next | previous | forward | backward | up | top | index | toc | Macaulay2 website
SparseResultants :: genericSymmetricMultidimensionalMatrix

genericSymmetricMultidimensionalMatrix -- make a generic symmetric multidimensional matrix of variables

Synopsis

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

Ways to use genericSymmetricMultidimensionalMatrix :

For the programmer

The object genericSymmetricMultidimensionalMatrix is a method function with options.