On Jun 2, 2008, at 9:47 AM, William Stein wrote: > On Mon, Jun 2, 2008 at 9:45 AM, Carl Witty <[EMAIL PROTECTED]> > wrote: >> >> On Jun 2, 9:17 am, "William Stein" <[EMAIL PROTECTED]> wrote: >>> On Mon, Jun 2, 2008 at 1:30 AM, Henryk Trappmann >>>> But back to SymbolicRing and SymbolicConstant. >>>> I have the following improvement >>>> SUGGESTION: when creating sqrt(2) or other roots from integers, >>>> then >>>> assign to them the parent AlgebraicReal or AlgebraicNumer >>>> accordingly >>>> instead of the too general Symbolic Ring. >>> >>> That's definitely planned. >> >> Actually, if you mean that sqrt(2) should become the same as >> AA(sqrt(2)) is now, I'm not sure that's a good idea, for two reasons. >> First, AA and QQbar by design don't maintain enough information to >> print nicely. (This could be improved somewhat from the current >> state, but not enough to compete with symbolic radical expressions.) >> Second, since AA and QQbar incorporate complete decision procedures, >> it is easy to construct examples where they are very, very slow; I >> think people would often be happier with the less complete but much >> faster techniques used in symbolics. > > I think the plan is that algebraic elements won't just be generic > symbolic > elements, e.g., sqrt(2) would be a generator for ZZ[sqrt(2)]. This > has > been discussed a few times. I didn't mean that using AA or QQbar > by default was precisely what is planned.
Yep. Specifically, the plan is for sqrt(2) to become an element of ZZ [sqrt(2)] *with* and embedding into RR (so stuff like RR(sqrt(2)) or even 1.123 + sqrt(2) works). We would want to use very nice AA/QQbar code to compute, say, sqrt(2) + sqrt(3) (the result would live in a specific number field with embedding). (Nice) number fields with embedding would coerce into SR. - Robert --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
