Useful, for example, when checking whether a map is a resolution of a complex in cases where the actual resolution is infinite
i1 : kk= ZZ/101 o1 = kk o1 : QuotientRing |
i2 : S = kk[a,b,c] o2 = S o2 : PolynomialRing |
i3 : R = S/ideal(a^3) o3 = R o3 : QuotientRing |
i4 : M = R^1/ideal(a) o4 = cokernel | a | 1 o4 : R-module, quotient of R |
i5 : C = chainComplex{map(M,R^0,0)} o5 = cokernel | a | <-- 0 0 1 o5 : ChainComplex |
i6 : m=cartanEilenbergResolution (C, LengthLimit => 10) 1 o6 = 0 : cokernel | a | <--------- R : 0 | 1 | 1 1 : 0 <----- R : 1 0 o6 : ChainComplexMap |
i7 : isQuasiIsomorphism(m, LengthLimit=> 10) o7 = true |
i8 : isQuasiIsomorphism(m, LengthLimit => 12) o8 = false |