f: Si(F)⊗Sj(F)→Si+j(F).
The output map is treated as a map of labeled modules, and the source and target are inherit the natural structure as labeled modules from F. For instance, if the basis list of F is L, then the basis list of the target of f is the list multiSubsets(i+j,L).i1 : S=ZZ/101[x,y,z]; |
i2 : F=labeledModule(S^2); o2 : free S-module with labeled basis |
i3 : f=symmetricMultiplication(F,2,2)
o3 = | 1 0 0 0 0 0 0 0 0 |
| 0 1 0 1 0 0 0 0 0 |
| 0 0 1 0 1 0 1 0 0 |
| 0 0 0 0 0 1 0 1 0 |
| 0 0 0 0 0 0 0 0 1 |
5 9
o3 : Matrix S <--- S
|
i4 : source f
9
o4 = S
o4 : free S-module with labeled basis
|
i5 : basisList F
o5 = {0, 1}
o5 : List
|
i6 : basisList source f
o6 = {{{0, 0}, {0, 0}}, {{0, 0}, {0, 1}}, {{0, 0}, {1, 1}}, {{0, 1}, {0, 0}},
------------------------------------------------------------------------
{{0, 1}, {0, 1}}, {{0, 1}, {1, 1}}, {{1, 1}, {0, 0}}, {{1, 1}, {0, 1}},
------------------------------------------------------------------------
{{1, 1}, {1, 1}}}
o6 : List
|
i7 : basisList target f
o7 = {{0, 0, 0, 0}, {0, 0, 0, 1}, {0, 0, 1, 1}, {0, 1, 1, 1}, {1, 1, 1, 1}}
o7 : List
|