Dear Dina, In the case f_1,..,f_k is a SAGBI basis, you could probably use Lemma 6.2 in https://www.sciencedirect.com/science/article/pii/S0747717116300815?via%3Dihub
It is not very well explained (and I just found a couple of typos; apologies), but I think that you could reproduce the idea. Hope this helps, Pedro El El mar, 4 jul 2023 a las 12:40, Dima Pasechnik <dimp...@gmail.com> escribió: > We're looking for the ways to deal in Sage with > finitely generated subrings S=<f_1,...,f_k> of the ring of > polynomials R[x_1,...,x_n] (R a field) > of multivariate polynomial rings and their Hilbert-Poincare series. > > Once you have a presentation for S, i.e. S isomorphic to R[y_1,...,y_k]/I, > with I an ideal in appropriately graded R[y_1,...,y_k], (the latter > ring should have grading deg(y_j)=deg(f_j)) one can compute > the Hilbert series H(S,t) of S as > H(S,t)=H(R[y_1,...,y_k])-H(R[y_1,...,y_k]/I), > and the terms in the RHS of the latter can be computed by Sage already. > > Also, as far as I understand, Sage can compute the minimal free resolution > of > the module of syzygies of S, and from the resolution the presentation can > be > assembled. > So it seems that the only missing bit is computation of a presentation of > S. > > Any pointers? > > Thanks, > Dima > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-support+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/CAAWYfq1sSfG_kT2LKoy-CT6ougsKExQvvjPufSetMsq2YsO-rg%40mail.gmail.com > . > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/CAOAJP6p9%3DctCh-mgZLRYcX1gV-DTx1%2BoorH3Jx6quq2Z7nHfNg%40mail.gmail.com.
