TensorModule -- The class of all tensor modules

Description

A tensor module is a module that is a tensor product of smaller modules, which "remembers" that it is a tensor product. Mathematically, one could define a tensor module as a module M augmented with a list of other modules M₁...M_n and a choice of isomorphism to M’=M₁**...**M_n. In Macaulay2, this isomoprhism is implicit in that M and M’ are == as modules, and the isomorphism is accessible as inducedMap(M,M’).

i1 : R=QQ[x]

o1 = R

o1 : PolynomialRing

i2 : M=R^3 ** R^3 ** R^4 -- doesn't remember it's a tensor product, but

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o2 = R

o2 : R-module, free

i3 : N=tensorModule(R,{3,3,4}) -- does.

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o3 = R  {3x3x4}

o3 : Free R-TensorModule of order 3, dimensions {3, 3, 4}

i4 : (class M,class N)

o4 = (Module, TensorModule)

o4 : Sequence

i5 : M==N -- they are equal as modules,

o5 = true

i6 : M'===M -- but not as typed objects, and

o6 = false

i7 : O=tensorModule(R,{4,3,4})

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o7 = R  {4x3x4}

o7 : Free R-TensorModule of order 3, dimensions {4, 3, 4}

i8 : not M==O -- tensor modules with different factors are considered different

o8 = true

i9 : N.factors

       3   3   4
o9 = {R , R , R }

o9 : List

i10 : O.factors

        4   3   4
o10 = {R , R , R }

o10 : List

Methods that use a tensor module :

module(TensorModule) (missing documentation)
net(TensorModule) (missing documentation)
tensor(TensorModule,Vector) (missing documentation)
tensor(TensorModule,VisibleList) (missing documentation)
TensorModule ** TensorModule
TensorModule ^ ZZ
tensorModule(TensorModule), see tensorModule -- Constructor for making modules whose elements are tensors
TensorModule == TensorModule (missing documentation)
TensorModule @ List (missing documentation)
TensorModule _ Sequence (missing documentation)

For the programmer

The object TensorModule is a type, with ancestor classes Module < ImmutableType < HashTable < Thing.