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# DGAlgebra ** DGAlgebra -- Tensor product of a DGAlgebra and another ring.

## Synopsis

• Operator: **
• Usage:
C = A ** B
• Inputs:
• Outputs:

## Description

Tensor product of a pair of DGAlgebras.

 i1 : R = ZZ/101[a,b,c,d] o1 = R o1 : PolynomialRing i2 : A = koszulComplexDGA({a,b}) o2 = {Ring => R } Underlying algebra => R[T ..T ] 1 2 Differential => {a, b} o2 : DGAlgebra i3 : B = koszulComplexDGA({c,d}) o3 = {Ring => R } Underlying algebra => R[T ..T ] 1 2 Differential => {c, d} o3 : DGAlgebra i4 : C = A ** B o4 = {Ring => R } Underlying algebra => R[T ..T ] 1 4 Differential => {a, b, c, d} o4 : DGAlgebra i5 : Cdd = toComplex C 1 4 6 4 1 o5 = R <-- R <-- R <-- R <-- R 0 1 2 3 4 o5 : ChainComplex i6 : Cdd.dd 1 4 o6 = 0 : R <--------------- R : 1 | a b c d | 4 6 1 : R <----------------------------- R : 2 {1} | -b -c 0 -d 0 0 | {1} | a 0 -c 0 -d 0 | {1} | 0 a b 0 0 -d | {1} | 0 0 0 a b c | 6 4 2 : R <----------------------- R : 3 {2} | c d 0 0 | {2} | -b 0 d 0 | {2} | a 0 0 d | {2} | 0 -b -c 0 | {2} | 0 a 0 -c | {2} | 0 0 a b | 4 1 3 : R <-------------- R : 4 {3} | -d | {3} | c | {3} | -b | {3} | a | o6 : ChainComplexMap

## Caveat

Currently, the tensor product function does not create a block order on the variables from A and B.