On May 16, 1:20 am, Robert Bradshaw <[EMAIL PROTECTED]> wrote: > What I think should happen is that sqrt(2) should be an element of QQ > [sqrt(2)] rather than an element of SR. There is work supporting this > kind of thing in the new coercion model (specifically, sqrt(2) would > be an element of QQ[sqrt(2)] with a specified embedding into RR, so > stuff like RR(1) + sqrt(2) would work). Then this kind of casting > could make a lot more sense.
Anybody who implements this should steal code from qqbar.py. AA/QQbar can basically be divided into two parts: a framework for lazy arbitrary-precision arithmetic, that does computations using interval arithmetic whenever the interval arithmetic suffices to give an answer to the desired precision; and an exact layer that is used when the interval arithmetic is insufficiently precise. This exact layer is almost exactly what you describe above: it maintains extensions of QQ with embeddings into RR or CC, and automatically combines the extensions to let you do arithmetic like sqrt(2) + sqrt(3). I probably won't do it myself, but I would be very happy if somebody cleaned up this exact layer and moved it into number fields. Carl --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
