On 3/27/07, David Harvey <[EMAIL PROTECTED]> wrote: > > Is there a much better way to find an inverse than > > the extended euclidean algorithm? > > In general, I don't think so, but it's quite possible (in fact I > think very likely) that magma has special code to deal with quadratic > extensions, in which case obviously everything can be done much more > efficiently.
Undoubtedly MAGMA has special code for quadratic fields. I don't know the situation today, but for a very long time my understanding is that MAGMA's quadratic field arithmetic was simply a wrapper around the highly optimized quadratic field arithmetic in the PARI C library. (MAGMA used KANT for general number fields and PARI for quadratic fields.) > For more data points, you could try two things: (1) try the same > tests as below, but for a more complicated number field, at least > degree 4, with a pretty random looking defining polynomial, and (2) > compare magma's performance in quadratic fields against its general > number field stuff. Agreed. Also, consider creating the same loops in %sagex block in the notebook. It's very good to have a sense of how that performs as well, since writing in SageX is an important and viable option when writing in SAGE. -- Willia --~--~---------~--~----~------------~-------~--~----~ 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://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
