Branch Cut

Author

Eric W. Weisstein
January 18, 2007

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/BranchCut.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/BranchCut.html.

©2007 Wolfram Research, Inc. except for portions noted otherwise

Listing

Eric's Package

fns=(#[[1]]/.BranchCuts[x_]:>x)[[1]]&/@DownValues[BranchCuts]

Length[fns]

BranchCuts[Sqrt]

Built-In

v6

The function can't figure out removable branch cuts are removable. There's also an internal inconsistency (sometimes variables are assumed to be real).

Visualization`VisualizationDiscontinuities;

?Visualization`VisualizationDiscontinuities

ComplexAnalysis`BranchCuts;

?ComplexAnalysis`BranchCuts

ComplexAnalysis`BranchCuts[Sqrt[z],z]

ComplexAnalysis`BranchCuts[Sqrt[z^2-1], z]

ComplexAnalysis`BranchCuts[LogGamma[z], z]

ComplexAnalysis`BranchCuts[Log[Gamma[z]], z]

Plots

<<Utilities`Plot`
<<Utilities`Typesetting`

Show[
Block[{$DisplayFunction=Identity},
GraphicsArray[
{Graphics[Text[TraditionalForm@BranchCuts[#],{0,0}]],
BranchCutPlot[#],Sequence@@ComplexPlot3D[#[z],{z,-2,2},DisplayFunction->Identity][[1]]
}&/@Take[fns,7]
]
],ImageSize->500,
GraphicsSpacing->{-.3,0}]

Show[
Block[{$DisplayFunction=Identity},
GraphicsArray[
{Graphics[Text[TraditionalForm@BranchCuts[#],{0,0}]],
BranchCutPlot[#],Sequence@@ComplexPlot3D[#[z],{z,-2,2},DisplayFunction->Identity][[1]]
}&/@Take[fns,-7]
]
],ImageSize->500,
GraphicsSpacing->{-.3,0}]