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## Implicit or Spherical

Maple
The following equation cannot be plotted correctly in the usual 3 dimensional plot with Cartesian coordinates. eq := (x^2+y^2+z^2-1)^3 - x^2*z*3 - y^2*z^3 = 0; Either a 3 dimensional implicit plot, or a spherical coordinates plot is needed. What surprised me was how long Maple 10.06 took to produce the latter with very roughly the same amount of detail as the former: 454 s versus 0.7 s. It seems as though one should always prefer the implicit plot to the spherical plot if the 3 dimensional Cartesian plot fails. I would be grateful for any thoughts about this and any improvements to the code below. (Apologies for not posting the worksheet – I think that File Manager might object to its 10MB size!) restart; eq := (x^2+y^2+z^2-1)^3 - x^2*z*3 - y^2*z^3 = 0; sol := solve(eq,z): start := time(): plot3d(sol,x=-2..2,y=-2..2, orientation=[30,50], axes=boxed); `time taken` := time() - start; start := time(): plots[implicitplot3d](eq,x=-1.5..1.5,y=-1.5..1.5,z=-1.5..1.5, numpoints=10^5, scaling=constrained, orientation=[60,70], axes=boxed); `time taken` := time() - start; eq1 := changecoords(eq,[x,y,z],spherical,[r,theta,phi]): sol := solve(eq1,r): start := time(): plot3d(sol,theta=0..Pi,phi=0..2*Pi, coords=spherical, numpoints=10^4, axes=box, scaling=constrained, orientation=[60,70]); `time taken` := time() - start; Many thanks, J. Tarr

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