Ok, I'll just add to this thread whatever I come across. For the moment I think I found a small bug in hilbert_class_field. R.<X> = PolynomialRing(QQ) K.<u> = NumberField(X^2 + 5) L.<v> = K.hilbert_class_field() causes an error. However, when I create K explicitly as a quadratic field: K.<u> = QuadraticField(-5) L.<v> = K.hilbert_class_field() everything is ok.
On May 31, 2:41 am, "William Stein" <[EMAIL PROTECTED]> wrote: > Hi Utpal, > > Unfortunately number fields are not in the best shape in SAGE right > now. There's > been much discussion about this among some of the SAGE developers recently, > and we will have a project about this at Sage Days 4 (which is in two weeks). > So, basically, keep your questions and comments coming. They will help. > > On 5/30/07, Utpal Sarkar <[EMAIL PROTECTED]> wrote: > > > > > > > To compute the abstract class group I can just create a number field > > K = QuadraticField(-23) > > and ask for it > > K.class_group() > > -> Multiplicative Abelian Group isomorphic to C3 > > Is there a way to obtain representatives of the ideal classes (like in > > Magma where there is a second return value that is a map from the > > abstract group to the set of prime ideals? > > When trying to obtain generators "by hand" I encountered the following > > problem: > > p = K.factor_integer(2)[0][0] > > is a prime divisor of 2, which happens to have order 3 (the function > > p.order() is not implemented yet). > > p.is_principal() > > -> False > > However: > > (p^3).is_principal() > > -> False > > gives the wrong answer. > > This roundabout gives the correct answer > > len((p^3).gens_reduced()) == 1 > > -> True > > but I encountered instances where the reduced set of generators is not > > as reduced as it could be, so this is not a reliable method. > > -- > William Stein > Associate Professor of Mathematics > University of Washingtonhttp://www.williamstein.org --~--~---------~--~----~------------~-------~--~----~ 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://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
