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

Synopsis

• Usage:

  tensorProduct L

  (tensorProduct List)

  (tensorProduct Sequence)

• Inputs:
  • L, a list, or Sequence of objects of type Matrix, Module, LabeledModule or LabeledModuleMap
• Outputs:
  • a matrix, or, in general, an object of the same type as the inputs.

Description

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

• basisList -- gives the list used to label the basis elements of a labeled module
• underlyingModules -- gives the list of underlying modules of a labeled module
• LabeledModule -- the class of free modules with a labeled basis
• LabeledModuleMap -- the class of maps between LabeledModules
• ** -- a binary operator, usually used for tensor product or Cartesian product