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

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

## Description

Tensor product of a DGAlgebra and another ring (typically a quotient of A.ring).

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