# TensorSymmetry

TensorSymmetry[tensor]

gives the symmetry of tensor under permutations of its slots.

TensorSymmetry[tensor,slots]

gives the symmetry under permutation of the specified list of slots.

# Details and Options • TensorSymmetry accepts any type of tensor, either symbolic or explicit, including any type of array.
• A general symmetry is specified by a generating set of pairs {perm,ϕ}, where perm is a permutation of the slots of the tensor, and ϕ is a root of unity. Each pair represents a symmetry of the tensor of the form ϕ TensorTranspose[tensor,perm]==tensor.
• Some symmetry specifications have names:
•  Symmetric[{s1,…,sn}] full symmetry in the slots si Antisymmetric[{s1,…,sn}] antisymmetry in the slots si ZeroSymmetric[{s1,…,sn}] symmetry of a zero tensor
• The following options can be given:
•  Assumptions \$Assumptions assumptions to make about tensors SameTest Automatic function to test equality of expressions Tolerance Automatic tolerance for approximate numbers
• For exact and symbolic arrays, the option SameTest->f indicates that two entries aij and akl are taken to be equal if f[aij,akl] gives True.
• For approximate arrays, the option Tolerance->t can be used to indicate that all entries Abs[aij]t are taken to be zero.
• For array entries Abs[aij]>t, equality comparison is done except for the last bits, where is \$MachineEpsilon for MachinePrecision arrays and for arrays of Precision .

# Examples

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## Basic Examples(2)

A symmetric matrix:

 In:= Out= An antisymmetric matrix:

 In:= Out= A symmetric array of rank 3:

 In:= In:= Out= ## Properties & Relations(5)

Introduced in 2012
(9.0)
|
Updated in 2017
(11.2)