Hello, is there any ongoing progress on implementing a multigraded Hilbert series? I needed a multigraded Hilbert series for a quotient of a polynomial ring and found
- Ticket #6416 and - thread http://groups.google.com/group/sage-devel/browse_thread/thread/d5ad19efd4d0d847/bbc3a2345c2f5d2b?lnk=gst&q=hilbert+series#bbc3a2345c2f5d2b. To me it seems as there were a simple way to get the multigraded Hilbert series out of singular: sage: P = PolynomialRing(QQ,'x',2) sage: x = P.gens() sage: I = P.ideal( [ x[0]^2, x[0]*x[1], x[1]^3 ] ) sage: I.hilbert_series() t^2 + 2*t + 1 sage: B = I.normal_basis() sage: B [x1^2, x1, x0, 1] I.normal_basis() uses singular to return a monomial vector space basis of the quotient P/I. So assigning an element in a given monoid to any monomial results in the needed multigraded HIlbert series of the quotient. all methods .vector_space_basis(), .normal_basis() and .hilbert_series() take about the same time; I checked it with the actual example I was computing: sage: time I.vector_space_dimension() 258456 Time: CPU 425.10 s, Wall: 425.38 s sage: time len( I.normal_basis() ) 258456 Time: CPU 427.27 s, Wall: 430.01 s sage: time H = I.hilbert_series() Time: CPU 461.74 s, Wall: 463.28 s sage: H(1) 258456 Do others also like to have a multigraded Hilbert series? Do you agree on open a ticket for this implementation? Best regards, Christian -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
