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Symmetrize[tensor,sym]

returns the symmetrization of tensor under the symmetry sym.

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Symmetrize

Symmetrize[tensor,sym]

returns the symmetrization of tensor under the symmetry sym.

Details

  • Symmetrize[tensor] assumes symmetrization by the full Symmetric[{1,…,r}], where r is the rank of tensor.

Examples

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Basic Examples  (2)

Antisymmetrize an array:

Wolfram Language code: Symmetrize[{{a, b}, {c, d}}, Antisymmetric[{1, 2}]]

In normal form:

Wolfram Language code: Normal[%]

Symmetrize a symbolic tensor:

Wolfram Language code: Symmetrize[T, Symmetric[{1, 2, 3}]]

Scope  (3)

Symmetrize an array by a given symmetry:

Wolfram Language code: Symmetrize[Array[Subscript[a, ##]&, {2, 2, 2}], Symmetric[{1, 2, 3}]]
Wolfram Language code: Normal[%]

Symmetrize a symbolic tensor by a general symmetry specification:

Wolfram Language code: $Assumptions = R∈Arrays[{d, d, d, d}, Reals]
Wolfram Language code: Symmetrize[R, {{{2, 1, 3, 4}, -1}, {{3, 4, 1, 2}, 1}}]

Without a second argument, Symmetric[All] is assumed:

Wolfram Language code: Normal@Symmetrize[{{a, b}, {c, d}}]

With symbolic tensors of a given rank:

Wolfram Language code: $Assumptions = A∈Matrices[{dim, dim}]
Wolfram Language code: Symmetrize[A]
Wolfram Research (2012), Symmetrize, Wolfram Language function, https://reference.wolfram.com/language/ref/Symmetrize.html.

Text

Wolfram Research (2012), Symmetrize, Wolfram Language function, https://reference.wolfram.com/language/ref/Symmetrize.html.

CMS

Wolfram Language. 2012. "Symmetrize." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Symmetrize.html.

APA

Wolfram Language. (2012). Symmetrize. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Symmetrize.html

BibTeX

@misc{reference.wolfram_2026_symmetrize, author="Wolfram Research", title="{Symmetrize}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/Symmetrize.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_symmetrize, organization={Wolfram Research}, title={Symmetrize}, year={2012}, url={https://reference.wolfram.com/language/ref/Symmetrize.html}, note=[Accessed: 13-June-2026]}