B = golodBetti(M,b)
Let S be a standard graded polynomial ring. A module M over R = S/I is Golod if the resolution H of M has maximal betti numbers given the betti numbers of the S-free resolutions F of R and K of M. This resolution, H, has underlying graded module H = R**K**T(B), where B is the truncated resolution F_1 <- F_2... and T(B) is the tensor algebra.
Since the component modules of H are given, the computation only requires the computation of the minimal S-free resolution of M, and then is purely numeric; the differentials in the R-free resolution of M are not computed.
In case M = coker vars R, the result is the Betti table of the Golod-Shamash-Eagon resolution of the residue field.
We say that M is a Golod module (over R) if the ranks of the free modules in a minimal R-free resolution of M are equal to the numbers produced by golodBetti. Theorems of Levin and Lescot assert that if R has a Golod module, then R is a Golod ring; and that if R is Golod, then the d-th syzygy of any R-module M is Golod for all d greater than or equal to the projective dimension of M as an S-module (more generally, the co-depth of M) (Avramov, 6 lectures, 5.3.2).
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The object golodBetti is a method function.