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Which[test1,value1,test2,value2,…]

evaluates each of the testi in turn, returning the value of the valuei corresponding to the first one that yields True.

Details
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Examples  
Basic Examples  
Scope  
Programming Behavior  
Symbolic Transformations  
Properties & Relations  
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Which

Which[test1,value1,test2,value2,…]

evaluates each of the testi in turn, returning the value of the valuei corresponding to the first one that yields True.

Details

  • Which has attribute HoldAll.
  • If any of the testi evaluated by Which give neither True nor False, then a Which object containing these remaining elements is returned unevaluated. »
  • You can make Which return a "default value" by taking the last testi to be True.
  • If all the testi evaluate to False, Which returns Null.

Examples

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Basic Examples  (1)

Wolfram Language code: a = 2;Which[a == 1, x, a == 2, b]

Scope  (4)

Programming Behavior  (3)

Which can be maintained in symbolic form:

Wolfram Language code: Which[a == 1, x, a == 2, b]
Wolfram Language code: % /. a -> 2

Conditions are evaluated until one is found that is neither True nor False:

Wolfram Language code: Which[1 < 0, a, x == 0, b, 0 < 1, c]

Use True for an else clause that always matches:

Wolfram Language code: sign[x_] := Which[ x < 0, -1, x > 0, 1, True, Indeterminate]
Wolfram Language code: sign /@ {-2, 0, 3}

Symbolic Transformations  (1)

Define a piecewise function:

Wolfram Language code: f = Which[x < -Pi / 2, -1, -Pi / 2 ≤ x ≤ Pi / 2, Sin[x], True, 1]

Expand it to use Piecewise:

Wolfram Language code: PiecewiseExpand[f]

Do symbolic operations:

Wolfram Language code: Reduce[f == 1 / 2, x]
Wolfram Language code: Integrate[f, {x, 0, 3}]
Wolfram Language code: D[f, x]
Wolfram Language code: Plot[f, {x, -Pi, Pi}]

Properties & Relations  (2)

Use Which rather than a nested if-then-elseif chain:

Wolfram Language code: cut1[x_] := If[x < -1, -1, If[x < 1, x, 1]]
Wolfram Language code: cut1 /@ {-2, -1, 0, 1, 2}
Wolfram Language code: cut2[x_] := Which[ x < -1, -1, x < 1, x, True, 1]
Wolfram Language code: cut2 /@ {-2, -1, 0, 1, 2}

Use PiecewiseExpand to convert Which to Piecewise:

Wolfram Language code: PiecewiseExpand[Which[c1, a1, c2, a2, True, a3]]
Wolfram Language code: PiecewiseExpand[Which[c1, Which[d1, b1, True, b2], True, a2]]
Wolfram Language code: PiecewiseExpand[Which[Which[d1, b1, True, b2], a1, True, a2]]
Wolfram Research (1988), Which, Wolfram Language function, https://reference.wolfram.com/language/ref/Which.html.

Text

Wolfram Research (1988), Which, Wolfram Language function, https://reference.wolfram.com/language/ref/Which.html.

CMS

Wolfram Language. 1988. "Which." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Which.html.

APA

Wolfram Language. (1988). Which. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Which.html

BibTeX

@misc{reference.wolfram_2026_which, author="Wolfram Research", title="{Which}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Which.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_which, organization={Wolfram Research}, title={Which}, year={1988}, url={https://reference.wolfram.com/language/ref/Which.html}, note=[Accessed: 13-June-2026]}