On Jan 15, 2008 8:46 AM, Martin Albrecht <[EMAIL PROTECTED]> wrote: > > Hi everybody, > > in a nutshell I want to compute something like this MAGMA session in Sage: > > %magma > P<a,b,c,d> := PolynomialRing(GF(127),4); > I := ideal<P|c^3-b*d^2,b*c-a*d,b^3-a^2*c,a*c^2-b^2*d>; > S<t> := HilbertSeries(I); > S; > L<u> := LaurentSeriesRing(IntegerRing()); > L ! S; > > The first part is quite easy as I wrapped the appropriate Singular function > (singular.hilb(I,1)/(1-t^n)). It is the second part that gives me trouble, > i.e. I need the first n Laurent series terms for the rational function which > describes the Hilbert series.
It might be a lot easier to help if you gave the rational function. Depending on how complicated the denominator is, you basically just have to compute the Taylor series of the rational function, by differentiation and evaluation (using Taylor's formula), i.e., kind of like this is doing, but over GF(p): sage: f = (x^3 + x +1)/((x^4 + x^2 + 2)*x^3*(x^3-5)) sage: f.taylor(x, 0, 4) -1/(10*x^3) - 1/(10*x^2) + 1/(20*x) - 7/100 + x/200 + 17*x^2/200 - 103*x^3/2000 - 23*x^4/2000 -- William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com 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://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
