C, a chain complex, The DG algebra A as a ChainComplex
Description
i1 : R = ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3,d^3}
o1 = R
o1 : QuotientRing
i2 : A = acyclicClosure(R,EndDegree=>3)
o2 = {Ring => R }
Underlying algebra => R[T ..T ]
1 8
2 2 2 2
Differential => {a, b, c, d, a T , b T , c T , d T }
1 2 3 4
o2 : DGAlgebra
The above will be a resolution of the residue field over R, since R is a complete intersection.
i3 : C = toComplex(A, 10)
1 4 10 20 35 56 84 120 165 220 286
o3 = R <-- R <-- R <-- R <-- R <-- R <-- R <-- R <-- R <-- R <-- R
0 1 2 3 4 5 6 7 8 9 10
o3 : ChainComplex
i4 : apply(10, i -> prune HH_i(C))
o4 = {cokernel | d c b a |, 0, 0, 0, 0, 0, 0, 0, 0, 0}
o4 : List