Seconded. I can see a role for some Sage representation of the 
(mathematical) set of reals (or complexes, BTW), well distinct from the set 
of finite binary approximations. Some of the Sympy operations on Sympy sets 
may be an inspiration....

HTH,

Le mercredi 14 octobre 2020 à 08:28:08 UTC+2, vdelecroix a écrit :

> Dear all,
>
> I would like to discuss the patchbomb at
>
> https://trac.sagemath.org/ticket/24523
>
> The ticket hopes to change the string representation from
> "Real Field with XX bits of precision" to "Real Floating-point
> field with XX bits of precision".
>
> Rationale: it was quite unfortunate from the beginning that
> RealField and ComplexField mean "floating-point arithmetic".
> On the one hand, one would like to be able to work with the
> (abstract) Parent modeling the real numbers (eg for coercions).
> On the other hand, in the setting of computer algebra it is
> very often much better to work with interval arithmetic or
> balls rather than floating-point. The ticket is a small
> step towards getting the genuine "RealField" standing for
> the set of real numbers. See
>
> https://trac.sagemath.org/ticket/17713
>
> I think this deserves an agreement from other developers! Any
> comment very welcome.
>
> Best
> Vincent
>
>

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