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 OptionsDetails 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 , 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
    Antisymmetric[{s1,,sn}]antisymmetry in the slots
    ZeroSymmetric[{s1,,sn}]symmetry of a zero tensor
Introduced in 2012
(9.0)