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Getting only 1 of 3 curves of intersection

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126292] Getting only 1 of 3 curves of intersection
  • From: Bill <WDWNORWALK at aol.com>
  • Date: Sun, 29 Apr 2012 02:09:26 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hi:

Consider the following plot:

g1=Plot3D[Sin[x*y],{x,0,Pi},{y,0,Pi},PlotStyle->None,MeshStyle->Red,Axes->True,AxesLabel->{"x","y","z"}];
g2=Plot3D[Cos[x*y],{x,0,Pi},{y,0,Pi},Mesh->None,PlotStyle->{Cyan,Opacity[.8]}];
nsSol=NSolve[{z-Sin[x*y],z-Cos[x*y]},{y,z}];//Quiet
g3=ParametricPlot3D[{x,y,z}/.nsSol[[2]],{x,0,Pi},PlotStyle->{Magenta,Thickness[.007]}];
Show[g1,g2,g3,Background->LightYellow,ImageSize->500]

Using the above Mathematica 8.0.4 code, I can plot one curve of intersection shown in magenta. 
Within the plotted area, I can see 2 more places where intersection curves should be.  
I've tried using Reduce in place of NSolve, but can't get it to work.

Question: If this can be done, can someone please give me the code?


Thanks,

Bill



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