BUILT-IN MATHEMATICA SYMBOL

# Arrays

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.

## DetailsDetails

• 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.

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

A fully symmetric real array of rank 3 in dimension 4:

 Out[1]=

Any transposition is equivalent to the original array:

 Out[2]=