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
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
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