{"id":7012,"date":"2023-11-17T12:06:41","date_gmt":"2023-11-17T03:06:41","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?p=7012"},"modified":"2023-11-17T15:49:26","modified_gmt":"2023-11-17T06:49:26","slug":"%e6%a5%95%e5%86%86%e8%bb%8c%e9%81%93%e4%b8%8a%e3%81%ae%e6%99%82%e5%88%bb%e3%81%94%e3%81%a8%e3%81%ae%e4%bd%8d%e7%bd%ae%e3%82%92-maxima-%e3%81%a7%e6%95%b0%e5%80%a4%e7%9a%84%e3%81%ab%e6%b1%82%e3%82%81","status":"publish","type":"post","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/7012\/","title":{"rendered":"\u6955\u5186\u8ecc\u9053\u4e0a\u306e\u6642\u523b\u3054\u3068\u306e\u4f4d\u7f6e\u3092 Maxima \u3067\u6570\u5024\u7684\u306b\u6c42\u3081\u308b"},"content":{"rendered":"

\u300c\u6955\u5186\u8ecc\u9053\u4e0a\u306e\u6642\u523b\u3054\u3068\u306e\u4f4d\u7f6e\u3092\u6c42\u3081\u308b\u305f\u3081\u306e\u4e0b\u3054\u3057\u3089\u3048<\/a>\u300d\u3067\u4e0b\u3054\u3057\u3089\u3048\u3057\u305f\u5f0f\u3092 Maxima \u3067\u6570\u5024\u7684\u306b\u89e3\u304f\u3002
\n<\/p>\n

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\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u5f0f<\/h3>\n

\u300c\u6955\u5186\u8ecc\u9053\u4e0a\u306e\u6642\u523b\u3054\u3068\u306e\u4f4d\u7f6e\u3092\u6c42\u3081\u308b\u305f\u3081\u306e\u4e0b\u3054\u3057\u3089\u3048<\/a>\u300d\u3067\u4e0b\u3054\u3057\u3089\u3048\u3057\u305f\u5f0f\uff08\u7121\u6b21\u5143\u5316\u6e08\u307f\uff09\u3002<\/p>\n

\\begin{eqnarray}
\n\\frac{d\\phi}{dT} &=& f(\\phi, e) = 2 \\pi \\frac{(1+e \\cos\\phi)^2}{(1-e^2)^{3\/2}} \\tag{1}\\\\
\nR(\\phi) &\\equiv& \\frac{r}{a} = \\frac{1-e^2}{1+e\\cos\\phi} \\tag{2}\\\\
\nX(\\phi) &\\equiv& \\frac{x}{a} =R(\\phi) \\cos\\phi \\tag{3}\\\\
\nY(\\phi) &\\equiv& \\frac{y}{a} =R(\\phi) \\sin\\phi \\tag{4}
\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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\/* \u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u53f3\u8fba *\/<\/span>\r\nf<\/span>(<\/span>phi<\/span>, e<\/span>)<\/span>:=<\/span> 2*<\/span>%pi<\/span>*<\/span>(<\/span>1+<\/span>e<\/span>*<\/span>cos<\/span>(<\/span>phi<\/span>))<\/span>**<\/span>2\/<\/span>(<\/span>1<\/span> -<\/span> e<\/span>**<\/span>2<\/span>)<\/span>**<\/span>(<\/span>3\/<\/span>2<\/span>)<\/span>;\r\n\r\nR<\/span>(<\/span>phi<\/span>, e<\/span>)<\/span>:=<\/span> (<\/span>1<\/span> -<\/span> e<\/span>**<\/span>2<\/span>)<\/span>\/<\/span>(<\/span>1<\/span> +<\/span> e<\/span>*<\/span>cos<\/span>(<\/span>phi<\/span>))<\/span>;\r\nX<\/span>(<\/span>phi<\/span>, e<\/span>)<\/span>:=<\/span> R<\/span>(<\/span>phi<\/span>, e<\/span>)<\/span> *<\/span> cos<\/span>(<\/span>phi<\/span>)<\/span>;\r\nY<\/span>(<\/span>phi<\/span>, e<\/span>)<\/span>:=<\/span> R<\/span>(<\/span>phi<\/span>, e<\/span>)<\/span> *<\/span> sin<\/span>(<\/span>phi<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[1]:<\/div>\n
\\[\\tag{${\\it \\%o}_{1}$}f\\left(\\varphi , e\\right):=\\frac{2\\,\\pi\\,\\left(1+e\\,\\cos \\varphi\\right)^2}{\\left(1-e^2\\right)^{\\frac{3}{2}}}\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{2}$}R\\left(\\varphi , e\\right):=\\frac{1-e^2}{1+e\\,\\cos \\varphi}\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{3}$}X\\left(\\varphi , e\\right):=R\\left(\\varphi , e\\right)\\,\\cos \\varphi\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{4}$}Y\\left(\\varphi , e\\right):=R\\left(\\varphi , e\\right)\\,\\sin \\varphi\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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rk()<\/code> \u3067\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u304f<\/h3>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[2]:<\/div>\n
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\/* T \u306e\u521d\u671f\u5024 *\/<\/span>\r\nT0<\/span>:<\/span> 0$\r\n\/* phi \u306e\u521d\u671f\u5024 *\/<\/span>\r\nphi0<\/span>:<\/span> 0$\r\n\/* T \u306e\u7d42\u4e86\u5024 *\/<\/span>\r\nTend<\/span>:<\/span> 1$\r\n\/* \u5206\u5272\u6570 *\/<\/span>\r\nndiv<\/span>:<\/span> 100$\r\nNdiv<\/span>:<\/span> 36$\r\nN<\/span>:<\/span> Ndiv<\/span> *<\/span> ndiv<\/span>$\r\n\/* \u523b\u307f\u5e45 h \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3057\u3066\u8a08\u7b97\u3055\u308c\u308b\u3002*\/<\/span>\r\nh<\/span>:<\/span> float<\/span>((<\/span>Tend<\/span> -<\/span> T0<\/span>)<\/span>\/<\/span>N<\/span>)<\/span>$\r\n\r\n\/* 1\u968e\u4e0a\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092 Runge-Kutta \u6cd5\u3067\u89e3\u304f *\/<\/span>\r\n\/* e = 0.6 *\/<\/span>\r\ne<\/span>:<\/span> 0.<\/span>6$\r\nrkphi<\/span>:<\/span> rk<\/span>(<\/span>f<\/span>(<\/span>phi<\/span>, e<\/span>)<\/span>, phi<\/span>, phi0<\/span>, [<\/span>T<\/span>, T0<\/span>, Tend<\/span>, h<\/span>])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u3061\u3087\u3046\u30691\u5468\u671f $T = T_{\\rm end}$ \u305f\u3066\u3070 $\\phi = 2 \\pi$ \u306b\u306a\u3063\u3066\u3044\u308b\u306f\u305a\u3060\u304b\u3089\uff0c\u6570\u5024\u8aa4\u5dee\u3092\u78ba\u8a8d\u3059\u308b\u3002<\/p>\n
$$\\phi(T_{\\rm end}) – 2 \\pi$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[3]:<\/div>\n
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rkphi<\/span>[<\/span>length<\/span>(<\/span>rkphi<\/span>)][<\/span>2]<\/span>-<\/span> float<\/span>(<\/span>2*<\/span>%pi<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[3]:<\/div>\n
\\[\\tag{${\\it \\%o}_{14}$}-2.303579549334245 \\times 10^{-11}\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4e00\u5b9a\u6642\u9593\u9593\u9694\u3054\u3068\u306e\u4f4d\u7f6e\u3092\u30b0\u30e9\u30d5\u306b<\/h3>\n
\u4e00\u5b9a\u6642\u9593\u9593\u9694 $\\displaystyle \\Delta T = \\frac{T_{\\rm end}}{N_{\\rm div}}$ \u3054\u3068\u306e\u4f4d\u7f6e\uff1a<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[4]:<\/div>\n
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phii<\/span>:<\/span> makelist<\/span>(<\/span>rkphi<\/span>[<\/span>i<\/span>][<\/span>2]<\/span>, i<\/span>, 1<\/span>, length<\/span>(<\/span>rkphi<\/span>)<\/span>, ndiv<\/span>)<\/span>$\r\n\r\npos<\/span>:<\/span> makelist<\/span>([<\/span>X<\/span>(<\/span>phii<\/span>[<\/span>i<\/span>]<\/span>, e<\/span>)<\/span>, Y<\/span>(<\/span>phii<\/span>[<\/span>i<\/span>]<\/span>, e<\/span>)]<\/span>, i<\/span>, length<\/span>(<\/span>phii<\/span>))<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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plot2d()<\/code> \u3067\u30b0\u30e9\u30d5\u4f5c\u6210<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[5]:<\/div>\n
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plot2d<\/span>([<\/span>discrete<\/span>, pos<\/span>]<\/span>, [<\/span>style<\/span>, [<\/span>points<\/span>,1]]<\/span>, \r\n       [<\/span>same_xy<\/span>]<\/span>, [<\/span>x<\/span>, -<\/span>2<\/span>, 1]<\/span>, [<\/span>y<\/span>, -<\/span>1.5<\/span>, 1.<\/span>5])<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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draw2d()<\/code> \u3067\u30b0\u30e9\u30d5\u4f5c\u6210<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[6]:<\/div>\n
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draw2d<\/span>(<\/span>\r\n  \/* \u70b9\u3092\u5857\u308a\u3064\u3076\u3057\u305f\u4e38\u306b *\/<\/span>\r\n  point_type<\/span> =<\/span> 7<\/span>, \r\n  \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  xrange<\/span> =<\/span> [<\/span>-<\/span>2<\/span>, 1]<\/span>, yrange<\/span> =<\/span> [<\/span>-<\/span>1.5<\/span>, 1.<\/span>5]<\/span>,\r\n  \/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  proportional_axes<\/span>=<\/span>xy<\/span>,\r\n  \/* x \u8ef8 y \u8ef8 *\/<\/span>\r\n  xaxis<\/span> =<\/span> true<\/span>, yaxis<\/span> =<\/span> true<\/span>,   \r\n  \r\n  \/* \u70b9\u306e\u5927\u304d\u3055 *\/<\/span>\r\n  point_size<\/span> =<\/span> 0.5<\/span>, \r\n  points<\/span>(<\/span>pos<\/span>)<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u53c2\u8003\uff1a\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\u3068\u306e\u6bd4\u8f03<\/h3>\n
\u300c\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u3066\u30b1\u30d7\u30e9\u30fc\u306e\u7b2c2\u6cd5\u5247\u3092\u8996\u899a\u7684\u306b\u78ba\u8a8d\u3059\u308b<\/a>\u300d\u306b\u307e\u3068\u3081\u3066\u3044\u308b\u3088\u3046\u306b\uff0c\u6955\u5186\u8ecc\u9053\u306e $x, y$ \u3092\u8ecc\u9053\u9577\u534a\u5f84 $a$ \u3067\u898f\u683c\u5316\u3057\u305f $X_u, Y_u$ \u3092\uff0c\u96e2\u5fc3\u8fd1\u70b9\u96e2\u89d2 $u$ \u3092\u4f7f\u3063\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u3042\u3089\u308f\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n
\\begin{eqnarray}
\nX_u &\\equiv& \\frac{x}{a} = \\cos u \u2013 e\\\\
\nY_u &\\equiv& \\frac{y}{a} = \\sqrt{1-e^2} \\sin u
\n\\end{eqnarray}<\/p>\n
\u96e2\u5fc3\u8fd1\u70b9\u96e2\u89d2 $u$ \u3068\u5468\u671f $P$ \u3067\u898f\u683c\u5316\u3055\u308c\u305f\u6642\u9593 $T$ \u3068\u306e\u95a2\u4fc2\u306f\uff0c\u4ee5\u4e0b\u306e\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u3066\u5f97\u3089\u308c\u308b\u3002<\/p>\n
\\begin{eqnarray}
\n2\\pi T &=& u \u2013 e \\sin u, \\quad T \\equiv \\frac{t}{P}
\n\\end{eqnarray}<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3<\/h4>\n
$$g(u_i) \\equiv u_i \u2013 e \\sin u_i = \\frac{2\\pi}{T} t_i = \\frac{2\\pi}{N_{\\rm div}} \\times i$$<\/p>\n
\u3092 $u_i$ \u306b\u3064\u3044\u3066 find_root()<\/code> \u95a2\u6570\u3067\u6570\u5024\u7684\u306b\u89e3\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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g<\/span>(<\/span>u<\/span>)<\/span>:=<\/span> u<\/span> -<\/span> e<\/span>*<\/span>sin<\/span>(<\/span>u<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[7]:<\/div>\n
\\[\\tag{${\\it \\%o}_{21}$}g\\left(u\\right):=u-e\\,\\sin u\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[8]:<\/div>\n
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for<\/span> i<\/span>:<\/span>0<\/span> thru<\/span> Ndiv<\/span> do<\/span> \r\n    ui<\/span>[<\/span>i<\/span>]<\/span>:<\/span> find_root<\/span>(<\/span>g<\/span>(<\/span>u<\/span>)<\/span> =<\/span> 2*<\/span>%pi<\/span>\/<\/span>Ndiv<\/span> *<\/span> i<\/span>, u<\/span>, 0<\/span>, 2*<\/span>%pi<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u4e00\u5b9a\u6642\u9593\u9593\u9694\u3054\u3068\u306e\u4f4d\u7f6e<\/h4>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[9]:<\/div>\n
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Xu<\/span>(<\/span>u<\/span>, e<\/span>)<\/span>:=<\/span> (<\/span>cos<\/span>(<\/span>u<\/span>)<\/span> -<\/span> e<\/span>)<\/span>;\r\nYu<\/span>(<\/span>u<\/span>, e<\/span>)<\/span>:=<\/span> sqrt<\/span>(<\/span>1-<\/span>e<\/span>**<\/span>2<\/span>)<\/span>*<\/span>sin<\/span>(<\/span>u<\/span>)<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[9]:<\/div>\n
\\[\\tag{${\\it \\%o}_{23}$}{\\it Xu}\\left(u , e\\right):=\\cos u-e\\]<\/div>\n<\/div>\n
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\\[\\tag{${\\it \\%o}_{24}$}{\\it Yu}\\left(u , e\\right):=\\sqrt{1-e^2}\\,\\sin u\\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[10]:<\/div>\n
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posu<\/span>:<\/span> makelist<\/span>([<\/span>Xu<\/span>(<\/span>ui<\/span>[<\/span>i<\/span>]<\/span>, e<\/span>)<\/span>, Yu<\/span>(<\/span>ui<\/span>[<\/span>i<\/span>]<\/span>, e<\/span>)]<\/span>, i<\/span>, 0<\/span>, Ndiv<\/span>)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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2\u3064\u306e\u89e3\u306e\u6bd4\u8f03<\/h4>\n
$\\phi$ \u306b\u95a2\u3059\u308b1\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u305f\u89e3\u3067\u3042\u308b pos<\/code> \u3068\uff0c\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u3092\u6570\u5024\u7684\u306b\u89e3\u3044\u305f\u89e3\u3067\u3042\u308b posu<\/code> \u306f\uff0c\u5f53\u7136\u306a\u304c\u3089\u6570\u5024\u8aa4\u5dee\u306e\u7bc4\u56f2\u3067\u4e00\u81f4\u3057\u3066\u308b\u306f\u305a\u3067\u3042\u308b\u3002<\/p>\n
2\u3064\u306e\u914d\u5217\u306e\u5f15\u304d\u7b97\u3092\u3057\u3066\u5dee\u3092\u8abf\u3079\u308b\u300237\u7d44\u5168\u3066\u8868\u793a\u3059\u308b\u3068\u5197\u9577\u306a\u306e\u3067\uff0c\u4ee3\u8868\u3057\u30663\u7d44\u307b\u3069\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[11]:<\/div>\n
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\/* 2\u3064\u306e\u6570\u5024\u89e3 X, Y \u306e\u5dee *\/<\/span>\r\n(<\/span>pos<\/span>-<\/span>posu<\/span>)[<\/span>10]<\/span>;\r\n(<\/span>pos<\/span>-<\/span>posu<\/span>)[<\/span>20]<\/span>;\r\n(<\/span>pos<\/span>-<\/span>posu<\/span>)[<\/span>30]<\/span>;\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Out[11]:<\/div>\n
\\[\\tag{${\\it \\%o}_{26}$}\\left[ 1.530775506353166 \\times 10^{-12} , 7.017719738655614 \\times 10^{-13} \\right] \\]<\/div>\n<\/div>\n
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Out[11]:<\/div>\n
\\[\\tag{${\\it \\%o}_{27}$}\\left[ -1.576516694967722 \\times 10^{-13} , 1.149330630667578 \\times 10^{-12} \\right] \\]<\/div>\n<\/div>\n
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Out[11]:<\/div>\n
\\[\\tag{${\\it \\%o}_{28}$}\\left[ -1.973976537783528 \\times 10^{-12} , 3.774758283725532 \\times 10^{-13} \\right] \\]<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\u5ff5\u306e\u305f\u3081\u306b2\u3064\u306e\u6570\u5024\u89e3\u3092\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3068\uff0c\u5f53\u7136\u306a\u304c\u3089\u91cd\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308b\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n
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In\u00a0[12]:<\/div>\n
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draw2d<\/span>(<\/span>\r\n  \/* \u70b9\u3092\u5857\u308a\u3064\u3076\u3057\u305f\u4e38\u306b *\/<\/span>\r\n  point_type<\/span> =<\/span> 7<\/span>, \r\n  \/* \u8868\u793a\u7bc4\u56f2 *\/<\/span>\r\n  xrange<\/span> =<\/span> [<\/span>-<\/span>2<\/span>, 1]<\/span>, yrange<\/span> =<\/span> [<\/span>-<\/span>1.5<\/span>, 1.<\/span>5]<\/span>,\r\n  \/* \u7e26\u6a2a\u6bd4 *\/<\/span>\r\n  proportional_axes<\/span>=<\/span>xy<\/span>,\r\n  \/* x \u8ef8 y \u8ef8 *\/<\/span>\r\n  xaxis<\/span> =<\/span> true<\/span>, yaxis<\/span> =<\/span> true<\/span>,   \r\n\r\n  point_size<\/span> =<\/span> 0.5<\/span>, color<\/span> =<\/span> red<\/span>, key<\/span> =<\/span> \"\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\"<\/span>,\r\n  points<\/span>(<\/span>pos<\/span>)<\/span>, \r\n  \r\n  point_size<\/span> =<\/span> 0.2<\/span>, color<\/span> =<\/span> blue<\/span>, key<\/span> =<\/span> \"\u30b1\u30d7\u30e9\u30fc\u65b9\u7a0b\u5f0f\u306e\u6570\u5024\u89e3\"<\/span>,\r\n  points<\/span>(<\/span>posu<\/span>)<\/span>\r\n)<\/span>$\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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\"\"<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
\u300c\u6955\u5186\u8ecc\u9053\u4e0a\u306e\u6642\u523b\u3054\u3068\u306e\u4f4d\u7f6e\u3092\u6c42\u3081\u308b\u305f\u3081\u306e\u4e0b\u3054\u3057\u3089\u3048\u300d\u3067\u4e0b\u3054\u3057\u3089\u3048\u3057\u305f\u5f0f\u3092 Maxima \u3067\u6570\u5024\u7684\u306b\u89e3\u304f\u3002<\/p>
\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[14,22],"tags":[],"class_list":["post-7012","post","type-post","status-publish","format-standard","hentry","category-maxima","category-22","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7012","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/post"}],"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=7012"}],"version-history":[{"count":5,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7012\/revisions"}],"predecessor-version":[{"id":7026,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/posts\/7012\/revisions\/7026"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=7012"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/categories?post=7012"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/tags?post=7012"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}