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ZeroSymmetric[{s1,…,sn}]

represents the symmetry of a zero tensor in the slots si.

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ZeroSymmetric

ZeroSymmetric[{s1,…,sn}]

represents the symmetry of a zero tensor in the slots si.

Details

  • The slots si must be different positive numbers. The order of the list is irrelevant.
  • TensorSymmetry on zero tensors canonicalizes the result to ZeroSymmetric[{}].

Examples

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Basic Examples  (2)

Symmetry of a zero array:

Wolfram Language code: TensorSymmetry[{{0, 0}, {0, 0}}]

Declare a symbolic array with the zero symmetry:

Wolfram Language code: $Assumptions = A∈Arrays[{3, 3, 3}, Reals, ZeroSymmetric[{1, 2, 3}]];

Then that symbolic array is actually a zero tensor:

Wolfram Language code: A//TensorReduce

Scope  (2)

Symmetry of arrays of zeros:

Wolfram Language code: TensorSymmetry[{{0, 0}, {0, 0}}]
Wolfram Language code: SparseArray[{}, {3, 3, 2}]//TensorSymmetry

Declare an antisymmetric symbolic array:

Wolfram Language code: $Assumptions = A∈Arrays[{3, 3, 3, 3}, Reals, Antisymmetric[All]]

Any contraction is then a zero tensor, and hence has zero symmetry:

Wolfram Language code: TensorContract[A, {{1, 3}}]
Wolfram Language code: TensorSymmetry[%]

Properties & Relations  (3)

A tensor with symmetry ZeroSymmetric[…] does not have independent components:

Wolfram Language code: SymmetrizedIndependentComponents[{4, 4, 4}, ZeroSymmetric[{1, 2, 3}]]

Construct a symmetrized array with ZeroSymmetric[…] symmetry:

Wolfram Language code: SymmetrizedArray[pos_ :> RandomInteger[100], {3, 3, 3}, ZeroSymmetric[All]]

It is the zero tensor:

Wolfram Language code: Normal[%]

Symmetrization with respect to the zero symmetry returns a zero tensor:

Wolfram Language code: Symmetrize[{{a, b}, {c, d}}, ZeroSymmetric[{1, 2}]]
Wolfram Language code: %//SymmetrizedArrayRules
Wolfram Research (2012), ZeroSymmetric, Wolfram Language function, https://reference.wolfram.com/language/ref/ZeroSymmetric.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_zerosymmetric, author="Wolfram Research", title="{ZeroSymmetric}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/ZeroSymmetric.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_zerosymmetric, organization={Wolfram Research}, title={ZeroSymmetric}, year={2012}, url={https://reference.wolfram.com/language/ref/ZeroSymmetric.html}, note=[Accessed: 13-June-2026]}