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 0.0150689 seconds Computing generators in degree 2 : -- used 0.0214275 seconds Computing generators in degree 3 : -- used 0.0529644 seconds Computing generators in degree 4 : -- used 0.0603665 seconds Computing generators in degree 5 : -- used 0.288648 seconds Computing generators in degree 6 : -- used 0.493459 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 0.0112939 seconds Computing generators in degree 2 : -- used 0.0294499 seconds Computing generators in degree 3 : -- used 0.0225726 seconds Computing generators in degree 4 : -- used 0.0196908 seconds o8 = false |