I do not agree with Miguel: it makes sense to have a Parent modeling the set of all real numbers (even if it has no element). And the natural name for it would be RR.
Now, concerning concrete computation, what you can do is either : - use floating points (ie approximate operations +, x, -, / and exact equality) - use computable numbers (ie exact operations but approximate equality) - deal with a nice subsets of RR (such as algebraic numbers, finite transcendantal extensions, ...) where you can deal with exact operations and exact equality. - mix of the one above It is bad that only QQ, QQbar and SR can handle arbitrary precision real number. It would make more sense to have pi, e, cos(3/4), ... in a ring of "exact reals". It deviates from the initial subject but it is always good to say that real numbers should not be in SR and that RR is misnamed ! Vincent 2014-03-12 21:29 UTC+01:00, mmarco <mma...@unizar.es>: > Since the ring you want will be an algebra over the reals, the best fit for > > base ring would be the reals. > > Now, since it is impossible to represent the real field in practice, there > are different possible solutions in sage: > > RR if you don't care about the lack of exactness > QQ or some extension (like AA) if you want exactness but don't mind the > lack of transcendentals > SR if you want to allow arbitrary expressions, with the problem of speed > and maybe the lack of a unique form for each element. > > I don't think that you can do much better than that to work with the reals. > > In practice, since in every computation there will only be a finite number > of symbols involved, it can be done in something like AA(t1,t2,...,tn) (a > trascendental extension of the algebraic reals) or QQ[a](t1,t2,...,tn) with > > a in AA. But working in those rings can be extremely slow, and you would > need in advance which numbers would appear, which are algebraic and which > trascendental and so on. So i wouldn't advise it. > > > El miércoles, 12 de marzo de 2014 20:37:00 UTC+1, Eric Gourgoulhon > escribió: >> >> Thanks for your answer and suggestions. >> >> Best wishes, >> >> Eric. >> >> Le mercredi 12 mars 2014 17:55:46 UTC+1, Nils Bruin a écrit : >>> >>> On Wednesday, March 12, 2014 6:41:07 AM UTC-7, Eric Gourgoulhon wrote: >>>> >>>> The issue here is that CommutativeRing.__init__ requires the argument >>>> "base_ring" and in the present context, I don't know what to put here: >>>> the >>>> ring C^oo(N) does not depend upon any other ring. Shall I put self, i.e. >>>> >>>> write CommutativeRing.__init__(self, self) ? >>>> >>> >>> Every ring ultimately has ZZ as a base, by virtue of being an additive >>> group. You could use that. On the other hand, if you expect the thing to >>> be >>> finitely generated over its base then perhaps the ring should be its own >>> >>> base (I don't think that's a formal requirement, given that >>> `ZZ[['x']].base_ring()==ZZ`). This does happen in Sage elsewhere: >>> >>> sage: ZZ.base_ring() >>> Integer Ring >>> sage: QQ.base_ring() >>> Rational Field >>> sage: GF(3).base_ring() >>> Finite Field of size 3 >>> >>> On the other hand, if you find it's doable to avoid specifying a base, >>> perhaps that's the better way to go. >>> >> > > -- > You received this message because you are subscribed to the Google Groups > "sage-devel" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sage-devel+unsubscr...@googlegroups.com. > To post to this group, send email to sage-devel@googlegroups.com. > Visit this group at http://groups.google.com/group/sage-devel. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
