Arrays[{d1, ..., dr}]
represents the domain of arrays of rank r and dimensions .

Arrays[{d1, ..., dr}, dom]
represents the domain of arrays of dimensions , with components in the domain dom.

Arrays[{d1, ..., dr}, dom, sym]
represents the subdomain of arrays with dimensions and symmetry sym.


  • The length r of the list of dimensions is the rank or depth of the arrays in the domain.
  • Valid dimension specifications in Arrays[{d1, ..., dr}, dom, sym] are positive integers. It is also possible to work with symbolic dimension specifications.
  • Valid component domain specifications dom are either Reals or Complexes. Arrays[{d1, ..., dr}] uses Complexes by default.
  • The symmetry sym can be given in several forms. First, it can be given as expressions like Symmetric[{s1, ..., sk}] or Antisymmetric[{si, ..., sk}], with the slots being different positive integers between 1 and the rank r. It can also be given as a list of generators of the form , representing that the array stays invariant under simultaneous transposition by the permutation perm and multiplication by the root of unity . In addition, it can be given as the internal direct product of those forms.
  • When the symmetry is not specified, then none is assumed. The absence of symmetry, or identity symmetry, is represented by an empty list of generators.
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