WOLFRAM

Wolfram Language & System Documentation Center

Exclusions

is an option that specifies where to exclude in regions used by functions like Plot, Plot3D, and NIntegrate.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Possible Issues  
See Also
Related Guides
History
Cite this Page

Exclusions

Exclusions

is an option that specifies where to exclude in regions used by functions like Plot, Plot3D, and NIntegrate.

Details

  • The following settings specify what to exclude:
  • Noneno exclusions
    Allall computed exclusions
    Automaticautomatically computed exclusions
    "Discontinuities"computed jump discontinuities
    "Singularities"computed singularities
    lhs==rhsexplicitly defined by an equation
    {lhsrhs,cond}explicitly defined by an equation and a condition
    {spec1,spec2,…}union of exclusions given by speci
  • Exclusions->Automatic is effectively equivalent to Exclusions->All if $PerformanceGoal is "Quality", and to Exclusions->None otherwise.
  • For a domain defined by n variables, exclusions must be of dimension .
  • For a domain defined by one variable, Exclusions->{x1,x2,…} will exclude the points xi.
  • Exclusions"Discontinuities" typically includes piecewise discontinuities and branch-cut discontinuities.
  • Exclusions"Singularities" typically includes poles and essential singularities.
  • The automatically computed exclusions will typically include potential discontinuities and singularities, including removable discontinuities and singularities.
  • For plotting functions, ExclusionsStyle specifies how to draw exclusions and their boundaries.

Examples

open all close all

Basic Examples  (5)

Exclude portions of a surface where it has jumps:

Leave the surface entirely connected:

Exclude portions of a curve where it has jumps:

Exclude a fixed set of points:

Specify where the function is discontinuous:

Scope  (6)

Exclude areas where the function has jump discontinuities:

Exclude areas where the function has singularities:

Specify the style to use for excluded portions of a curve:

Use dotted lines to connect portions of the curve and red points where there are jumps:

Use transparency to show excluded portions of the surface:

Use thick, red lines around the edges of the excluded portions of the surface:

Possible Issues  (2)

Removable singularities may be detected:

Use Exclusions->None to ignore the singularity:

Sinc[x] is equivalent to Sin[x]/x but does not have a singularity at :

Some discontinuities and singularities may not be detected:

Specify where the discontinuities are:

Wolfram Research (2007), Exclusions, Wolfram Language function, https://reference.wolfram.com/language/ref/Exclusions.html (updated 2016).

Text

Wolfram Research (2007), Exclusions, Wolfram Language function, https://reference.wolfram.com/language/ref/Exclusions.html (updated 2016).

CMS

Wolfram Language. 2007. "Exclusions." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/Exclusions.html.

APA

Wolfram Language. (2007). Exclusions. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Exclusions.html

BibTeX

@misc{reference.wolfram_2025_exclusions, author="Wolfram Research", title="{Exclusions}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/Exclusions.html}", note=[Accessed: 07-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_exclusions, organization={Wolfram Research}, title={Exclusions}, year={2016}, url={https://reference.wolfram.com/language/ref/Exclusions.html}, note=[Accessed: 07-August-2025]}