On Friday 16 March 2007 14:10, William Stein wrote: > > On the other hand, the user should be allowed to make number fields > > by polys with non-integral coefficients. Perhaps you want to > > translate for them, to make the arithmetic fast and the user > > experience transparent. Sounds like a pain though. > > I strongly encourage you to do this. MAGMA can do it, and it's > a feature users really really appreciate. They *will* have to do it > themselves a lot if you don't -- and it's better to have the pain happen > once and be thought out, than have it happen often.
Ok, then you are agreeing that the polynomial defining the number field should be a member of ZZ['x']? It is currently a member of QQ['x']. Given a general element of QQ['x'], I can clear the denominator and get a member of ZZ['x'], but this won't (necessarily) be monic. Is that ok? The current code complains about non-monics. > > Of course to represent *elements* of the number field, you need > > denominators. Probably best to represent elements using a polynomial > > in Z[x], with a single denominator, which is I think what you've been > > suggesting. > > I suspect Joel was really asking about this, and I agree with your > suggestion. That's not what I was asking. David answered my question. Elements already have a ZZX numerator and ZZ denominator in my implementation. -- Joel --~--~---------~--~----~------------~-------~--~----~ 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-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
