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
|
The object genericSymmetricMultidimensionalMatrix is a method function with options.