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tensorProduct -- tensor product of Modules and LabeledModules, Matrices, Maps and LabeledModuleMaps

Synopsis

Description

Forms the tensor product of the objects in the input list or sequence. In the case where the inputs are of type LabeledModule, the output is a labeled module whose basis list is the set of tuples of elements of the basis lists of the input modules

i1 : S = ZZ/101[x,y]

o1 = S

o1 : PolynomialRing
 
i2 : M = labeledModule(S^4)

      4
o2 = S

o2 : free S-module with labeled basis
 
i3 : basisList M

o3 = {0, 1, 2, 3}

o3 : List
 
i4 : E = exteriorPower(2,M)

      6
o4 = S

o4 : free S-module with labeled basis
 
i5 : basisList E

o5 = {{0, 1}, {0, 2}, {1, 2}, {0, 3}, {1, 3}, {2, 3}}

o5 : List
 
i6 : underlyingModules E

       4
o6 = {S }

o6 : List
 
i7 : N = tensorProduct(E,labeledModule(S^2))

      12
o7 = S

o7 : free S-module with labeled basis
 
i8 : basisList N

o8 = {{{0, 1}, 0}, {{0, 1}, 1}, {{0, 2}, 0}, {{0, 2}, 1}, {{1, 2}, 0}, {{1,
     ------------------------------------------------------------------------
     2}, 1}, {{0, 3}, 0}, {{0, 3}, 1}, {{1, 3}, 0}, {{1, 3}, 1}, {{2, 3}, 0},
     ------------------------------------------------------------------------
     {{2, 3}, 1}}

o8 : List
 
i9 : underlyingModules N

       6   2
o9 = {S , S }

o9 : List

See also

Ways to use tensorProduct :

For the programmer

The object tensorProduct is a method function with a single argument.