $\\tan x =$ tan(x)<\/code><\/p>\n
$\\sin^2 x + \\cos^2 x = 1$ \u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n
\u7c21\u5358\u5316 simplify()<\/code><\/h5>\n
simplify()<\/code> \u3092\u4f7f\u3063\u3066\u7c21\u5358\u5316\u3055\u305b\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[53]:<\/div>\n
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simplify<\/span>(<\/span>sin<\/span>(<\/span>x<\/span>)<\/span>**<\/span>2<\/span> +<\/span> cos<\/span>(<\/span>x<\/span>)<\/span>**<\/span>2<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[53]:<\/div>\n
$\\displaystyle 1$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$\\displaystyle 1 + \\tan^2 x = \\frac{1}{\\cos^2 x}$ \u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3082\u78ba\u8a8d\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\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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\u5f15\u6570\u306e\u5358\u4f4d<\/h5>\n
\u4e09\u89d2\u95a2\u6570\u306e\u5f15\u6570\u306e\u5358\u4f4d\u306f\u30e9\u30b8\u30a2\u30f3\u3067\u3059\u3002<\/p>\n
$\\displaystyle \\sin \\frac{\\pi}{3}$ \u306e\u5024\u306f…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[54]:<\/div>\n
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sin<\/span>(<\/span>pi<\/span>\/<\/span>3<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[54]:<\/div>\n
$\\displaystyle \\frac{\\sqrt{3}}{2}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u5ea6\u304b\u3089\u30e9\u30b8\u30a2\u30f3\u3078\u306e\u5909\u63db rad()<\/code><\/h5>\n
\u5ea6\uff08\u00b0\uff09\u304b\u3089\u30e9\u30b8\u30a2\u30f3\u3078\u306e\u5909\u63db\u306f SymPy \u3067\u306f rad()<\/code> \u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n
$\\displaystyle 30^{\\circ} = \\frac{\\pi}{6}\\, \\mbox{(rad)}$ \u3092\u78ba\u304b\u3081\u308b\u306b\u306f…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[55]:<\/div>\n
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rad<\/span>(<\/span>30<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[55]:<\/div>\n
$\\displaystyle \\frac{\\pi}{6}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u30e9\u30b8\u30a2\u30f3\u304b\u3089\u5ea6\u3078\u306e\u5909\u63db deg()<\/code><\/h5>\n
\u9006\u306b\uff0c\u30e9\u30b8\u30a2\u30f3\u304b\u3089\u5ea6\uff08\u00b0\uff09\u3078\u306e\u5909\u63db\u306f SymPy \u3067\u306f deg()<\/code> \u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n
$\\displaystyle \\frac{\\pi}{4}\\, \\mbox{(rad)} = 45^{\\circ}$ \u3092\u78ba\u304b\u3081\u308b\u306b\u306f…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[56]:<\/div>\n
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deg<\/span>(<\/span>pi<\/span>\/<\/span>4<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[56]:<\/div>\n
$\\displaystyle 45$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u52a0\u6cd5\u5b9a\u7406<\/h5>\n
$\\sin (x + y) = \\sin x \\, \\cos y + \\cos x \\, \\sin y$ \u304a\u3088\u3073<\/p>\n
$\\cos (x + y) = \\cos x \\, \\cos y \u2013\\sin x \\, \\sin y$ \u306e\u78ba\u8a8d\u3002<\/p>\n
\u4e09\u89d2\u95a2\u6570\u3092\u300c\u5c55\u958b\u300d\u3059\u308b\u3068\u304d\u306f\uff0cexpand()<\/code> \u95a2\u6570\u306b trig = True<\/code> \u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u3064\u3051\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[57]:<\/div>\n
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Eq<\/span>(<\/span>sin<\/span>(<\/span>x<\/span> +<\/span> y<\/span>),<\/span> \r\n   expand<\/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
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Out[57]:<\/div>\n
$\\displaystyle \\sin{\\left(x + y \\right)} = \\sin{\\left(x \\right)} \\cos{\\left(y \\right)} + \\sin{\\left(y \\right)} \\cos{\\left(x \\right)}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[58]:<\/div>\n
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Eq<\/span>(<\/span>cos<\/span>(<\/span>x<\/span> +<\/span> y<\/span>),<\/span> \r\n   expand<\/span>(<\/span>cos<\/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
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Out[58]:<\/div>\n
$\\displaystyle \\cos{\\left(x + y \\right)} = -\\sin{\\left(x \\right)} \\sin{\\left(y \\right)} + \\cos{\\left(x \\right)} \\cos{\\left(y \\right)}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u25cb\u7df4\u7fd2\uff1a$\\tan$ \u306e\u52a0\u6cd5\u5b9a\u7406<\/h5>\n
$\\tan(x+y)$ \u3092 $\\tan x$ \u3068 $\\tan y$ \u3092\u4f7f\u3063\u3066\u8868\u3057\u306a\u3055\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[\u00a0]:<\/div>\n
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\u25cb\u7df4\u7fd2\uff1a\u4e09\u500d\u89d2\u306e\u516c\u5f0f<\/h5>\n
$\\sin 3x$ \u3092 $\\sin x$ \u305f\u3099\u3051\u3092\u4f7f\u3063\u3066\u8868\u3057\u306a\u3055\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[\u00a0]:<\/div>\n
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\u9006\u4e09\u89d2\u95a2\u6570 asin(x)<\/code>, acos(x)<\/code>, atan(x)<\/code><\/h4>\n
\u9006\u4e09\u89d2\u95a2\u6570\u306f\u4e09\u89d2\u95a2\u6570\u306e\u9006\u95a2\u6570\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\uff0c\u305d\u308c\u305e\u308c<\/p>\n
$\\sin^{-1} x = \\arcsin x = $ asin(x)<\/code>
\n$\\cos^{-1} x = \\arccos x = $ acos(x)<\/code>
\n$\\tan^{-1} x = \\arctan x = $ atan(x)<\/code><\/p>\n
\u3068\u66f8\u304d\u307e\u3059\u3002\u9006\u95a2\u6570\u3067\u3059\u304b\u3089\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064\u306f\u305a\u3067\u3059\u3002<\/p>\n
$\\sin\\left(\\sin^{-1} x\\right) = x$
\n$\\cos\\left(\\cos^{-1} x\\right) = x$
\n$\\tan\\left(\\tan^{-1} x\\right) = x$<\/p>\n
\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[59]:<\/div>\n
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sin<\/span>(<\/span>asin<\/span>(<\/span>x<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[59]:<\/div>\n
$\\displaystyle x$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[60]:<\/div>\n
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cos<\/span>(<\/span>acos<\/span>(<\/span>x<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[60]:<\/div>\n
$\\displaystyle x$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[61]:<\/div>\n
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tan<\/span>(<\/span>atan<\/span>(<\/span>x<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[61]:<\/div>\n
$\\displaystyle x$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u3057\u304b\u3057\uff0c$\\sin^{-1} \\left(\\sin x\\right) = x$ \u306a\u3069\u3068\u306f\u4e00\u822c\u306b\u306f\u306a\u308a\u307e\u305b\u3093\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[\u00a0]:<\/div>\n
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\u25cb\u7df4\u7fd2\uff1a\u9006\u4e09\u89d2\u95a2\u6570\u306e\u5f15\u6570\u306b\u4e09\u89d2\u95a2\u6570\u3092\u5165\u308c\u308b\u3068<\/h5>\n
\u9006\u4e09\u89d2\u95a2\u6570\u306f\u4e09\u89d2\u95a2\u6570\u306e\u9006\u95a2\u6570\u3067\u306f\u3042\u308b\u304c\uff0c\u4e00\u822c\u306b\u306f\u4ee5\u4e0b\u306e\u5f0f\u306f\u6210\u308a\u7acb\u305f\u306a\u3044<\/strong>\u3002<\/p>\n
\\begin{eqnarray}
\n\\sin^{-1} \\left(\\sin x\\right) &=& x \\\\
\n\\cos^{-1} \\left(\\cos x\\right) &=& x \\\\
\n\\tan^{-1} \\left(\\tan x\\right) &=& x
\n\\end{eqnarray}<\/p>\n
\u3053\u306e\u3053\u3068\u3092\u53cd\u4f8b\u3092\u6319\u3052\u3066\uff08\u3064\u307e\u308a $x$ \u306b\u3042\u308b\u5024\u3092\u5165\u308c\u308b\u3068\u4e0a\u8a18\u306e\u7b49\u53f7\u304c\u6210\u308a\u7acb\u305f\u306a\u3044\u3053\u3068\u3092\uff09\u793a\u305b\u3002<\/p>\n
\u307e\u305f\uff0c\u306a\u305c\u6210\u308a\u7acb\u305f\u306a\u3044\u306e\u304b\u7406\u7531\u3092\u8003\u3048\u3066\u307f\u3088\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[\u00a0]:<\/div>\n
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\u25cb\u7df4\u7fd2\uff1a\u9006\u4e09\u89d2\u95a2\u6570\u306e\u9593\u306e\u95a2\u4fc2\u5f0f<\/h5>\n
\u4ee5\u4e0b\u306e\u95a2\u4fc2\u3092\u78ba\u304b\u3081\u3088\u3002<\/p>\n
$\\displaystyle \\cos^{-1} x + \\sin^{-1} x = \\frac{\\pi}{2}
\n$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[62]:<\/div>\n
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# \u30d2\u30f3\u30c8 acos(x) \u3092 asin(x) \u3092\u4f7f\u3063\u3066\u66f8\u304d\u76f4\u3059<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\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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\u4ee5\u4e0b\u306e\u95a2\u4fc2\u5f0f\u3092 SymPy \u3067\u78ba\u304b\u3081\u308b\u306e\u306f\u96e3\u3057\u305d\u3046\u3067\u3059…<\/p>\n
$\\displaystyle \\tan^{-1} x + \\tan^{-1} \\frac{1}{x} =\u00a0 \\frac{\\pi}{2}
\n$<\/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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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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\u25cb\u7df4\u7fd2\uff1a\u5c4b\u6839\u52fe\u914d<\/h5>\n
\u554f\uff1a\u4eba\u751f\u306b\u306a\u305c\u300c\u9006\u4e09\u89d2\u95a2\u6570\u300d\u304c\u5fc5\u8981\u304b\u3002
\n\u7b54\uff1a\u5bb6\u3092\u5efa\u3066\u308b\u305f\u3081\u306b\u5fc5\u8981\u3067\u3059\u3002\u30ed\u30b0\u30cf\u30a6\u30b9\u3092\u5efa\u3066\u305f\u672c\u4eba\u304c\u8a00\u3063\u3066\u3044\u308b\u306e\u3060\u3089\u9593\u9055\u3044\u306a\u3044\uff01<\/p><\/blockquote>\n
\u5927\u5de5\u3055\u3093\u306f\uff0c\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
\u4e00\u65b9\u3067\uff0c\u50be\u659c\u5929\u4e95\u306b\u3064\u3051\u308b\u7167\u660e\u5668\u5177\u3092\u96fb\u6c17\u5c4b\u3055\u3093\u306b\u554f\u3044\u5408\u308f\u305b\u308b\u3068\uff0c\u50be\u659c\u89d2\u5ea6\u306f\u4f55\u5ea6\u3060\u3068\u805e\u304b\u308c\u307e\u3059\u3002<\/p>\n
\u3064\u307e\u308a\uff0c\u30ed\u30b0\u30cf\u30a6\u30b9\u3092\u5efa\u3066\u308b\u305f\u3081\u306b\u306f\u9006\u4e09\u89d2\u95a2\u6570\uff0c\u7279\u306b $\\tan^{-1} x$ \u304c\u5fc5\u8981\u306b\u306a\u308b\u308f\u3051\u3067\u3059\uff01\uff1f<\/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? \u5c0f\u6570\u70b9\u4ee5\u4e0b1\u6841\u307e\u3067\u306e\u6570\u5024\u3067\u3002<\/p>\n
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8 \u5bf8\u52fe\u914d\u306e\u50be\u659c\u89d2\u5ea6\u3068\u306f\uff0c\u50be\u304d\u304c $\\displaystyle \\tan \\theta = \\frac{8}{10}$ \u3068\u306a\u308b\u89d2\u5ea6 $\\theta$ \u3092\u5ea6\u3067\u8868\u3057\u305f\u3082\u306e\u3060\u304b\u3089…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[\u00a0]:<\/div>\n
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\u4ee5\u4e0b\u306e\u3088\u3046\u306b 1 \u5bf8\u52fe\u914d\u304b\u3089 10 \u5bf8\u52fe\u914d\uff08\u77e9\u52fe\u914d\u3000\u304b\u306d\u3053\u3046\u3070\u3044\uff09\u307e\u3067\u8868\u793a\u3055\u305b\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n
 1 \u5bf8\u52fe\u914d\u306e\u50be\u659c\u89d2\u5ea6\u306f ##.#\u00b0\r\n 2 \u5bf8\u52fe\u914d\u306e\u50be\u659c\u89d2\u5ea6\u306f ##.#\u00b0\r\n 3 \u5bf8\u52fe\u914d\u306e\u50be\u659c\u89d2\u5ea6\u306f ##.#\u00b0\r\n     ...\r\n\r\n10 \u5bf8\u52fe\u914d\u306e\u50be\u659c\u89d2\u5ea6\u306f ##.#\u00b0<\/code><\/pre>\n<\/div>\n<\/div>\n<\/div>\n
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\u53cc\u66f2\u7dda\u95a2\u6570 sinh(x)<\/code>, cosh(x)<\/code>, tanh(x)<\/code><\/h4>\n
\u53cc\u66f2\u7dda\u95a2\u6570\u306f\u6307\u6570\u95a2\u6570\u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n
$\\displaystyle \\cosh x \\equiv \\frac{e^{x} + e^{-x}}{2} =$ cosh(x)<\/code><\/p>\n
$\\displaystyle \\sinh x \\equiv \\frac{e^{x} -e^{-x}}{2} =$ sinh(x)<\/code><\/p>\n
$\\displaystyle \\tanh x \\equiv \\frac{\\sinh x}{\\cosh x} = \\frac{e^{x} -e^{-x}}{e^{x} + e^{-x}} =$ tanh(x)<\/code><\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\u25cb\u7df4\u7fd2\uff1a\u53cc\u66f2\u7dda\u95a2\u6570\u3092\u6307\u6570\u95a2\u6570\u3067\u8868\u3059<\/h5>\n
\u53cc\u66f2\u7dda\u95a2\u6570\u3092\u6307\u6570\u95a2\u6570 exp()<\/code> \u3067\u66f8\u304d\u76f4\u3059\u306b\u306f\uff0c\u66f8\u304d\u76f4\u3059\u95a2\u6570\u306b .rewrite(exp)<\/code> \u3092\u4ed8\u3051\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[63]:<\/div>\n
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Eq<\/span>(<\/span>cosh<\/span>(<\/span>x<\/span>),<\/span>\r\n   cosh<\/span>(<\/span>x<\/span>)<\/span>.<\/span>rewrite<\/span>(<\/span>exp<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[63]:<\/div>\n
$\\displaystyle \\cosh{\\left(x \\right)} = \\frac{e^{x}}{2} + \\frac{e^{-x}}{2}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$\\sinh x, \\ \\tanh x$ \u306b\u3064\u3044\u3066\u3082\u540c\u69d8\u306b\u6307\u6570\u95a2\u6570\u3067\u66f8\u304d\u76f4\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[\u00a0]:<\/div>\n
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$\\cosh^2 x -\\sinh^2 x = 1$ \u3092 SimPy \u3067\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3059\u3002simplify()<\/code> \u3067\u300c\u7c21\u5358\u5316\u300d\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[64]:<\/div>\n
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eq<\/span> =<\/span> cosh<\/span>(<\/span>x<\/span>)<\/span>**<\/span>2<\/span> -<\/span> sinh<\/span>(<\/span>x<\/span>)<\/span>**<\/span>2<\/span>\r\n\r\nEq<\/span>(<\/span>eq<\/span>,<\/span> simplify<\/span>(<\/span>eq<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[64]:<\/div>\n
$\\displaystyle -\\sinh^{2}{\\left(x \\right)} + \\cosh^{2}{\\left(x \\right)} = 1$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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$1 -\\tanh^2 x$ \u3082\u7c21\u5358\u5316\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[\u00a0]:<\/div>\n
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\u52a0\u6cd5\u5b9a\u7406<\/h5>\n
\u53cc\u66f2\u7dda\u95a2\u6570\u306b\u3082\uff0c\u4e09\u89d2\u95a2\u6570\u306e\u5834\u5408\u3068\u4f3c\u305f\u3088\u3046\u306a\u52a0\u6cd5\u5b9a\u7406\u304c\u3042\u308a\u307e\u3059\u3002expand()<\/code> \u306f\u300c\u5c55\u958b\u300d\u3059\u308b\u95a2\u6570\u3067\u3059\u3002\u53cc\u66f2\u7dda\u95a2\u6570\u3092\u300c\u5c55\u958b\u300d\u3059\u308b\u3068\u304d\u306f\uff0c\uff08\u53cc\u66f2\u7dda\u95a2\u6570\u306f\u4e09\u89d2\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304c\uff09\u4e09\u89d2\u95a2\u6570\u306e\u5834\u5408\u3068\u540c\u69d8\u306b<\/p>\n
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trig<\/span> =<\/span> True<\/span>\r\n<\/pre>\n<\/div>\n
\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u3064\u3051\u307e\u3059\u3002<\/p>\n
$\\displaystyle \\cosh (x + y) = \\cosh x\\, \\cosh y + \\sinh x\\, \\sinh y$ \u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[65]:<\/div>\n
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Eq<\/span>(<\/span>expand<\/span>(<\/span>cosh<\/span>(<\/span>x<\/span> +<\/span> y<\/span>)),<\/span> \r\n   expand<\/span>(<\/span>cosh<\/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
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Out[65]:<\/div>\n
$\\displaystyle \\cosh{\\left(x + y \\right)} = \\sinh{\\left(x \\right)} \\sinh{\\left(y \\right)} + \\cosh{\\left(x \\right)} \\cosh{\\left(y \\right)}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u9006\u306b\uff0c\u53f3\u8fba\u306e\u5f0f\u304c\u5de6\u8fba\u306b\u306a\u308b\u3053\u3068\u3092\u793a\u3059\u306b\u306f\uff0csimplify()<\/code> \u3067\u826f\u3055\u305d\u3046\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[66]:<\/div>\n
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sscc<\/span> =<\/span> sinh<\/span>(<\/span>x<\/span>)<\/span>*<\/span>sinh<\/span>(<\/span>y<\/span>)<\/span> +<\/span> cosh<\/span>(<\/span>x<\/span>)<\/span>*<\/span>cosh<\/span>(<\/span>y<\/span>)<\/span>\r\n\r\nEq<\/span>(<\/span>sscc<\/span>,<\/span> simplify<\/span>(<\/span>sscc<\/span>))<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[66]:<\/div>\n
$\\displaystyle \\sinh{\\left(x \\right)} \\sinh{\\left(y \\right)} + \\cosh{\\left(x \\right)} \\cosh{\\left(y \\right)} = \\cosh{\\left(x + y \\right)}$<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u25cb\u7df4\u7fd2\uff1a\u53cc\u66f2\u7dda\u95a2\u6570\u306e\u52a0\u6cd5\u5b9a\u7406<\/h5>\n
$\\sinh(x+y)$\uff0c$\\tanh(x+y)$ \u306b\u3064\u3044\u3066\u306e\u52a0\u6cd5\u5b9a\u7406\u3092\u78ba\u8a8d\u3057\u306a\u3055\u3044\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[\u00a0]:<\/div>\n
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In\u00a0[\u00a0]:<\/div>\n
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\u9006\u53cc\u66f2\u7dda\u95a2\u6570 asinh(x)<\/code>, acosh(x)<\/code>, atanh(x)<\/code><\/h4>\n
\u9006\u53cc\u66f2\u7dda\u95a2\u6570\u306f\u53cc\u66f2\u7dda\u95a2\u6570\u306e\u9006\u95a2\u6570\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\uff0c\u305d\u308c\u305e\u308c<\/p>\n
$\\sinh^{-1} x = \\mbox{arsinh}\\ x = $ asinh(x)<\/code>
\n$\\cosh^{-1} x = \\mbox{arcosh}\\ x = $ acosh(x)<\/code>
\n$\\tanh^{-1} x = \\mbox{artanh}\\ x = $ atanh(x)<\/code><\/p>\n
\u3068\u66f8\u304d\u307e\u3059\u3002\uff08ar \u3067\u3042\u308a\uff0carc \u3068\u306f\u66f8\u304b\u306a\u3044\u3002\uff09<\/p>\n