genericSymmetricMultidimensionalMatrix -- make a generic symmetric multidimensional matrix of variables

Synopsis

• Usage:
genericSymmetricMultidimensionalMatrix(n,d)
• Inputs:
• (n,d), two positive integers.
• Optional inputs:
• CoefficientRing => ..., default value QQ
• Variable => ..., default value a
• Outputs:

Description

An $n$-dimensional matrix $M$ is symmetric if for every permutation $s$ of the set $\{0,\ldots,n-1\}$ we have permute(M,s) == M.

 i1 : genericSymmetricMultidimensionalMatrix(3,2) o1 = {{{a , a }, {a , a }}, {{a , a }, {a , a }}} 0 1 1 2 1 2 2 3 o1 : 3-dimensional matrix of shape 2 x 2 x 2 over QQ[a ..a ] 0 3 i2 : genericSymmetricMultidimensionalMatrix(3,2,CoefficientRing=>ZZ/101) o2 = {{{a , a }, {a , a }}, {{a , a }, {a , a }}} 0 1 1 2 1 2 2 3 ZZ o2 : 3-dimensional matrix of shape 2 x 2 x 2 over ---[a ..a ] 101 0 3 i3 : genericSymmetricMultidimensionalMatrix(3,2,CoefficientRing=>ZZ/101,Variable=>"b") o3 = {{{b , b }, {b , b }}, {{b , b }, {b , b }}} 0 1 1 2 1 2 2 3 ZZ o3 : 3-dimensional matrix of shape 2 x 2 x 2 over ---[b ..b ] 101 0 3