{"id":2076,"date":"2022-04-17T13:06:12","date_gmt":"2022-04-17T04:06:12","guid":{"rendered":"https:\/\/mathematicians.korea.ac.kr\/sdyang\/?p=2076"},"modified":"2023-04-15T23:50:38","modified_gmt":"2023-04-15T14:50:38","slug":"sagemath%eb%a1%9c-costa-%ea%b3%a1%eb%a9%b4-%ea%b7%b8%eb%a6%ac%ea%b8%b0-2","status":"publish","type":"post","link":"https:\/\/mathematicians.korea.ac.kr\/sdyang\/sagemath%eb%a1%9c-costa-%ea%b3%a1%eb%a9%b4-%ea%b7%b8%eb%a6%ac%ea%b8%b0-2\/","title":{"rendered":"SageMath\ub85c Costa \uace1\uba74 \uadf8\ub9ac\uae30"},"content":{"rendered":"\n

\uc591\uc131\ub355
20210413<\/p>\n\n\n\n

\uc138 \ubc88\uc9f8 \uc2dc\ub3c4 \ub2f9\uc2dc \uc54c\uc9c0 \ubabb\ud588\ub358 \uae30\ubc95\uc744 \uc54c\uac8c \ub418\uc11c \uc774\uc81c \ub2e4\uc74c\uacfc \uac19\uc774 \uadf8\ub9bc\uc744 \uc644\uc131\ud55c\ub2e4. \uc774\ub7ec\uba74 Weber\uac00 \uadf8\ub9b0 \ubc29\ubc95\uc744 \uadf8\ub300\ub85c \ub530\ub978 \uc148\uc774 \ub41c\ub2e4.<\/p>\n\n\n\n

\ucc38\uace0 \ubb38\ud5cc
[2] Matthias Weber, Costa’s Minimal Surface, Mathematica Notebook File<\/p>\n\n\n\n

%display latexIn [1]:<\/p>\n\n\n\n

var('rho')\n\nrho =<\/strong> ( gamma(3\/<\/strong>4)\/<\/strong>sqrt(2)\/<\/strong>gamma(5\/<\/strong>4) ).<\/strong>n()\n<\/pre>\n\n\n\n
In [2]:<\/p>\n\n\n\n
Phi1(w) =<\/strong> 2*<\/strong>rho*<\/strong>I*<\/strong>sqrt(w)*<\/strong>hypergeometric((1\/<\/strong>4,3\/<\/strong>2,), (5\/<\/strong>4,), w^<\/strong>2)\nPhi2(w) =<\/strong> -<\/strong>2\/<\/strong>(3*<\/strong>rho)*<\/strong>I*<\/strong>w*<\/strong>sqrt(w)*<\/strong>hypergeometric((1\/<\/strong>2,3\/<\/strong>4,), (7\/<\/strong>4,), w^<\/strong>2)\n<\/pre>\n\n\n\n
In [3]:<\/p>\n\n\n\n
omega1(z) =<\/strong> -<\/strong>1\/<\/strong>2*<\/strong>( Phi1(z) -<\/strong> Phi2(z))\nomega2(z) =<\/strong>  I\/<\/strong>2*<\/strong>( Phi1(z) +<\/strong> Phi2(z))\nomega3(z) =<\/strong>  1\/<\/strong>2*<\/strong>log(-<\/strong>1+<\/strong>z) -<\/strong> 1\/<\/strong>2*<\/strong>log(1+<\/strong>z)\n<\/pre>\n\n\n\n
In [4]:<\/p>\n\n\n\n
F(z) =<\/strong> ( omega1(z).<\/strong>real(), omega2(z).<\/strong>real(), omega3(z).<\/strong>real() ) \n<\/pre>\n\n\n\n
In [5]:<\/p>\n\n\n\n
p(w) =<\/strong> sqrt( 1 +<\/strong> exp(w) )\n<\/pre>\n\n\n\n
In [6]:<\/p>\n\n\n\n
var('y');\n<\/pre>\n\n\n\n
In [7]:<\/p>\n\n\n\n
points =<\/strong> [(p(x+<\/strong>I*<\/strong>y).<\/strong>real(), p(x+<\/strong>I*<\/strong>y).<\/strong>imag()) for<\/strong> x in<\/strong> srange(-<\/strong>1,3,0.1) for<\/strong> y in<\/strong> srange(0*<\/strong>pi, pi, 0.05*<\/strong>pi, include_endpoint=<\/strong>True<\/strong>)] \n<\/pre>\n\n\n\n
In [8]:<\/p>\n\n\n\n
list_plot(points, aspect_ratio=<\/strong>1)\n<\/pre>\n\n\n\n
Out[8]:<\/p>\n\n\n\n
\"\"<\/figure>\n\n\n\n
In [9]:<\/p>\n\n\n\n
xlist=<\/strong>  [-<\/strong>3.5,-<\/strong>3.0,-<\/strong>2.5, -<\/strong>2.0,-<\/strong>1.5, -<\/strong>1.0,-<\/strong>0.5,-<\/strong>0.3,-<\/strong>0.2,-<\/strong>0.1,-<\/strong>0.05,-<\/strong>0.03,0.0,0.03,0.05,0.1,0.2,0.4,0.6,0.8,1.0,1.2,1.5,2.0 ,2.5,3.0 ,3.5,4.0,5.0,6.0 ];\nxlen=<\/strong> len(xlist);\n\n\nylist=<\/strong> list(pi*<\/strong>vector([0.001,0.05,0.08,0.16,0.24,0.32,0.4,0.48,0.56,0.64,0.72, 0.8,0.88,0.95,0.98,0.99,1.0]));\nylen=<\/strong>len(ylist);\n<\/pre>\n\n\n\n
In [10]:<\/p>\n\n\n\n
var('x y');\n<\/pre>\n\n\n\n
In [11]:<\/p>\n\n\n\n
X =<\/strong> lambda<\/strong> x: xlist[ int(round(x)) -<\/strong>1] if<\/strong> x<<\/strong>0.5 or<\/strong> x><\/strong>xlen +<\/strong> 0.4 else<\/strong> xlist[ int(round(x)) -<\/strong>1]\nY =<\/strong> lambda<\/strong> y: ylist[ int(round(y)) -<\/strong>1] if<\/strong> y<<\/strong>0.5 or<\/strong> y><\/strong>ylen +<\/strong> 0.4 else<\/strong> ylist[ int(round(y)) -<\/strong>1]\n<\/pre>\n\n\n\n
In [12]:<\/p>\n\n\n\n
f =<\/strong> (lambda<\/strong> x,y: omega1(p(X(x)+<\/strong> I*<\/strong>Y(y))).<\/strong>real(), \n     lambda<\/strong> x,y: omega2(p(X(x)+<\/strong> I*<\/strong>Y(y))).<\/strong>real(),\n     lambda<\/strong> x,y: omega3(p(X(x)+<\/strong> I*<\/strong>Y(y))).<\/strong>real()\n     )\ngr1 =<\/strong> parametric_plot3d( f, (x, 1,xlen),(y,1,ylen))\n<\/pre>\n\n\n\n
In [13]:<\/p>\n\n\n\n
gr1.<\/strong>show(frame=<\/strong>False<\/strong>)\n<\/pre>\n\n\n\n
\ud55c \uc870\uac01\uc5d0\uc11c \uc804\uccb4 \uadf8\ub9ac\uae30<\/h1>\n\n\n\n
\uc774\uc81c \uace1\uba74\uc744 \ubcc0\ud658\ud55c\ub2e4. \uc6b0\ub9ac\uac00 \uc6d0\ud558\ub294 \ubcc0\ud658\uc740\u239b\u239c\u239dxyz\u239e\u239f\u23a0\u2192\u239b\u239c\u239dyx\u2212z\u239e\u239f\u23a0=\u239b\u239c\u239d01010000\u22121\u239e\u239f\u23a0\u239b\u239c\u239dxyz\u239e\u239f\u23a0=\u239b\u239c\u239d\u221210001000\u22121\u239e\u239f\u23a0\u239b\u239c\u239d0\u221210100001\u239e\u239f\u23a0\u239b\u239c\u239dxyz\u239e\u239f\u23a0(1)(1)(xyz)\u2192(yx\u2212z)=(01010000\u22121)(xyz)=(\u221210001000\u22121)(0\u221210100001)(xyz)<\/p>\n\n\n\n
\ub9c8\uc9c0\ub9c9\uc5d0 \ub098\ud0c0\ub09c \ubc14\uc640 \uac19\uc774 \ud589\ub82c\uc744 \ubd84\ud574\ud55c \uc774\uc720\ub294, \uc18c\uc2a4 \ucf54\ub4dc\uae4c\uc9c0 \ub4e4\uc5ec\ub2e4 \ubcf4\uc544\ub3c4 \ud68c\uc804\uacfc scaling\uc744 \uc801\uc6a9\ud558\ub294 \ubc29\ubc95\uc740 \uc54c\uaca0\ub294\ub370 \uc77c\ubc18\uc801 \uc120\ud615\ubcc0\ud658\uc744 \uc801\uc6a9\ud558\ub294 \ubc29\ubc95\uc740 \uc54c\uc544\ub0bc \uc218\uac00 \uc5c6\uc5b4\uc11c\ub2e4.In [14]:<\/p>\n\n\n\n
gr2 =<\/strong> gr1.<\/strong>transform(rot=<\/strong>(0,0,1,pi\/<\/strong>2)).<\/strong>transform(scale=<\/strong>(-<\/strong>1,1,-<\/strong>1))\n<\/pre>\n\n\n\n
\uadf8\ub7f0\ub370 \ud574 \ubcf4\uba74<\/p>\n\n\n\n
gr1.transform(rot=(0,0,1,pi\/2)).transform(scale=(-1,1,-1))\n\n<\/code><\/pre>\n\n\n\n
\ub3c4 \uac19\uc740 \uacb0\uacfc\ub97c \uc8fc\ub294 \uac83 \uac19\ub2e4. \ud655\uc2e4\ud55c \uacb0\uacfc\ub294 \ubaa8\ub974\uaca0\ub2e4.<\/p>\n\n\n\n
\ucc38\uace0\ub85c \uc704 \ubcc0\ud658\uc744 \uc54c\uc544\ub0b8 \ubc29\ubc95\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n\n\n\n
  • dir(gr1)\ub85c \ubaa8\ub4e0 attributes\uc640 methods\ub97c \uc54c\uc544\ub0b4\uace0\uc790 \ud588\uc73c\ub098 \uc2e4\ud328.<\/li>
  • type(gr1)\ub85c \ub098\uc624\ub294 a\uc758 \ud074\ub798\uc2a4 \uc774\ub984\uacfc \uadf8 \ub0b4\uc6a9\uc774 \uc815\uc758\ub418\uc5b4 \uc788\ub294 \uc18c\uc2a4 \ud30c\uc77c \uc704\uce58 \ud30c\uc545<\/li>
  • \ud574\ub2f9 \uc704\uce58\ub85c \uac00 \uc18c\uc2a4 \ud30c\uc77c \uc77d\ub2e4\uac00 \uc704 \ub0b4\uc6a9\uc744 \uc54c\uac8c \ub428.<\/li><\/ul>\n\n\n\n
    In [15]:<\/p>\n\n\n\n
    type(gr1)\n<\/pre>\n\n\n\n
    Out[15]:<\/p>\n\n\n\n
    <class 'sage.plot.plot3d.parametric_surface.ParametricSurface'><\/pre>\n\n\n\n
    In [16]:<\/p>\n\n\n\n
    gr12 =<\/strong> gr1.<\/strong>transform(scale=<\/strong>(-<\/strong>1,1,1))\ngr13 =<\/strong> gr1.<\/strong>transform(scale=<\/strong>(-<\/strong>1,-<\/strong>1,1))\ngr14 =<\/strong> gr1.<\/strong>transform(scale=<\/strong>(1,-<\/strong>1,1))\n\ngr22 =<\/strong> gr2.<\/strong>transform(scale=<\/strong>(-<\/strong>1,1,1))\ngr23 =<\/strong> gr2.<\/strong>transform(scale=<\/strong>(-<\/strong>1,-<\/strong>1,1))\ngr24 =<\/strong> gr2.<\/strong>transform(scale=<\/strong>(1,-<\/strong>1,1))\n\ngr =<\/strong> gr1 +<\/strong> gr2 +<\/strong> gr12 +<\/strong> gr13 +<\/strong> gr14 +<\/strong> gr22 +<\/strong> gr23 +<\/strong> gr24\n<\/pre>\n\n\n\n
    In [17]:<\/p>\n\n\n\n
    gr.<\/strong>show(frame=<\/strong>False<\/strong>)\n<\/pre>\n\n\n\n
    \ucc38\uace0) \uc774 \ud30c\uc77c\uc744 html \ud30c\uc77c\ub85c \ubcc0\ud658\ud560 \ub54c displayed equation\uc744 \uadf8\uac83\ub9cc \ub530\ub85c \ud55c markdown \uc140\uc5d0 \ub123\uc9c0 \uc54a\uc73c\uba74 \ubcc0\ud658\uc774 \uc81c\ub300\ub85c \ub418\uc9c0 \uc54a\ub294\ub2e4.<\/p>\n","protected":false},"excerpt":{"rendered":"
    \uc591\uc131\ub35520210413 \uc138 \ubc88\uc9f8 \uc2dc\ub3c4 \ub2f9\uc2dc \uc54c\uc9c0 \ubabb\ud588\ub358 \uae30\ubc95\uc744 \uc54c\uac8c \ub418\uc11c \uc774\uc81c \ub2e4\uc74c\uacfc \uac19\uc774 \uadf8\ub9bc\uc744 \uc644\uc131\ud55c\ub2e4. \uc774\ub7ec\uba74 Weber\uac00 \uadf8\ub9b0 \ubc29\ubc95\uc744 \uadf8\ub300\ub85c \ub530\ub978 \uc148\uc774 \ub41c\ub2e4. \ucc38\uace0 \ubb38\ud5cc[2] Matthias Weber, Costa’s Minimal Surface, Mathematica Notebook File %display latexIn [1]: var(‘rho’) rho = ( gamma(3\/4)\/sqrt(2)\/gamma(5\/4) ).n() In [2]: Phi1(w) = 2*rho*I*sqrt(w)*hypergeometric((1\/4,3\/2,), (5\/4,), w^2) Phi2(w) = -2\/(3*rho)*I*w*sqrt(w)*hypergeometric((1\/2,3\/4,), (7\/4,), w^2) In [3]: omega1(z) = […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center 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