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.
