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Re: To verify Cauchy-Riemann relations in complex variable graphically

• To: mathgroup at smc.vnet.net
• Subject: [mg39212] Re: To verify Cauchy-Riemann relations in complex variable graphically
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Tue, 4 Feb 2003 02:21:14 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <b1idcj$bje$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

Mathematica can't draw transparent surfaces but MathGL3d can

Get["MathGL3d`OpenGLViewer`"]

MVShow3D[z2r, MVNewScene -> True, MVAlpha -> 0.5];
MVShow3D[z2i, MVAlpha -> 0.5];

you can get MathGL3d from

http://phong.informatik.uni-leipzig.de/~kuska/mathgl3dv3/id3.htm

Regards
  Jens

"Narasimham G.L." wrote:
> 
> Is it possible to have a semi transparent view of surfaces so that one
> may verify slopes by ParametricPlot3D for Cauchy-Riemann relations?
> The following is program for 3 functions Z^2, Z^3, Sin[Z].It was
> expected to check slopes at the line of intersection of Re and Im parts.
> 
> R1=x^2-y^2 ; I1= 2 x y ;
> z2r=Plot3D[R1 , {x,-Pi,Pi},{y,-Pi,Pi} ];
> z2i=Plot3D[I1 , {x,-Pi,Pi},{y,-Pi,Pi} ];
> Show[z2r,z2i] ; 'Top view >> Re,Im Intxn';
> Plot[{x ArcTan[-Sqrt[2]+1],x ArcTan[Sqrt[2]+1]}, {x,-Pi,Pi} ];
> 
> R3=x^3 - 3 x y^2 ; I3= 3 x^2 y - y ^3 ;
> z3r=Plot3D[R3 , {x,-Pi,Pi},{y,-Pi,Pi} ];
> z3i=Plot3D[I3 , {x,-Pi,Pi},{y,-Pi,Pi} ];
> Show[z3r,z3i] ; 'Top view >> Re,Im Intxn';
> Plot[{x,x (-Sqrt[3]+2) , x (-Sqrt[3]-2) }, {x,-Pi,Pi} ];
> 
> R2=Cosh[y] Sin[x] ; I2=Sinh[y] Cos[x] ;
> scr=Plot3D[R2,{x,-Pi/2,Pi/2},{y,-Pi/2,Pi/2}];
> sci=Plot3D[I2,{x,-Pi/2,Pi/2},{y,-Pi/2,Pi/2}];
> Show[scr,sci]; 'Top view >>  Re,Im Intxn';
> Plot[{ArcTanh[Tan[x]]},{x,-Pi/2,Pi/2 }];
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