On Saturday 01 November 2008, mmarco wrote: > I agree that, when it is possible, it is better to work in exact > rings. But sometimes (not in this particular example, but in other > similar ones) you actually need to use complex numbers. I guess there > is a way to do it in an alggebraic extension of Q, but i am not sure > how to handle that with sage.
Here is how to construct polynomial rings over absolute number fields. sage: P.<x> = PolynomialRing(QQ) sage: K.<i> = NumberField(x^2 + 1) sage: i i sage: i^2 -1 sage: P.<x,y,z> = PolynomialRing(K) sage: I = sage.rings.ideal.Katsura(P) sage: J = Ideal(i*f for f in I.gens()) sage: J.groebner_basis() [x + 2*y + 2*z - 1, y*z + 6/5*z^2 - 1/10*y - 2/5*z, y^2 - 3/5*z^2 - 1/5*y + 1/5*z, z^3 - 79/210*z^2 + 1/30*y + 1/70*z] sage: %timeit x*y 1000000 loops, best of 3: 343 ns per loop Note that if you choose the complex numbers as base field a generic much slower polynomial implementation is chosen. sage: P.<x,y,z> = PolynomialRing(CC) sage: %timeit x*y 100000 loops, best of 3: 11.7 µs per loop -- 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 sage-devel@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-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
