{"id":2182,"date":"2023-04-08T11:16:34","date_gmt":"2023-04-08T02:16:34","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2182"},"modified":"2023-04-09T11:26:07","modified_gmt":"2023-04-09T02:26:07","slug":"maxima-%e3%81%a6%e3%82%99-1-%e5%a4%89%e6%95%b0%e9%96%a2%e6%95%b0%e3%81%ae%e5%be%ae%e5%88%86","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/maxima-%e3%81%a7%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6b\/maxima-%e3%81%a6%e3%82%99-1-%e5%a4%89%e6%95%b0%e9%96%a2%e6%95%b0%e3%81%ae%e5%be%ae%e5%88%86\/","title":{"rendered":"Maxima \u3066\u3099 1 \u5909\u6570\u95a2\u6570\u306e\u5fae\u5206"},"content":{"rendered":"

<\/p>\n

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<\/div>\n
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    \n
  1. Maxima \u3067\u306f\u30bb\u30eb\u306b\u5b9f\u884c\u6587\u3092\u66f8\u304d\uff0c<\/li>\n
  2. \u884c\u672b\u306b\u30bb\u30df\u30b3\u30ed\u30f3 ; \u3092\u5165\u529b\u5f8c\uff0c<\/li>\n
  3. 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
  4. 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<\/ol>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n

    \u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9<\/h3>\n

    $f(x) = x^2$ \u3092\u5fae\u5206\u3059\u308b\u3002<\/p>\n

    Maxima \u3067\u306f\u95a2\u6570\u306e\u5b9a\u7fa9\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b :=<\/code> \u3092\u4f7f\u3044\u307e\u3059\uff0e<\/p>\n

    \n
    f<\/span>(<\/span>x<\/span>)<\/span> :=<\/span> x<\/span>**<\/span>2<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[1]:<\/div>\n
    \n
    \n
    \n
    \/* Maxima \u3067\u306e\u95a2\u6570 f(x) \u306e\u5b9a\u7fa9 *\/<\/span>\r\n\r\nf<\/span>(<\/span>x<\/span>)<\/span> :=<\/span> x<\/span>**<\/span>2<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[1]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{1}$}f\\left(x\\right):=x^2\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u307e\u305a\u306f\u4ee5\u4e0b\u306e\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\u306b\u57fa\u3065\u3044\u3066\u6975\u9650\u3092\u8a08\u7b97\u3059\u308b\u3002<\/p>\n
    $$ \\lim_{h \\rightarrow 0} \\frac{f(x+h) – f(x)}{h}$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[2]:<\/div>\n
    \n
    \n
    \n
    limit<\/span>((<\/span>f<\/span>(<\/span>x<\/span> +<\/span> h<\/span>)<\/span> -<\/span> f<\/span>(<\/span>x<\/span>))<\/span>\/<\/span>h<\/span>, h<\/span>, 0<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[2]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{2}$}2\\,x\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u3068\u3082\u304b\u304f\u7b54\u3048\u3092\u6c42\u3081\u305f\u3044\u5834\u5408\u306f\u3053\u308c\u3067 OK \u3067\u3059\u3002\u6975\u9650\u306e\u8a08\u7b97\u3092\u3059\u308b\u524d\u306e\u8868\u793a\u3092\u3057\u305f\u3044\u5834\u5408\u306f
    \n'limit((f(x + h) - f(x))\/h, h, 0)<\/code>
    \n\u306e\u3088\u3046\u306b '<\/code> \u3067\u59cb\u3081\u308b\u3068\uff0c\u5b9f\u884c\u305b\u305a\u306b\u8868\u793a\u306e\u307f\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[3]:<\/div>\n
    \n
    \n
    \n
    '<\/span>limit<\/span>((<\/span>f<\/span>(<\/span>x<\/span> +<\/span> h<\/span>)<\/span> -<\/span> f<\/span>(<\/span>x<\/span>))<\/span>\/<\/span>h<\/span>, h<\/span>, 0<\/span>)<\/span> =<\/span> \r\n limit<\/span>((<\/span>f<\/span>(<\/span>x<\/span> +<\/span> h<\/span>)<\/span> -<\/span> f<\/span>(<\/span>x<\/span>))<\/span>\/<\/span>h<\/span>, h<\/span>, 0<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[3]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{3}$}\\lim_{h\\rightarrow 0}{\\frac{\\left(x+h\\right)^2-x^2}{h}}=2\\,x\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u5fae\u5206\u3092\u8a08\u7b97\u3059\u308b\u306e\u306b\u3044\u3061\u3044\u3061\u6975\u9650\u3092\u3068\u3063\u3066\u3044\u308b\u308f\u3051\u306b\u306f\u3044\u304d\u307e\u305b\u3093\u3002\u6b21\u306b\u5fae\u5206\u3092\u884c\u3046\u95a2\u6570 diff()<\/code> \u3092\u4f7f\u3063\u3066\u76f4\u63a5 f(x)<\/code> \u3092\u5fae\u5206\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[4]:<\/div>\n
    \n
    \n
    \n
    \/* \u5fae\u5206\u3092\u884c\u3046 diff() \u95a2\u6570\u3067\u76f4\u63a5\u5fae\u5206\u3057\u307e\u3059\u3002*\/<\/span>\r\n\r\ndiff<\/span>(<\/span>f<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[4]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{4}$}2\\,x\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[5]:<\/div>\n
    \n
    \n
    \n
    \/* f(x) \u306e\u5b9a\u7fa9\u3092\u306a\u3057\u306b\u3057\u307e\u3059\u3002*\/<\/span>\r\nkill<\/span>(<\/span>f<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u5fae\u5206\u6cd5\u306e\u516c\u5f0f<\/h3>\n
    \u5fae\u5206\u6cd5\u306e\u516c\u5f0f<\/a> \u306b\u3042\u308b\u516c\u5f0f\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    $\\displaystyle 1. \\left\\{ f(x) \\pm g(x) \\right\\}’ = f'(x) \\pm g'(x)$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[6]:<\/div>\n
    \n
    \n
    \n
    '<\/span>diff<\/span>(<\/span> (<\/span>f<\/span>(<\/span>x<\/span>)<\/span> +<\/span> g<\/span>(<\/span>x<\/span>))<\/span>, x<\/span> )<\/span> =<\/span> \r\n diff<\/span>(<\/span> (<\/span>f<\/span>(<\/span>x<\/span>)<\/span> +<\/span> g<\/span>(<\/span>x<\/span>))<\/span>, x<\/span> )<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[6]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{6}$}\\frac{d}{d\\,x}\\,\\left(g\\left(x\\right)+f\\left(x\\right)\\right)=\\frac{d}{d\\,x}\\,g\\left(x\\right)+\\frac{d}{d\\,x}\\,f\\left(x\\right)\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    $\\displaystyle 2. \\left\\{ c f(x) \\right\\}’ = c f'(x) $<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[7]:<\/div>\n
    \n
    \n
    \n
    '<\/span>diff<\/span>((<\/span>c<\/span>*<\/span>f<\/span>(<\/span>x<\/span>))<\/span>, x<\/span>)<\/span> =<\/span> \r\n diff<\/span>((<\/span>c<\/span>*<\/span>f<\/span>(<\/span>x<\/span>))<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[7]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{7}$}\\frac{d}{d\\,x}\\,\\left(c\\,f\\left(x\\right)\\right)=c\\,\\left(\\frac{d}{d\\,x}\\,f\\left(x\\right)\\right)\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    $\\displaystyle 3. \\left\\{ f(x)\\, g(x) \\right\\}’ = f'(x)\\,g(x) + f(x)\\,g'(x) $<\/p>\n
    \u30e9\u30a4\u30d7\u30cb\u30c3\u30c4\u30eb\u30fc\u30eb\u3092\u77e5\u3063\u3066\u3044\u308b\u304b\uff1f<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[8]:<\/div>\n
    \n
    \n
    \n
    '<\/span>diff<\/span>(<\/span> (<\/span>f<\/span>(<\/span>x<\/span>)<\/span>*<\/span>g<\/span>(<\/span>x<\/span>))<\/span>, x<\/span> )<\/span> =<\/span> \r\n diff<\/span>(<\/span> (<\/span>f<\/span>(<\/span>x<\/span>)<\/span>*<\/span>g<\/span>(<\/span>x<\/span>))<\/span>, x<\/span> )<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[8]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{8}$}\\frac{d}{d\\,x}\\,\\left(f\\left(x\\right)\\,g\\left(x\\right)\\right)=f\\left(x\\right)\\,\\left(\\frac{d}{d\\,x}\\,g\\left(x\\right)\\right)+g\\left(x\\right)\\,\\left(\\frac{d}{d\\,x}\\,f\\left(x\\right)\\right)\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    $\\displaystyle 4. \\left\\{ \\frac{1}{g(x)} \\right\\}’ = – \\frac{g'(x)}{\\left\\{g(x)\\right\\}^2} $<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[9]:<\/div>\n
    \n
    \n
    \n
    '<\/span>diff<\/span>(<\/span>1\/<\/span>g<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> \r\n diff<\/span>(<\/span>1\/<\/span>g<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[9]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{9}$}\\frac{d}{d\\,x}\\,\\left(\\frac{1}{g\\left(x\\right)}\\right)=-\\frac{\\frac{d}{d\\,x}\\,g\\left(x\\right)}{g\\left(x\\right)^2}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    $\\displaystyle 5. \\left\\{ \\frac{f(x)}{g(x)} \\right\\}’ = \\frac{f'(x)\\,g(x) – f(x)\\, g'(x)}{\\left\\{g(x)\\right\\}^2} $<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[10]:<\/div>\n
    \n
    \n
    \n
    '<\/span>diff<\/span>(<\/span>f<\/span>(<\/span>x<\/span>)<\/span>\/<\/span>g<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> \r\n diff<\/span>(<\/span>f<\/span>(<\/span>x<\/span>)<\/span>\/<\/span>g<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[10]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{10}$}\\frac{d}{d\\,x}\\,\\left(\\frac{f\\left(x\\right)}{g\\left(x\\right)}\\right)=\\frac{\\frac{d}{d\\,x}\\,f\\left(x\\right)}{g\\left(x\\right)}-\\frac{f\\left(x\\right)\\,\\left(\\frac{d}{d\\,x}\\,g\\left(x\\right)\\right)}{g\\left(x\\right)^2}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    ratsimp()<\/code> \u95a2\u6570\u306f\uff0c\u901a\u5206\u306a\u3069\u3092\u884c\u306a\u3063\u3066\u7c21\u5358\u5316\u3057\u3066\u304f\u308c\u307e\u3059\u3002<\/p>\n
    %<\/code> \u306f\u76f4\u524d\u306e\u7d50\u679c\u3092\u3042\u3089\u308f\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[11]:<\/div>\n
    \n
    \n
    \n
    ratsimp<\/span>(<\/span>%<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[11]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{11}$}\\frac{d}{d\\,x}\\,\\left(\\frac{f\\left(x\\right)}{g\\left(x\\right)}\\right)=-\\frac{f\\left(x\\right)\\,\\left(\\frac{d}{d\\,x}\\,g\\left(x\\right)\\right)-g\\left(x\\right)\\,\\left(\\frac{d}{d\\,x}\\,f\\left(x\\right)\\right)}{g\\left(x\\right)^2}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u5408\u6210\u95a2\u6570\u306e\u5fae\u5206\u6cd5<\/h3>\n
    $y = y(u), \\ u = u(x)$\uff0c\u3064\u307e\u308a $y$ \u304c $u$ \u3092\u901a\u3057\u3066 $x$ \u306e\u95a2\u6570\u3067\u3042\u308b\u3068\u304d\uff0c<\/p>\n
    $$\\frac{dy}{dx} = \\frac{dy}{du} \\frac{du}{dx}$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[12]:<\/div>\n
    \n
    \n
    \n
    \/* y \u306f u \u306b\u4f9d\u5b58\u3059\u308b\uff0c\u3068\u5ba3\u8a00\u3059\u308b\uff0e*\/<\/span>\r\ndepends<\/span>(<\/span>y<\/span>, u<\/span>)<\/span>;\r\n\/* u \u306f x \u306b\u4f9d\u5b58\u3059\u308b\uff0c\u3068\u5ba3\u8a00\u3059\u308b\uff0e*\/<\/span>\r\ndepends<\/span>(<\/span>u<\/span>, x<\/span>)<\/span>;\r\n'<\/span>diff<\/span>(<\/span>y<\/span>, x<\/span>)<\/span> =<\/span> diff<\/span>(<\/span>y<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[12]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{12}$}\\left[ y\\left(u\\right) \\right] \\]<\/div>\n<\/div>\n
    \n
    Out[12]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{13}$}\\left[ u\\left(x\\right) \\right] \\]<\/div>\n<\/div>\n
    \n
    Out[12]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{14}$}\\frac{d}{d\\,x}\\,y=\\frac{d}{d\\,x}\\,u\\,\\left(\\frac{d}{d\\,u}\\,y\\right)\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[13]:<\/div>\n
    \n
    \n
    \n
    \/* \u4eca\u5f8c\u306e\u305f\u3081\u306b\u5ba3\u8a00\u3092\u6d88\u53bb *\/<\/span>\r\nkill<\/span>(<\/span>y<\/span>, u<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[13]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{15}$}\\mathbf{done}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[14]:<\/div>\n
    \n
    \n
    \n
    \/* \u4eca\u5ea6\u306f y \u306f x \u306b\u4f9d\u5b58\u3057\u306a\u3044\u306e\u3067... *\/<\/span>\r\n'<\/span>diff<\/span>(<\/span>y<\/span>, x<\/span>)<\/span> =<\/span> diff<\/span>(<\/span>y<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[14]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{16}$}\\frac{d}{d\\,x}\\,y=0\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u4f8b\uff1a $ y = (a x^2 + b x + c)^5 $ \u306e\u5fae\u5206\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[15]:<\/div>\n
    \n
    \n
    \n
    u<\/span>:<\/span> a<\/span>*<\/span>x<\/span>**<\/span>2<\/span> +<\/span> b<\/span>*<\/span>x<\/span> +<\/span> c<\/span>;\r\ny<\/span>:<\/span> u<\/span>**<\/span>5<\/span>;\r\ndiff<\/span>(<\/span>y<\/span>, x<\/span>)<\/span>;\r\n\r\n\/* \u5f8c\u3005\u306e\u305f\u3081\u306b *\/<\/span>\r\nkill<\/span>(<\/span>y<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[15]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{17}$}a\\,x^2+b\\,x+c\\]<\/div>\n<\/div>\n
    \n
    Out[15]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{18}$}\\left(a\\,x^2+b\\,x+c\\right)^5\\]<\/div>\n<\/div>\n
    \n
    Out[15]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{19}$}5\\,\\left(2\\,a\\,x+b\\right)\\,\\left(a\\,x^2+b\\,x+c\\right)^4\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u3079\u304d\u95a2\u6570\u306e\u5fae\u5206<\/h3>\n
    \u3079\u304d\u4e57\uff08\u7d2f\u4e57\uff09\u306f **<\/code> \u3067\u8868\u3059\uff08^<\/code>\u3067\u3082\u3044\u3044\u3067\u3059\u304c\uff0cMaxima \u4ee5\u5916\u306e\u51e6\u7406\u7cfb\u3067\u306f ^<\/code> \u304c\u4f7f\u3048\u306a\u3044\u5834\u5408\u3082\u3042\u308b\u306e\u3067 **<\/code> \u3067\u901a\u3057\u307e\u3059\uff09\u3002$x^p$ \u306f\uff0cx**p<\/code>\u3002\u3079\u304d\u95a2\u6570 x**p<\/code> \u3092\u76f4\u63a5\u5fae\u5206\u3057\u3066\u307f\u307e\u3059\u3002\u5fae\u5206\u306b\u306f diff()<\/code> \u95a2\u6570\u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[16]:<\/div>\n
    \n
    \n
    \n
    '<\/span>diff<\/span>(<\/span>x<\/span>**<\/span>p<\/span>, x<\/span>)<\/span> =<\/span> diff<\/span>(<\/span>x<\/span>**<\/span>p<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    Out[16]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{21}$}\\frac{d}{d\\,x}\\,x^{p}=p\\,x^{p-1}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u4f8b\u3068\u3057\u3066\uff0c\u3079\u304d\u95a2\u6570\u306e\u5408\u6210\u95a2\u6570\u3067\u3042\u308b\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u95a2\u6570\u306e\u5fae\u5206\u3002<\/p>\n
    $$\\frac{d}{dx} \\frac{1}{\\sqrt{1 + x^2}}$$<\/p>\n
    $\\sqrt{x} = $ sqrt(x)<\/code> \u3068\u66f8\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[17]:<\/div>\n
    \n
    \n
    \n
    '<\/span>diff<\/span>(<\/span>1\/<\/span>sqrt<\/span>(<\/span>1<\/span> +<\/span> x<\/span>**<\/span>2<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> \r\n diff<\/span>(<\/span>1\/<\/span>sqrt<\/span>(<\/span>1<\/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[17]:<\/div>\n
    \\[\\tag{${\\it \\%o}_{22}$}\\frac{d}{d\\,x}\\,\\left(\\frac{1}{\\sqrt{x^2+1}}\\right)=-\\frac{x}{\\left(x^2+1\\right)^{\\frac{3}{2}}}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    \u53c2\u8003\uff1a\u3079\u304d\u95a2\u6570\u306e\u30b0\u30e9\u30d5<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    $y = x^2$ \u3092 $ -3 \\leq x 3$ \u306e\u7bc4\u56f2\u3067\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u4f8b\u30022\u6b21\u5143\u30b0\u30e9\u30d5\u306f plot2d()<\/code> \u3067\u63cf\u304d\u307e\u3059\u3002(darw2d()<\/code> \u3067\u3082\u63cf\u3051\u307e\u3059\u3002plot \u7cfb\u3068 draw \u7cfb\u3067\u306f\u66f8\u5f0f\u304c\u7570\u306a\u308a\u307e\u3059\u3002
    \n\u3053\u3053\u3067\u306f plot2d()<\/code> \u3067\u8a71\u3092\u9032\u3081\u307e\u3059\u304c\uff0c plot2d()<\/code> \u3068 darw2d()<\/code> \u306e\u5bfe\u5fdc\u306b\u3064\u3044\u3066\u306f\u300c\u53c2\u8003\uff1aMaxima \u3067\u521d\u7b49\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f<\/a>\u300d\u306a\u3069\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002)<\/p>\n
    plot2d()<\/code> \u306f \u884c\u672b\u3092 $<\/code> \u3068\u3057\u3066\u3082\u30b0\u30e9\u30d5\u3092\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    In\u00a0[18]:<\/div>\n
    \n
    \n
    \n
    plot2d<\/span>(<\/span>x<\/span>**<\/span>2<\/span>, [<\/span>x<\/span>, -<\/span>3<\/span>, 3])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    \n
    \n
    <\/div>\n
    \n
    <\/p>\n
    \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
    \n
    <\/div>\n
    \n
    \n
    $y = x, x^2, x^3$ \u3092 $ -3 \\leq x 3$ \u306e\u7bc4\u56f2\u3067\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u4f8b\u3002<\/p>\n
      \n
    • \u8907\u6570\u306e\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u307e\u3068\u3081\u3066\u63cf\u304f\u3068\u304d\u306f [x, x**2, x**3]<\/code> \u306a\u3069\u306e\u3088\u3046\u306b\u3057\u307e\u3059\u3002<\/li>\n
    • $y$ \u306e\u8868\u793a\u7bc4\u56f2\u3092\u8a2d\u5b9a\u3059\u308b\u3068\u304d\u306f [y, -3, 7]<\/code> \u306a\u3069\u306e\u3088\u3046\u306b\u3057\u307e\u3059\u3002<\/li>\n
    • \u51e1\u4f8b\uff08legend\uff09\u306e\u4f4d\u7f6e\u3092\u5909\u66f4\u3059\u308b\u306e\u306b gnuplot_preamble<\/code> \u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u4f7f\u3063\u3066\u3044\u307e\u3059\u3002<\/li>\n
    • grid2d<\/code> \u30aa\u30d7\u30b7\u30e7\u30f3\u3082\u3064\u3051\u3066\u307f\u307e\u3057\u305f\u3002<\/li>\n
    • plot2d()<\/code> \u306e\u6700\u5f8c\u306e\u30ed\u30b0\u51fa\u529b\u304c\u4e0d\u8981\u306a\u5834\u5408\u306f\uff0c\u884c\u672b\u306b $<\/code> \u3092\u3064\u3051\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      In\u00a0[19]:<\/div>\n
      \n
      \n
      \n
      plot2d<\/span>([<\/span>x<\/span>, x<\/span>**<\/span>2<\/span>, x<\/span>**<\/span>3]<\/span>, [<\/span>x<\/span>, -<\/span>3<\/span>, 3]<\/span>, [<\/span>y<\/span>, -<\/span>3<\/span>, 7]<\/span>, \r\n       [<\/span>gnuplot_preamble<\/span>, \"set key bottom right\"<\/span>]<\/span>, grid2d<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      \n
      \n
      <\/div>\n
      \n
      <\/p>\n
      \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
      \n
      <\/div>\n
      \n
      \n
      $y = x, x^{1\/2}, x^{1\/3}$ \u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u4f8b\u3067\u3059\u3002<\/p>\n
        \n
      • \u51e1\u4f8b\uff08legend\uff09\u3092\u6307\u5b9a\u3059\u308b\u5834\u5408\u306f [legend, ...]<\/code> \u306e\u3088\u3046\u306b\u66f8\u304d\u307e\u3059\u3002<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        In\u00a0[20]:<\/div>\n
        \n
        \n
        \n
        plot2d<\/span>([<\/span>x<\/span>, x<\/span>**<\/span>(<\/span>1\/<\/span>2<\/span>)<\/span>, x<\/span>**<\/span>(<\/span>1\/<\/span>3<\/span>)]<\/span>, [<\/span>x<\/span>, 0<\/span>, 3]<\/span>, \r\n       [<\/span>legend<\/span>, \"x\"<\/span>, \"x^(1\/2)\"<\/span>, \"x^(1\/3)\"<\/span>]<\/span>,\r\n       [<\/span>gnuplot_preamble<\/span>, \"set key top left\"<\/span>]<\/span>, grid2d<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        \n
        <\/div>\n
        \n
        <\/p>\n
        \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        <\/div>\n
        \n
        \n
        $y = x^{-2}, \\ x^{-3}$ \u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u4f8b\u3002$x=0$ \u3067\u767a\u6563\u3059\u308b\u305f\u3081\u6587\u53e5\u3092\u3064\u3051\u3089\u308c\u307e\u3059\u304c\uff0c\u3061\u3083\u3093\u3068\u63cf\u3044\u3066\u304f\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        In\u00a0[21]:<\/div>\n
        \n
        \n
        \n
        plot2d<\/span>([<\/span>1\/<\/span>x<\/span>**<\/span>2<\/span>, 1\/<\/span>x<\/span>**<\/span>3]<\/span>, [<\/span>x<\/span>, -<\/span>3<\/span>, 3]<\/span>, [<\/span>y<\/span>, -<\/span>5<\/span>, 5])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        \n
        <\/div>\n
        \n
        plot2d: expression evaluates to non-numeric value somewhere in plotting range.\r\nplot2d: expression evaluates to non-numeric value somewhere in plotting range.\r\n<\/pre>\n<\/div>\n<\/div>\n
        \n
        <\/div>\n
        \n
        <\/p>\n
        \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        <\/div>\n
        \n
        \n
        \u6307\u6570\u95a2\u6570\u306e\u5fae\u5206<\/h3>\n
        \u5ff5\u306e\u305f\u3081\uff0cMaxima \u304c $\\displaystyle \\lim_{h \\rightarrow 0}(1 + h)^{\\frac{1}{h}}$ \u304c\u308f\u304b\u308b\u304b\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        In\u00a0[22]:<\/div>\n
        \n
        \n
        \n
        '<\/span>limit<\/span>((<\/span>1<\/span> +<\/span> h<\/span>)<\/span>**<\/span>(<\/span>1\/<\/span>h<\/span>)<\/span>, h<\/span>, 0<\/span>)<\/span> =<\/span> \r\n limit<\/span>((<\/span>1<\/span> +<\/span> h<\/span>)<\/span>**<\/span>(<\/span>1\/<\/span>h<\/span>)<\/span>, h<\/span>, 0<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        \n
        Out[22]:<\/div>\n
        \\[\\tag{${\\it \\%o}_{31}$}\\lim_{h\\rightarrow 0}{\\left(h+1\\right)^{\\frac{1}{h}}}=e\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        <\/div>\n
        \n
        \n
        \u30cd\u30a4\u30d4\u30a2\u6570 $e$ \u3092\u5e95\u3068\u3057\u305f\u6307\u6570\u95a2\u6570 $e^x$ \u306f exp(x)<\/code> \u3067\u8868\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        In\u00a0[23]:<\/div>\n
        \n
        \n
        \n
        '<\/span>diff<\/span>(<\/span>exp<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> diff<\/span>(<\/span>exp<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        \n
        Out[23]:<\/div>\n
        \\[\\tag{${\\it \\%o}_{32}$}\\frac{d}{d\\,x}\\,e^{x}=e^{x}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        <\/div>\n
        \n
        \n
        \u304f\u3069\u3044\u3088\u3046\u3067\u3059\u304c\uff0c\u5fae\u5206\u3057\u305f\u7b54\u3048\u3060\u3051\u3092\u77e5\u308a\u305f\u3044\u306a\u3089\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3059\u308b\u3060\u3051\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        In\u00a0[24]:<\/div>\n
        \n
        \n
        \n
        diff<\/span>(<\/span>exp<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        \n
        Out[24]:<\/div>\n
        \\[\\tag{${\\it \\%o}_{33}$}e^{x}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        <\/div>\n
        \n
        \n
        \u53c2\u8003\uff1aMaxima \u306e\u57fa\u672c\u7684\u306a\u5b9a\u6570\u3068\u3057\u3066\uff0c\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n\n\n
        \u3000\u3000\u5186\u5468\u7387 $\\pi$<\/th>\n\u3000\u3000\u30cd\u30a4\u30d4\u30a2\u6570 $e$<\/th>\n\u3000\u3000\u865a\u6570\u5358\u4f4d $i$<\/th>\n\u3000\u3000\u7121\u9650\u5927 $\\infty$<\/th>\n<\/tr>\n<\/thead>\n
        %pi<\/code><\/td>\n%e<\/code><\/td>\n%i<\/code><\/td>\ninf<\/code><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        <\/div>\n
        \n
        \n
        $\\exp(1) = e^1 = e$ \u3067\u3042\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        In\u00a0[25]:<\/div>\n
        \n
        \n
        \n
        exp<\/span>(<\/span>1<\/span>)<\/span> -<\/span> %e<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        \n
        Out[25]:<\/div>\n
        \\[\\tag{${\\it \\%o}_{34}$}0\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        <\/div>\n
        \n
        \n
        float()<\/code> \u95a2\u6570\u3067 %e<\/code> \u3064\u307e\u308a $e$ \u306e\u5024\u3092\u5c0f\u6570\u70b9\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        In\u00a0[26]:<\/div>\n
        \n
        \n
        \n
        float<\/span>(<\/span>%e<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        \n
        Out[26]:<\/div>\n
        \\[\\tag{${\\it \\%o}_{35}$}2.718281828459045\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        <\/div>\n
        \n
        \n
        \u53c2\u8003\uff1a\u6307\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5<\/h4>\n
        $y = e^x, e^{-x}$ \u306e\u30b0\u30e9\u30d5\u3002\u51e1\u4f8b\uff08legend\uff09\u3092\u3064\u3051\u3066\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        In\u00a0[27]:<\/div>\n
        \n
        \n
        \n
        plot2d<\/span>([<\/span>exp<\/span>(<\/span>-<\/span>x<\/span>)<\/span>, exp<\/span>(<\/span>x<\/span>)]<\/span>, [<\/span>x<\/span>, -<\/span>3<\/span>, 3]<\/span>, \r\n       [<\/span>legend<\/span>, \"exp(-x)\"<\/span>, \"exp(x)\"<\/span>]<\/span>, grid2d<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        \n
        <\/div>\n
        \n
        <\/p>\n
        \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        <\/div>\n
        \n
        \n
        \u5bfe\u6570\u95a2\u6570<\/h3>\n
        \u5b9a\u7fa9<\/h4>\n
        \u81ea\u7136\u5bfe\u6570\u306f log(x)<\/code> \u3067\u3059\u3002\u81ea\u7136\u5bfe\u6570\u306f\uff0c\u30cd\u30a4\u30d4\u30a2\u6570 $e$ \u3092\u5e95\u3068\u3057\u305f\u6307\u6570\u95a2\u6570 $e^x$ \u306e\u9006\u95a2\u6570\u3067\u3042\u308b\u304b\u3089\uff0c<\/p>\n
        $$e^{\\log x} = x, \\quad \\log e^x = x$$<\/p>\n
        \u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        In\u00a0[28]:<\/div>\n
        \n
        \n
        \n
        exp<\/span>(<\/span>log<\/span>(<\/span>x<\/span>))<\/span>;\r\nlog<\/span>(<\/span>exp<\/span>(<\/span>x<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        \n
        Out[28]:<\/div>\n
        \\[\\tag{${\\it \\%o}_{38}$}x\\]<\/div>\n<\/div>\n
        \n
        Out[28]:<\/div>\n
        \\[\\tag{${\\it \\%o}_{39}$}x\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        <\/div>\n
        \n
        \n
        \u5fae\u5206<\/h4>\n
        $x$ \u306e\u7d76\u5bfe\u5024 $|x|$ \u306f abs(x)<\/code> \u3068\u8868\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        In\u00a0[29]:<\/div>\n
        \n
        \n
        \n
        '<\/span>diff<\/span>(<\/span>log<\/span>(<\/span>abs<\/span>(<\/span>x<\/span>))<\/span>, x<\/span>)<\/span> =<\/span> \r\n diff<\/span>(<\/span>log<\/span>(<\/span>abs<\/span>(<\/span>x<\/span>))<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n
        \n
        Out[29]:<\/div>\n
        \\[\\tag{${\\it \\%o}_{40}$}\\frac{d}{d\\,x}\\,\\log \\left| x\\right| =\\frac{1}{x}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        <\/div>\n
        \n
        \n
        \u53c2\u8003\uff1a\u5bfe\u6570\u6cd5\u5247<\/h4>\n
          \n
        1. $\\log(x y) = \\log x + \\log y$<\/li>\n
        2. $\\log(x^y) = y \\log x$<\/li>\n<\/ol>\n
          radcan()<\/code> \u95a2\u6570\u306f\u6307\u6570\u95a2\u6570\u3084\u5bfe\u6570\u95a2\u6570\u3092\u542b\u3080\u5f0f\u3092\u7c21\u5358\u5316\u3057\u3066\u304f\u308c\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[30]:<\/div>\n
          \n
          \n
          \n
          log<\/span>(<\/span>x<\/span>*<\/span>y<\/span>)<\/span> =<\/span> radcan<\/span>(<\/span>log<\/span>(<\/span>x<\/span>*<\/span>y<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[30]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{41}$}\\log \\left(x\\,y\\right)=\\log y+\\log x\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[31]:<\/div>\n
          \n
          \n
          \n
          log<\/span>((<\/span>x<\/span>**<\/span>y<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[31]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{42}$}\\log x\\,y\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u4e0a\u5f0f\u306e\u8868\u793a\u304c $\\log x\\, y$ \u3068\u7d1b\u3089\u308f\u3057\u3044\u3067\u3059\u304c\uff0c
          \n$\\left(\\log x\\right) \\cdot y = y \\, \\log x$ \u306e\u3053\u3068\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u53c2\u8003\uff1a\u5bfe\u6570\u95a2\u6570\u306e\u30b0\u30e9\u30d5<\/h4>\n
          $y = \\log x$ \u306e\u30b0\u30e9\u30d5\u3092 $0 < x < 5$ \u306e\u7bc4\u56f2\u3067\u63cf\u304f\u3002$y$ \u306e\u8868\u793a\u7bc4\u56f2\u3092 $ -3 < y < 3$ \u304f\u3089\u3044\u306b\u3057\u3066\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[32]:<\/div>\n
          \n
          \n
          \n
          plot2d<\/span>(<\/span>log<\/span>(<\/span>x<\/span>)<\/span>, [<\/span>x<\/span>, 0.01<\/span>, 5]<\/span>, [<\/span>y<\/span>, -<\/span>3<\/span>, 3]<\/span>, grid2d<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          <\/div>\n
          \n
          <\/p>\n
          \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u4e09\u89d2\u95a2\u6570<\/h3>\n
          \u6027\u8cea<\/h4>\n
          \u4e09\u89d2\u95a2\u6570\u306f sin(x), cos(x), tan(x)<\/code> \u306e\u3088\u3046\u306b\u66f8\u304d\u307e\u3059\u3002<\/p>\n
          $\\sin^2 x + \\cos^2 x = 1$ \u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[33]:<\/div>\n
          \n
          \n
          \n
          sin<\/span>(<\/span>x<\/span>)<\/span>**<\/span>2<\/span> +<\/span> cos<\/span>(<\/span>x<\/span>)<\/span>**<\/span>2<\/span> =<\/span> trigsimp<\/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
          \n
          \n
          \n
          Out[33]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{45}$}\\sin ^2x+\\cos ^2x=1\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u6975\u9650\u516c\u5f0f\u306e\u78ba\u8a8d<\/h4>\n
          \u4e09\u89d2\u95a2\u6570\u306e\u5fae\u5206\u3092\u6c42\u3081\u308b\u305f\u3081\u306b\u306f\uff0c\u4ee5\u4e0b\u306e\u6975\u9650<\/p>\n
          $$ \\lim_{x \\rightarrow 0} \\frac{\\sin x}{x} $$<\/p>\n
          \u306e\u5024\u304c\u5fc5\u8981\u3067\u3057\u305f\u3002\u3053\u306e\u6975\u9650\u304c\u3067\u304d\u308b\u304b\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[34]:<\/div>\n
          \n
          \n
          \n
          '<\/span>limit<\/span>(<\/span>sin<\/span>(<\/span>x<\/span>)<\/span>\/<\/span>x<\/span>, x<\/span>, 0<\/span>)<\/span> =<\/span> \r\n limit<\/span>(<\/span>sin<\/span>(<\/span>x<\/span>)<\/span>\/<\/span>x<\/span>, x<\/span>, 0<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[34]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{46}$}\\lim_{x\\rightarrow 0}{\\frac{\\sin x}{x}}=1\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          $\\displaystyle \\lim_{x \\rightarrow 0} \\frac{1 – \\cos x}{x} = 0$ \u3067\u3042\u308b\u3053\u3068\u3082\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[35]:<\/div>\n
          \n
          \n
          \n
          '<\/span>limit<\/span>((<\/span>1-<\/span>cos<\/span>(<\/span>x<\/span>))<\/span>\/<\/span>x<\/span>, x<\/span>, 0<\/span>)<\/span> =<\/span> \r\n limit<\/span>((<\/span>1-<\/span>cos<\/span>(<\/span>x<\/span>))<\/span>\/<\/span>x<\/span>, x<\/span>, 0<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[35]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{47}$}\\lim_{x\\rightarrow 0}{\\frac{1-\\cos x}{x}}=0\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u52a0\u6cd5\u5b9a\u7406\u306e\u78ba\u8a8d<\/h4>\n
          $\\sin (x + h) = \\sin x \\, \\cos h + \\cos x \\, \\sin h$ \u304a\u3088\u3073<\/p>\n
          $\\cos (x + h) = \\cos x \\, \\cos h – \\sin x \\, \\sin h$ \u306e\u78ba\u8a8d\u3002<\/p>\n
          \u4e09\u89d2\u95a2\u6570\u3092\u300c\u5c55\u958b\u300d\u3059\u308b\u3068\u304d\u306f\uff0ctrigexpand()<\/code> \u95a2\u6570\u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[36]:<\/div>\n
          \n
          \n
          \n
          sin<\/span>(<\/span>x<\/span> +<\/span> h<\/span>)<\/span> =<\/span> trigexpand<\/span>(<\/span>sin<\/span>(<\/span>x<\/span> +<\/span> h<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[36]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{48}$}\\sin \\left(x+h\\right)=\\cos h\\,\\sin x+\\sin h\\,\\cos x\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[37]:<\/div>\n
          \n
          \n
          \n
          cos<\/span>(<\/span>x<\/span> +<\/span> h<\/span>)<\/span> =<\/span> trigexpand<\/span>(<\/span>cos<\/span>(<\/span>x<\/span> +<\/span> h<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[37]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{49}$}\\cos \\left(x+h\\right)=\\cos h\\,\\cos x-\\sin h\\,\\sin x\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u5fae\u5206<\/h4>\n
          \u307e\u305a\u306f\u5c0e\u95a2\u6570\u306e\u5b9a\u7fa9\u306b\u5f93\u3063\u3066 $\\sin x$ \u306e\u5fae\u5206\u3092\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n
          $\\displaystyle \\lim_{h \\rightarrow 0} \\frac{\\sin(x+h) – \\sin (x)}{h} = \\cdots$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[38]:<\/div>\n
          \n
          \n
          \n
          '<\/span>limit<\/span>((<\/span>sin<\/span>(<\/span>x<\/span> +<\/span> h<\/span>)<\/span> -<\/span> sin<\/span>(<\/span>x<\/span>))<\/span>\/<\/span>h<\/span>, h<\/span>, 0<\/span>)<\/span> =<\/span> \r\n limit<\/span>((<\/span>sin<\/span>(<\/span>x<\/span> +<\/span> h<\/span>)<\/span> -<\/span> sin<\/span>(<\/span>x<\/span>))<\/span>\/<\/span>h<\/span>, h<\/span>, 0<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[38]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{50}$}\\lim_{h\\rightarrow 0}{\\frac{\\sin \\left(x+h\\right)-\\sin x}{h}}=\\cos x\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          diff()<\/code> \u95a2\u6570\u3067\u4e09\u89d2\u95a2\u6570\u3092\u5fae\u5206\u3057\u3066\u3082\u540c\u3058\u7b54\u3048\u304c\u51fa\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[39]:<\/div>\n
          \n
          \n
          \n
          '<\/span>diff<\/span>(<\/span>sin<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> \r\n diff<\/span>(<\/span>sin<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[39]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{51}$}\\frac{d}{d\\,x}\\,\\sin x=\\cos x\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          $\\cos x, \\tan x$ \u306e\u5fae\u5206\u306b\u3064\u3044\u3066\u3082 diff()<\/code> \u95a2\u6570\u3067\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[40]:<\/div>\n
          \n
          \n
          \n
          '<\/span>diff<\/span>(<\/span>cos<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> \r\n diff<\/span>(<\/span>cos<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[40]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{52}$}\\frac{d}{d\\,x}\\,\\cos x=-\\sin x\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[41]:<\/div>\n
          \n
          \n
          \n
          '<\/span>diff<\/span>(<\/span>tan<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> \r\n diff<\/span>(<\/span>tan<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[41]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{53}$}\\frac{d}{d\\,x}\\,\\tan x=\\sec ^2x\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          $\\sec^2 x$ \u3063\u3066\u898b\u6163\u308c\u306a\u3044\u3067\u3059\u306d\u3002<\/p>\n
          \u4e09\u89d2\u95a2\u6570\u3092\u300c\u7c21\u5358\u5316\u300d\u3059\u308b trigsimp()<\/code> \u95a2\u6570\u3067\u307f\u308b\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[42]:<\/div>\n
          \n
          \n
          \n
          diff<\/span>(<\/span>tan<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> trigsimp<\/span>(<\/span>diff<\/span>(<\/span>tan<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[42]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{54}$}\\sec ^2x=\\frac{1}{\\cos ^2x}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          $\\sec^2 x$ \u3068\u306f $\\ \\displaystyle \\frac{1}{\\cos^2 x}\\ $ \u306e\u3053\u3068\u3067\u3057\u305f\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u53c2\u8003\uff1a\u4e09\u89d2\u95a2\u6570\u306e\u30b0\u30e9\u30d5<\/h4>\n
          $y = \\sin x, \\cos x, \\tan x$ \u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3002$ -2 \\pi \\leq x \\leq 2 \\pi$ \u306e\u7bc4\u56f2\u3067\u3002$\\tan x$ \u306f\u975e\u5e38\u306b\u5927\u304d\u3044\u5024\u306b\u306a\u308b\u5834\u5408\u304c\u3042\u308b\u306e\u3067\uff0c$y$ \u306e\u8868\u793a\u7bc4\u56f2\u3092\u9069\u5b9c\u8a2d\u5b9a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[43]:<\/div>\n
          \n
          \n
          \n
          plot2d<\/span>([<\/span>sin<\/span>(<\/span>x<\/span>)<\/span>, cos<\/span>(<\/span>x<\/span>)<\/span>, tan<\/span>(<\/span>x<\/span>)]<\/span>, \r\n       [<\/span>x<\/span>, -<\/span>2*<\/span>%pi<\/span>, 2*<\/span>%pi<\/span>]<\/span>, [<\/span>y<\/span>, -<\/span>3<\/span>, 3]<\/span>, grid2d<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          <\/div>\n
          \n
          <\/p>\n
          \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u53c2\u8003\uff1a\u6a2a\u8ef8\u306e\u76ee\u76db\u3092 $\\pi\/2$ \u3054\u3068\u306b<\/h4>\n
          $x$ \u8ef8\uff08\u6a2a\u8ef8\uff09\u306e\u76ee\u76db\u3092 $\\pi\/2$ \u3054\u3068\u306b\u3057\u3066\u307f\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[44]:<\/div>\n
          \n
          \n
          \n
          plot2d<\/span>(<\/span>\r\n  [<\/span>sin<\/span>(<\/span>x<\/span>)<\/span>, cos<\/span>(<\/span>x<\/span>)<\/span>, tan<\/span>(<\/span>x<\/span>)]<\/span>, [<\/span>x<\/span>, -<\/span>2*<\/span>%pi<\/span>, 2*<\/span>%pi<\/span>]<\/span>, \r\n  \/* \u7dda\u306e\u592a\u3055\u3092 2 \u306b *\/<\/span>\r\n  [<\/span>style<\/span>, [<\/span>lines<\/span>, 2]<\/span>, [<\/span>lines<\/span>, 2]<\/span>, [<\/span>lines<\/span>, 2]]<\/span>, \r\n  \/* \u51e1\u4f8b\u306e\u8a2d\u5b9a *\/<\/span>\r\n  [<\/span>legend<\/span>, \"sin x\"<\/span>, \"cos x\"<\/span>, \"tan x\"<\/span>]<\/span>, \r\n  \r\n  [<\/span>y<\/span>, -<\/span>3<\/span>, 3]<\/span>, grid2d<\/span>, \r\n  \/* x \u8ef8\u306e\u76ee\u76db\u3092 \u03c0\/2 \u3054\u3068\u306b *\/<\/span>\r\n  [<\/span>xtics<\/span>, %pi<\/span>\/<\/span>2]<\/span>, \r\n  \/* x \u8ef8\u306e\u30e9\u30d9\u30eb\u306e\u30d5\u30a9\u30fc\u30de\u30c3\u30c8\u8a2d\u5b9a; \u51e1\u4f8b\u306e\u7dda\u306e\u9577\u3055\u8a2d\u5b9a *\/<\/span>\r\n  [<\/span>gnuplot_preamble<\/span>, \"set format x '%3.1P \u03c0';set key sample 0.2;\"<\/span>]<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          <\/div>\n
          \n
          <\/p>\n
          \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u9006\u4e09\u89d2\u95a2\u6570<\/h3>\n
          \u5b9a\u7fa9<\/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
          \n
          \n
          In\u00a0[45]:<\/div>\n
          \n
          \n
          \n
          sin<\/span>(<\/span>asin<\/span>(<\/span>x<\/span>))<\/span>;\r\ncos<\/span>(<\/span>acos<\/span>(<\/span>x<\/span>))<\/span>;\r\ntan<\/span>(<\/span>atan<\/span>(<\/span>x<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[45]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{59}$}x\\]<\/div>\n<\/div>\n
          \n
          Out[45]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{60}$}x\\]<\/div>\n<\/div>\n
          \n
          Out[45]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{61}$}x\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \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
          \u53cd\u4f8b\u306f $x = \\pi$ \u3068\u3059\u308c\u3070…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[46]:<\/div>\n
          \n
          \n
          \n
          asin<\/span>(<\/span>sin<\/span>(<\/span>%pi<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[46]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{62}$}0\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u7b54\u3048\u306f $\\pi$ \u3067\u306f\u306a\u304f\uff0c$0$ \u3067\u3059\u3002$x = \\pi$ \u306e\u5834\u5408\u306f $\\sin^{-1} \\left( \\sin x \\right) \\neq x$ \u3068\u3044\u3046\u3053\u3068\u3067\u3059\u306d\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u5fae\u5206<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[47]:<\/div>\n
          \n
          \n
          \n
          '<\/span>diff<\/span>(<\/span>asin<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> \r\n diff<\/span>(<\/span>asin<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[47]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{63}$}\\frac{d}{d\\,x}\\,\\arcsin x=\\frac{1}{\\sqrt{1-x^2}}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[48]:<\/div>\n
          \n
          \n
          \n
          '<\/span>diff<\/span>(<\/span>acos<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> \r\n diff<\/span>(<\/span>acos<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[48]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{64}$}\\frac{d}{d\\,x}\\,\\arccos x=-\\frac{1}{\\sqrt{1-x^2}}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[49]:<\/div>\n
          \n
          \n
          \n
          '<\/span>diff<\/span>(<\/span>atan<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> \r\n diff<\/span>(<\/span>atan<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[49]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{65}$}\\frac{d}{d\\,x}\\,\\arctan x=\\frac{1}{x^2+1}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u53c2\u8003\uff1a\u9006\u4e09\u89d2\u95a2\u6570\u306e\u30b0\u30e9\u30d5<\/h4>\n
          $\\sin^{-1} x$ \u3068 $\\cos^{-1} x$ \u306e\u5b9a\u7fa9\u57df\u306f $ -1 < x < 1$\uff0c
          \n$\\tan^{-1} x$ \u306e\u5b9a\u7fa9\u6a5f\u306f $-\\infty < x < \\infty$
          \n\u3067\u3042\u308b\u3053\u3068\u306b\u7559\u610f\u3057\u3066\uff0c\u9006\u4e09\u89d2\u95a2\u6570\u306e\u30b0\u30e9\u30d5\u3092\u63cf\u304f\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[50]:<\/div>\n
          \n
          \n
          \n
          plot2d<\/span>([<\/span>asin<\/span>(<\/span>x<\/span>)<\/span>, acos<\/span>(<\/span>x<\/span>)]<\/span>, [<\/span>x<\/span>, -<\/span>1<\/span>, 1]<\/span>, grid2d<\/span>, \r\n       \/* y \u8ef8\u306e\u76ee\u76db\u3092 \u03c0\/4 \u3054\u3068\u306b *\/<\/span>\r\n       [<\/span>ytics<\/span>, %pi<\/span>\/<\/span>4]<\/span>, \r\n       [<\/span>gnuplot_preamble<\/span>, \"set format y '%4.2P \u03c0';\"<\/span>])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          <\/div>\n
          \n
          <\/p>\n
          \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[51]:<\/div>\n
          \n
          \n
          \n
          plot2d<\/span>(<\/span>atan<\/span>(<\/span>x<\/span>)<\/span>, [<\/span>x<\/span>, -<\/span>10<\/span>, 10]<\/span>, grid2d<\/span>, \r\n       \/* y \u8ef8\u306e\u76ee\u76db\u3092 \u03c0\/4 \u3054\u3068\u306b *\/<\/span>\r\n       [<\/span>ytics<\/span>, %pi<\/span>\/<\/span>4]<\/span>, \r\n       [<\/span>gnuplot_preamble<\/span>, \"set format y '%4.2P \u03c0';\"<\/span>])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          <\/div>\n
          \n
          <\/p>\n
          \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u53cc\u66f2\u7dda\u95a2\u6570<\/h3>\n
          \u5b9a\u7fa9<\/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
          $\\displaystyle \\sinh x \\equiv \\frac{e^{x} – e^{-x}}{2} =$ sinh(x)<\/code><\/p>\n
          $\\displaystyle \\cosh x \\equiv \\frac{e^{x} + e^{-x}}{2} =$ cosh(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
          \u53cc\u66f2\u7dda\u95a2\u6570\u3092\u6307\u6570\u95a2\u6570\u3092\u4f7f\u3063\u3066\u66f8\u304d\u76f4\u3059\u306b\u306f
          \nexponentialize()<\/code> \u95a2\u6570\u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[52]:<\/div>\n
          \n
          \n
          \n
          sinh<\/span>(<\/span>x<\/span>)<\/span> =<\/span> exponentialize<\/span>(<\/span>sinh<\/span>(<\/span>x<\/span>))<\/span>;\r\ncosh<\/span>(<\/span>x<\/span>)<\/span> =<\/span> exponentialize<\/span>(<\/span>cosh<\/span>(<\/span>x<\/span>))<\/span>;\r\ntanh<\/span>(<\/span>x<\/span>)<\/span> =<\/span> exponentialize<\/span>(<\/span>tanh<\/span>(<\/span>x<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[52]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{70}$}\\sinh x=\\frac{e^{x}-e^ {- x }}{2}\\]<\/div>\n<\/div>\n
          \n
          Out[52]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{71}$}\\cosh x=\\frac{e^{x}+e^ {- x }}{2}\\]<\/div>\n<\/div>\n
          \n
          Out[52]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{72}$}\\tanh x=\\frac{e^{x}-e^ {- x }}{e^{x}+e^ {- x }}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u6027\u8cea<\/h4>\n
          $\\cosh^2 x – \\sinh^2 x = 1$ \u3092\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3059\u3002\u53cc\u66f2\u7dda\u95a2\u6570\u3082\u4e09\u89d2\u95a2\u6570\u3068\u540c\u69d8\u306b trigsimp()<\/code> \u3092\u4f7f\u3063\u3066\u300c\u7c21\u5358\u5316\u300d\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[53]:<\/div>\n
          \n
          \n
          \n
          cosh<\/span>(<\/span>x<\/span>)<\/span>**<\/span>2<\/span> -<\/span> sinh<\/span>(<\/span>x<\/span>)<\/span>**<\/span>2<\/span> =<\/span> \r\ntrigsimp<\/span>(<\/span>cosh<\/span>(<\/span>x<\/span>)<\/span>**<\/span>2<\/span> -<\/span> sinh<\/span>(<\/span>x<\/span>)<\/span>**<\/span>2<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[53]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{73}$}\\cosh ^2x-\\sinh ^2x=1\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u52a0\u6cd5\u5b9a\u7406\u306e\u78ba\u8a8d<\/h4>\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\u3002trigexpand()<\/code> \u3067\u300c\u5c55\u958b\u300d\u3057\u3066\u78ba\u8a8d\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[54]:<\/div>\n
          \n
          \n
          \n
          cosh<\/span>(<\/span>x<\/span> +<\/span> y<\/span>)<\/span> =<\/span> trigexpand<\/span>(<\/span>cosh<\/span>(<\/span>x<\/span> +<\/span> y<\/span>))<\/span>;\r\nsinh<\/span>(<\/span>x<\/span> +<\/span> y<\/span>)<\/span> =<\/span> trigexpand<\/span>(<\/span>sinh<\/span>(<\/span>x<\/span> +<\/span> y<\/span>))<\/span>;\r\ntanh<\/span>(<\/span>x<\/span> +<\/span> y<\/span>)<\/span> =<\/span> trigexpand<\/span>(<\/span>tanh<\/span>(<\/span>x<\/span> +<\/span> y<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[54]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{74}$}\\cosh \\left(y+x\\right)=\\sinh x\\,\\sinh y+\\cosh x\\,\\cosh y\\]<\/div>\n<\/div>\n
          \n
          Out[54]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{75}$}\\sinh \\left(y+x\\right)=\\cosh x\\,\\sinh y+\\sinh x\\,\\cosh y\\]<\/div>\n<\/div>\n
          \n
          Out[54]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{76}$}\\tanh \\left(y+x\\right)=\\frac{\\tanh y+\\tanh x}{\\tanh x\\,\\tanh y+1}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u5fae\u5206<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[55]:<\/div>\n
          \n
          \n
          \n
          '<\/span>diff<\/span>(<\/span>cosh<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> diff<\/span>(<\/span>cosh<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n'<\/span>diff<\/span>(<\/span>sinh<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> diff<\/span>(<\/span>sinh<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n'<\/span>diff<\/span>(<\/span>tanh<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> diff<\/span>(<\/span>tanh<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[55]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{77}$}\\frac{d}{d\\,x}\\,\\cosh x=\\sinh x\\]<\/div>\n<\/div>\n
          \n
          Out[55]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{78}$}\\frac{d}{d\\,x}\\,\\sinh x=\\cosh x\\]<\/div>\n<\/div>\n
          \n
          Out[55]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{79}$}\\frac{d}{d\\,x}\\,\\tanh x=\\left({\\rm sech}\\; x\\right)^2\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          $\\operatorname{sech} x$ \u3092\u7c21\u5358\u5316\u3059\u308b\u3068…<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[56]:<\/div>\n
          \n
          \n
          \n
          '<\/span>diff<\/span>(<\/span>tanh<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> trigsimp<\/span>(<\/span>diff<\/span>(<\/span>tanh<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[56]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{80}$}\\frac{d}{d\\,x}\\,\\tanh x=\\frac{1}{\\cosh ^2x}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u53c2\u8003\uff1a\u53cc\u66f2\u7dda\u95a2\u6570\u306e\u30b0\u30e9\u30d5<\/h4>\n
          $y = \\sinh x, \\ \\cosh x$ \u306e\u30b0\u30e9\u30d5\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[57]:<\/div>\n
          \n
          \n
          \n
          plot2d<\/span>([<\/span>sinh<\/span>(<\/span>x<\/span>)<\/span>, cosh<\/span>(<\/span>x<\/span>)]<\/span>, [<\/span>x<\/span>, -<\/span>3<\/span>, 3]<\/span>, grid2d<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          <\/div>\n
          \n
          <\/p>\n
          \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          $ y = \\tanh x$ \u306e\u30b0\u30e9\u30d5\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[58]:<\/div>\n
          \n
          \n
          \n
          plot2d<\/span>(<\/span>tanh<\/span>(<\/span>x<\/span>)<\/span>, [<\/span>x<\/span>, -<\/span>5<\/span>, 5]<\/span>, grid2d<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          <\/div>\n
          \n
          <\/p>\n
          \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u9006\u53cc\u66f2\u7dda\u95a2\u6570<\/h3>\n
          \u5b9a\u7fa9<\/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 \u3067\u306f\u306a\u3044\u3002\uff09\u9006\u95a2\u6570\u3067\u3059\u304b\u3089\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3064\u306f\u305a\u3067\u3059\u3002<\/p>\n
          $\\sinh\\left(\\sinh^{-1} x\\right) = x$
          \n$\\cosh\\left(\\cosh^{-1} x\\right) = x$
          \n$\\tanh\\left(\\tanh^{-1} x\\right) = x$<\/p>\n
          \u78ba\u8a8d\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[59]:<\/div>\n
          \n
          \n
          \n
          sinh<\/span>(<\/span>asinh<\/span>(<\/span>x<\/span>))<\/span>;\r\ncosh<\/span>(<\/span>acosh<\/span>(<\/span>x<\/span>))<\/span>;\r\ntanh<\/span>(<\/span>atanh<\/span>(<\/span>x<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[59]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{85}$}x\\]<\/div>\n<\/div>\n
          \n
          Out[59]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{86}$}x\\]<\/div>\n<\/div>\n
          \n
          Out[59]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{87}$}x\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u53cc\u66f2\u7dda\u95a2\u6570\u306f\u6307\u6570\u95a2\u6570\u3092\u4f7f\u3063\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u304c\uff0c\u9006\u53cc\u66f2\u7dda\u95a2\u6570\u306f\u5bfe\u6570\u95a2\u6570\u3092\u4f7f\u3063\u3066\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u4f8b\u306e\u3088\u3046\u306b\uff0clogarc()<\/code> \u95a2\u6570\u3092\u4f7f\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[60]:<\/div>\n
          \n
          \n
          \n
          asinh<\/span>(<\/span>x<\/span>)<\/span> =<\/span> logarc<\/span>(<\/span>asinh<\/span>(<\/span>x<\/span>))<\/span>;\r\nacosh<\/span>(<\/span>x<\/span>)<\/span> =<\/span> logarc<\/span>(<\/span>acosh<\/span>(<\/span>x<\/span>))<\/span>;\r\natanh<\/span>(<\/span>x<\/span>)<\/span> =<\/span> logarc<\/span>(<\/span>atanh<\/span>(<\/span>x<\/span>))<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[60]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{88}$}{\\rm asinh}\\; x=\\log \\left(\\sqrt{x^2+1}+x\\right)\\]<\/div>\n<\/div>\n
          \n
          Out[60]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{89}$}{\\rm acosh}\\; x=\\log \\left(\\sqrt{x-1}\\,\\sqrt{x+1}+x\\right)\\]<\/div>\n<\/div>\n
          \n
          Out[60]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{90}$}{\\rm atanh}\\; x=\\frac{\\log \\left(x+1\\right)-\\log \\left(1-x\\right)}{2}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u5fae\u5206<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[61]:<\/div>\n
          \n
          \n
          \n
          '<\/span>diff<\/span>(<\/span>asinh<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> diff<\/span>(<\/span>asinh<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n'<\/span>diff<\/span>(<\/span>acosh<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> diff<\/span>(<\/span>acosh<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n'<\/span>diff<\/span>(<\/span>atanh<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span> =<\/span> diff<\/span>(<\/span>atanh<\/span>(<\/span>x<\/span>)<\/span>, x<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          Out[61]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{91}$}\\frac{d}{d\\,x}\\,{\\rm asinh}\\; x=\\frac{1}{\\sqrt{x^2+1}}\\]<\/div>\n<\/div>\n
          \n
          Out[61]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{92}$}\\frac{d}{d\\,x}\\,{\\rm acosh}\\; x=\\frac{1}{\\sqrt{x^2-1}}\\]<\/div>\n<\/div>\n
          \n
          Out[61]:<\/div>\n
          \\[\\tag{${\\it \\%o}_{93}$}\\frac{d}{d\\,x}\\,{\\rm atanh}\\; x=\\frac{1}{1-x^2}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          \u53c2\u8003\uff1a\u9006\u53cc\u66f2\u7dda\u95a2\u6570\u306e\u30b0\u30e9\u30d5<\/h4>\n
          $y = \\sinh^{-1} x$ \u306e\u5b9a\u7fa9\u57df\u306f $-\\infty < x < \\infty$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[62]:<\/div>\n
          \n
          \n
          \n
          plot2d<\/span>(<\/span>asinh<\/span>(<\/span>x<\/span>)<\/span>, [<\/span>x<\/span>, -<\/span>10<\/span>, 10]<\/span>, grid2d<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          <\/div>\n
          \n
          <\/p>\n
          \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          $y = \\cosh^{-1} x$ \u306e\u5b9a\u7fa9\u57df\u306f $x \\geq 1$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[63]:<\/div>\n
          \n
          \n
          \n
          plot2d<\/span>(<\/span>acosh<\/span>(<\/span>x<\/span>)<\/span>, [<\/span>x<\/span>, 1<\/span>, 10]<\/span>, grid2d<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          <\/div>\n
          \n
          <\/p>\n
          \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          <\/div>\n
          \n
          \n
          $y = \\tanh^{-1} x$ \u306e\u5b9a\u7fa9\u57df\u306f $-1 < x < 1$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          In\u00a0[64]:<\/div>\n
          \n
          \n
          \n
          plot2d<\/span>(<\/span>atanh<\/span>(<\/span>x<\/span>)<\/span>, [<\/span>x<\/span>, -<\/span>0.999<\/span>, 0.<\/span>999]<\/span>, grid2d<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
          \n
          \n
          \n
          <\/div>\n
          \n
          <\/p>\n
          \"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":33,"featured_media":0,"parent":6032,"menu_order":10,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-2182","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2182","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=2182"}],"version-history":[{"count":8,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2182\/revisions"}],"predecessor-version":[{"id":6089,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2182\/revisions\/6089"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/6032"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=2182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}