This function determines if the canonical map from ambient R --> R is Golod. It does this by computing an acyclic closure of ambient R (which is a DGAlgebra), then tensors this with R, and determines if this DG Algebra has a trivial Massey operation up to a certain homological degree provided by the option GenDegreeLimit.
i1 : R = ZZ/101[a,b,c,d]/ideal{a^4+b^4+c^4+d^4} o1 = R o1 : QuotientRing |
i2 : isGolodHomomorphism(R,GenDegreeLimit=>5) o2 = true |
If R is a Golod ring, then ambient R $\rightarrow$ R is a Golod homomorphism.
i3 : Q = ZZ/101[a,b,c,d]/ideal{a^4,b^4,c^4,d^4} o3 = Q o3 : QuotientRing |
i4 : R = Q/ideal (a^3*b^3*c^3*d^3) o4 = R o4 : QuotientRing |
i5 : isGolodHomomorphism(R,GenDegreeLimit=>5,TMOLimit=>3) o5 = true |
The map from Q to R is Golod by a result of Avramov and Levin; we can only find the trivial Massey operations out to a given degree.
The object isGolodHomomorphism is a method function with options.