On Fri, Oct 23, 2020 at 11:19 AM Vincent Delecroix <20100.delecr...@gmail.com> wrote: > > Le 23/10/2020 à 10:27, Dima Pasechnik a écrit : > > On Fri, Oct 23, 2020 at 8:04 AM Vincent Delecroix > > <20100.delecr...@gmail.com> wrote: > >> > >> Le 23/10/2020 à 08:38, Kwankyu Lee a écrit : > >>> > >>>> > >>>> Currently working on that (see http://fredrikj.net/calcium/ and > >>>> http://fredrikj.net/blog/2020/09/benchmarking-exact-dft-computation/). > >>>> > >>> > >>> Looks great! The standard question is then: do you think your library fits > >>> for the throne of RealField and could rule peacefully other "real fields" > >>> of Sage? > >>> > >> > >> The answer is no. The GenuineRealField is not meant to have elements. > > > > Are we now into computing with uncomputable ? > > What are you talking about? The set of real numbers is perfectly > manageable by a computer. Its elements are not. For example, the > genuine real field would be used for things like > > sage: QQ.metric_completion() > Real Field > sage: RR.is_complete() > True
Right, but how is it useful for a CAS, apart from pedagogical purposes (it certainly is useful in a proof assistant, though) ? No computable subfield would be complete, anyway. > > It is explained in https://trac.sagemath.org/ticket/24456 and you > are welcome to participate. > > > The next non-virtual Sagemath event is in danger of turning into a > > bacchanalia, > > as it'll have unlimited supply of wine from an unmeasurable bottle > > from Bordeaux... :P > > > > For all practical purposes, it seems that Calcium is ripe for becoming an > > important part of Sage. Anyone working on it? > > > > Dima > > > >> Even though Calcium is doing an amazing job at symbolic computations > >> with real numbers and might contain all other exact implementations > >> there is in SageMath, it will remain a set of computable real > >> numbers. That is a tiny subset of all the real numbers. > >> > >> The need for a GenuineRealField is explained in > >> > >> https://trac.sagemath.org/ticket/24456 > >> > >> Vincent > >> > >> -- > >> 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 view this discussion on the web visit > >> https://groups.google.com/d/msgid/sage-devel/bab7621b-8b98-9026-ad61-65567975f32f%40gmail.com. > > > > -- > 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 view this discussion on the web visit > https://groups.google.com/d/msgid/sage-devel/4b1546d2-4b62-edf5-163c-08693274a8a6%40gmail.com. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAAWYfq15dpiy5Ua0xtNh_b38M8O9hRLQpo2QfCsu4kxwF%2Bd29Q%40mail.gmail.com.
