EndDegree => ..., default value 3, Option to specify the degree to stop computing the acyclic closure
StartDegree => ..., default value 1, Option to specify the degree to start computing the acyclic closure.
Outputs:
B, an instance of the type DGAlgebra, The acyclic closure of the DG Algebra A up to homological degree provided in the EndDegree option (default value is 3).
Description
i1 : R = ZZ/101[a,b,c]/ideal{a^3,b^3,c^3}
o1 = R
o1 : QuotientRing
i2 : A = koszulComplexDGA(R);
i3 : B = acyclicClosure(A,EndDegree=>3)
o3 = {Ring => R }
Underlying algebra => R[T ..T ]
1 6
2 2 2
Differential => {a, b, c, a T , b T , c T }
1 2 3
o3 : DGAlgebra
i4 : toComplex(B,8)
1 3 6 10 15 21 28 36 45
o4 = R <-- R <-- R <-- R <-- R <-- R <-- R <-- R <-- R
0 1 2 3 4 5 6 7 8
o4 : ChainComplex
i5 : B.diff
2 2 2
o5 = map (R[T ..T ], R[T ..T ], {a, b, c, a T , b T , c T , a, b, c})
1 6 1 6 1 2 3
o5 : RingMap R[T ..T ] <-- R[T ..T ]
1 6 1 6
See also
acyclicClosure(Ring) -- Compute the acyclic closure of the residue field of a ring up to a certain degree
Ways to use acyclicClosure :
acyclicClosure(DGAlgebra)
acyclicClosure(Ring) -- Compute the acyclic closure of the residue field of a ring up to a certain degree