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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:
- the generic symmetric multidimensional matrix of shape $d\times\cdots\times d$ ($n$ times).

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

See also

genericMultidimensionalMatrix -- make a generic multidimensional matrix of variables
genericSkewMultidimensionalMatrix -- make a generic skew symmetric multidimensional matrix of variables

Ways to use genericSymmetricMultidimensionalMatrix:

genericSymmetricMultidimensionalMatrix(ZZ,ZZ)

For the programmer

The object genericSymmetricMultidimensionalMatrix is a method function with options.