Signature

Signature[list]

gives the signature of the permutation needed to place the elements of list in canonical order.

Details

  • The signature of the permutation is (-1)n, where n is the number of transpositions of pairs of elements that must be composed to build up the permutation.
  • If any two elements of list are the same, Signature[list] gives 0.
  • Signature can be used on expressions with any head, not only List.

Examples

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Basic Examples  (1)

Applications  (3)

Find even permutations:

Rank-3 totally antisymmetric (Levi-Civita) tensor:

Contractions of Levi-Civita tensors:

Properties & Relations  (2)

Find components of a 3D cross product:

Compute a determinant:

Compare with built‐in Det:

Possible Issues  (2)

The precision of a number influences its ordering:

Signature evaluates even for symbolic arguments:

Use Unevaluated to insert an unevaluated Signature:

Use Signature directly inside Table:

Neat Examples  (1)

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_signature, author="Wolfram Research", title="{Signature}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/Signature.html}", note=[Accessed: 24-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_signature, organization={Wolfram Research}, title={Signature}, year={1988}, url={https://reference.wolfram.com/language/ref/Signature.html}, note=[Accessed: 24-July-2025 ]}