i1 : R = ZZ/101[a,b,c,d]/ideal{a^3,b^4,c^5,d^6} o1 = R o1 : QuotientRing |
i2 : A = koszulComplexDGA(R) o2 = {Ring => R } Underlying algebra => R[T , T , T , T ] 1 2 3 4 Differential => {a, b, c, d} isHomogeneous => true o2 : DGAlgebra |
i3 : apply(maxDegree A + 1, i -> numgens prune homology(i,A)) o3 = {1, 4, 6, 4, 1} o3 : List |
i4 : HA = homologyAlgebra(A) Computing generators in degree 1 : -- used 0.0087306 seconds Computing generators in degree 2 : -- used 0.0583344 seconds Computing generators in degree 3 : -- used 0.0554041 seconds Computing generators in degree 4 : -- used 0.0513124 seconds Finding easy relations : -- used 0.102478 seconds Computing relations in degree 1 : -- used 0.0126755 seconds Computing relations in degree 2 : -- used 0.0126657 seconds Computing relations in degree 3 : -- used 0.0124862 seconds Computing relations in degree 4 : -- used 0.0123697 seconds Computing relations in degree 5 : -- used 0.0112564 seconds o4 = HA o4 : PolynomialRing |
i5 : numgens HA o5 = 4 |
i6 : HA.cache.cycles 2 3 4 5 o6 = {a T , b T , c T , d T } 1 2 3 4 o6 : List |