gives the symmetry of tensor under permutations of its 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$Assumptionsassumptions to make about tensors
    SameTestAutomaticfunction to test equality of expressions
    ToleranceAutomatictolerance 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 .


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Basic Examples  (2)

A symmetric matrix:

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An antisymmetric matrix:

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A symmetric array of rank 3:

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Scope  (7)

Options  (3)

Properties & Relations  (5)

Introduced in 2012
Updated in 2017