ContourPlot3D taking too long

Question

I want to run my code

ContourPlot3D[(2 Zeta[1 + \[Alpha]] - 
   PolyLog[1 + \[Alpha], Exp[I*k]] - 
   PolyLog[1 + \[Alpha], Exp[-I*k]] - 2 A^2), {k, -2 \[Pi], 
  2 \[Pi]}, {A, 0, 30}, {\[Alpha], 0.001, 2}, 
 PlotLegends -> Automatic]

but even after a very long time it does not complete. Is there something I can do to make it finish compiling?

This has long been a problem, even in 2D. See [https://mathematica.stackexchange.com/q/1008/5467] . I'm not aware of some improvement since then. — andre314, Aug 24 '23 at 21:54

E. Chan-López · Accepted Answer · 2023-08-24T23:14:42.280

An alternative method using ListContourPlot3D:

expr = 2 Zeta[1 + α] - PolyLog[1 + α, Exp[I*k]] - PolyLog[1 + α, Exp[-I*k]] - 2 A^2;
ListContourPlot3D[Table[expr, {k, -2 π, 2 π}, {A, 0, 30}, {α, 0.001, 2}], 
Contours -> 4, Mesh -> None, AxesLabel -> {Style["k", Black, 18], 
Style["A", Black, 18], Style["α", Black, 18]}, PlotLegends -> Automatic]

Or using MaTeX:

<< MaTeX`
ListContourPlot3D[Table[expr, {k, -2 π, 2 π}, {A, 0, 30}, {α, 0.001, 2}], 
Contours -> 4, Mesh -> None, AxesLabel -> {MaTeX["k", Magnification -> 1.5], 
MaTeX["A", Magnification -> 1.5], MaTeX["\\alpha", Magnification -> 1.5]}, 
PlotLegends -> Automatic]

Evaluate ResourceFunction["MaTeXInstall"][] to install or upgrade MaTeX.

ContourPlot3D taking too long

1 Answers1