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DiscreteIndicator[x,x1,{u1,u2,…}]

yields the discrete indicator function, equal to 1 if x=x1 and, otherwise, to 0 if x=ui for some i.

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DiscreteIndicator

DiscreteIndicator[x,x1,{u1,u2,…}]

yields the discrete indicator function, equal to 1 if x=x1 and, otherwise, to 0 if x=ui for some i.

Details

Examples

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Basic Examples  (1)

Give 1 if the first arguments are equal:

Wolfram Language code: DiscreteIndicator[a, a, {a, b, c}]

Give 0 if they are not equal:

Wolfram Language code: DiscreteIndicator[b, a, {a, b, c}]

If the first argument does not appear in the third argument, return unevaluated:

Wolfram Language code: DiscreteIndicator[a, a, {x, y}]

Applications  (1)

Represent nominal terms in fitting results:

Wolfram Language code: lm = LinearModelFit[{{a, 1.5}, {b, 2.3}, {b, 1.8}, {a, 2.5}}, x, x, NominalVariables -> x]

See the functional form:

Wolfram Language code: Normal[lm]

Evaluate the FittedModel at points a and b:

Wolfram Language code: {lm[a], lm[b]}

Properties & Relations  (2)

DiscreteIndicator is equivalent to Boole when both values are in the set:

Wolfram Language code: Table[{DiscreteIndicator[x, a, {a, b, c}], Boole[x === a]}, {x, {a, b, c}}]

They differ if either of the first two values is not in the set:

Wolfram Language code: {DiscreteIndicator[x, a, {a, b, c}], Boole[x === a]}

Products of indicator functions effectively correspond to an outer product:

Wolfram Language code: Flatten[Table[{{x, y}, DiscreteIndicator[x, a, {a, b}]DiscreteIndicator[y, b, {a, b}], DiscreteIndicator[{x, y}, {a, b}, {{a, a}, {a, b}, {b, a}, {b, b}}]}, {x, {a, b}}, {y, {a, b}}], 1] //Grid
Wolfram Research (2008), DiscreteIndicator, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscreteIndicator.html.

Text

Wolfram Research (2008), DiscreteIndicator, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscreteIndicator.html.

CMS

Wolfram Language. 2008. "DiscreteIndicator." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DiscreteIndicator.html.

APA

Wolfram Language. (2008). DiscreteIndicator. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DiscreteIndicator.html

BibTeX

@misc{reference.wolfram_2026_discreteindicator, author="Wolfram Research", title="{DiscreteIndicator}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/DiscreteIndicator.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_discreteindicator, organization={Wolfram Research}, title={DiscreteIndicator}, year={2008}, url={https://reference.wolfram.com/language/ref/DiscreteIndicator.html}, note=[Accessed: 13-June-2026]}