Sign Function (3D)

3d surface plot of the sign function over the complex plane.

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% 3d surface plot of the sign function over the complex plane.
\documentclass{standalone}
\usepackage{mathtools,pgfplots}
\pgfplotsset{compat=newest}
\let\Im\relax
\DeclareMathOperator{\Im}{Im}
\let\Re\relax
\DeclareMathOperator{\Re}{Re}
\begin{document}
\begin{tikzpicture}
  \begin{axis}[
      xlabel=$\Re(p_0)$,
      ylabel=$\Im(p_0)$,
      zlabel=$s(p_0)$,
      domain=-1:1, surf, shader=flat,
      xtick distance=1,
      ytick distance=1,
      ztick distance=1,
      tickwidth=0,
    ]
    \addplot3[blue!30] coordinates {
        (-1, 1, -1) (0, 1, -1)
        (-1, 0, -1) (0, 0, -1)
      };
    \addplot3[blue!30] coordinates {
        (1, -1, -1) (0, -1, -1)
        (1, 0, -1) (0, 0, -1)
      };
    % Zero plane
    \addplot3[gray, opacity=0.1, samples=2]{0};
    \addplot3[orange!80] coordinates {
 
 
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