i1 : R = ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3-d^4} o1 = R o1 : QuotientRing |
i2 : A = koszulComplexDGA(R) o2 = {Ring => R } Underlying algebra => R[T ..T ] 1 4 Differential => {a, b, c, d} o2 : DGAlgebra |
i3 : A.diff o3 = map(R[T ..T ],R[T ..T ],{a, b, c, d, a, b, c, d}) 1 4 1 4 o3 : RingMap R[T ..T ] <--- R[T ..T ] 1 4 1 4 |
i4 : B = killCycles(A) o4 = {Ring => R } Underlying algebra => R[T ..T ] 1 7 2 2 2 3 Differential => {a, b, c, d, a T , b T , - c T + d T } 1 2 3 4 o4 : DGAlgebra |
i5 : B.diff 2 2 2 3 o5 = map(R[T ..T ],R[T ..T ],{a, b, c, d, a T , b T , - c T + d T , a, b, c, d}) 1 7 1 7 1 2 3 4 o5 : RingMap R[T ..T ] <--- R[T ..T ] 1 7 1 7 |
The object killCycles is a method function with options.