On Thursday 02 October 2008, Simon King wrote: > Dear Sage team, > > I often have to deal with graded commutative algebras, which I emulate > in Singular using SuperCommutative plus a weighted monomial ordering. > I also have weighted homogeneous ideals, and I want to compute the > Hilbert function. > > Problem 1: > Singular can compute the Hilbert function only for commutative rings. > > Problem 2: > I have one commutative example where Singular apparently has an > integer overflow. > The nasty thing is that Singular does not complain but simply returns > a wrong answer > (fortunately I knew the result from other sources). > > Now I see that MPolynomialRing ideals in Sage also have a method > hilbert_series. The doc-string says: > Let I = self be a homogeneous ideal and R = > self.ring() be a graded commutative algebra (R = > oplus R_d) over a field K. Then the Hilbert function is... > > I was very surprised to see "graded commutative algebra" being > mentioned. But how can one create them? Up to now I thought that > generators of polynomial rings in Sage have degree 1, and there is no > way to change it. And now even "graded commutative" (hence, in > general, NON-commutative)? > > The index of the Sage reference manual contains the word "graded" only > once (in a different context), so, it didn't help.
Hi Simon, that function just wraps Singular so you're out of luck. The docstring is due to my lack of rigor. Cheers, Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _www: http://www.informatik.uni-bremen.de/~malb _jab: [EMAIL PROTECTED] --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
