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tensorAssociativity -- associativity isomorphisms for tensor products

Description

Produce the isomorphism that exhibits associativity of the tensor product construction.

i1 : kk = ZZ/101

o1 = kk

o1 : QuotientRing
 
i2 : R = kk[a, b, c]

o2 = R

o2 : PolynomialRing
 
i3 : I = ideal (a, b); A = I/I^2

o3 : Ideal of R

o4 = subquotient (| a b |, | a2 ab b2 |)

                               1
o4 : R-module, subquotient of R
 
i5 : J = ideal (b, c); B = J/J^2

o5 : Ideal of R

o6 = subquotient (| b c |, | b2 bc c2 |)

                               1
o6 : R-module, subquotient of R
 
i7 : K = ideal (a, c); C = K/K^2

o7 : Ideal of R

o8 = subquotient (| a c |, | a2 ac c2 |)

                               1
o8 : R-module, subquotient of R
 
i9 : T =  A_0 ** (B_0 ** C_0)

o9 = | 1 |
     | 0 |
     | 0 |
     | 0 |
     | 0 |
     | 0 |
     | 0 |
     | 0 |

o9 : Vector
 
i10 : T' = (A_0 ** B_0) ** C_0

o10 = | 1 |
      | 0 |
      | 0 |
      | 0 |
      | 0 |
      | 0 |
      | 0 |
      | 0 |

o10 : Vector
 
i11 : assert(tensorAssociativity(A, B, C) * T == T')

See also

Ways to use tensorAssociativity:

  • tensorAssociativity(Module,Module,Module)

For the programmer

The object tensorAssociativity is a method function.

The source of this document is in Macaulay2Doc/functions/tensor-doc.m2:481:0.