On Thu, Mar 13, 2014 at 01:32:10PM -0700, Volker Braun wrote:
> On Wednesday, March 12, 2014 8:45:57 PM UTC-4, Thierry
> (sage-googlesucks@xxx) wrote:
> >
> > - create RSF (for "real symbolic field") to isolate pi and sqrt(2) from
> > cos(x) in the symbolic ring.
>
> Thats essentially what RLF does.
RLF loses some symbolic (resp. algebraic) information compared to SR:
sage: a = sqrt(2)
sage: a^2
2
sage: b = RLF(a)
sage: b^2
2.000000000000000?
sage: b^2 == 2
False
> > - re-create RR as an "overlay field" over the different representations
>
> Its a basic fact that you can't represent a "generic" real number on a
> computer. You can argue that one should default to a lazy evaluation and
> not pick a favorite, but that also means that it'll be useless in practice.
> You can't safely & effectively do floating-point computations without
> picking a particular representation first. Trying to pretend otherwise is
> just kidding yourself.
This is not about floating-point arithmetic nor evaluation, but about a
common parent with some semantics in it.
Not all binary infinite words can be represented by a computer (with the
same countability argument), still Sage proposes a
Words('01', finite=False) parent.
Ciao,
Thierry
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