-1. First, everything cwitty said is correct. Second, if we start using ZZ[sqrt(2)] and ZZ[sqrt(3)], then sqrt(2)+sqrt(3) requires going through the coercion system which was designed to be elegant instead of fast, so this becomes insanely slow for any serious use. Finally, this is going to require serious code duplication from symbolics, so I'm not sure what the big gain is over just using symbolics to do this in the first place.
On Mon, Jun 2, 2008 at 12:31 PM, Robert Bradshaw <[EMAIL PROTECTED]> wrote: > > 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 -~----------~----~----~----~------~----~------~--~---
