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 Washington http://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/ -~----------~----~----~----~------~----~------~--~---
