i1 : R = ZZ/101[a,b,c,d]/ideal{a^4,b^4,c^4,d^4}
o1 = R
o1 : QuotientRing
|
i2 : S = R/ideal{a^3*b^3*c^3*d^3}
o2 = S
o2 : QuotientRing
|
i3 : A = acyclicClosure(R,EndDegree=>3)
o3 = {Ring => R }
Underlying algebra => R[T , T , T , T , T , T , T , T ]
1 2 3 4 5 6 7 8
3 3 3 3
Differential => {a, b, c, d, a T , b T , c T , d T }
1 2 3 4
isHomogeneous => true
o3 : DGAlgebra
|
i4 : B = A ** S
o4 = {Ring => S }
Underlying algebra => S[T , T , T , T , T , T , T , T ]
1 2 3 4 5 6 7 8
3 3 3 3
Differential => {a, b, c, d, a T , b T , c T , d T }
1 2 3 4
isHomogeneous => true
o4 : DGAlgebra
|
i5 : isHomologyAlgebraTrivial(B,GenDegreeLimit=>6) Computing generators in degree 1 : -- used 0.0143018 seconds Computing generators in degree 2 : -- used 0.0192639 seconds Computing generators in degree 3 : -- used 0.0557056 seconds Computing generators in degree 4 : -- used 0.0588502 seconds Computing generators in degree 5 : -- used 0.278697 seconds Computing generators in degree 6 : -- used 0.460483 seconds o5 = true |
i6 : R = ZZ/101[a,b,c,d]/ideal{a^4,b^4,c^4,d^4}
o6 = R
o6 : QuotientRing
|
i7 : A = koszulComplexDGA(R)
o7 = {Ring => R }
Underlying algebra => R[T , T , T , T ]
1 2 3 4
Differential => {a, b, c, d}
isHomogeneous => true
o7 : DGAlgebra
|
i8 : isHomologyAlgebraTrivial(A) Computing generators in degree 1 : -- used 0.0287691 seconds Computing generators in degree 2 : -- used 0.0226204 seconds Computing generators in degree 3 : -- used 0.020955 seconds Computing generators in degree 4 : -- used 0.0188258 seconds o8 = false |