Hi,

On Thu, Oct 15, 2020 at 10:19:25AM -0700, Nils Bruin wrote:
> I like RealFloats and ComplexFloats as well; however, I think it's too 
> early to relinquish RR and CC. There's no "exact real field" presently and 
> if it is ever realized, it should probably be called ExactRealField or 
> something similar to stress that it is NOT what people generally expect it 
> to be for the coming 25 years at least (because programming and calculators 
> will continue to deal primarily with floats). Any implementation of 
> ExactRealField will need to prove itself over an extended time period and 
> in a variety of applications before we can propose it as a default choice.

The question is not about exact or inexact, not even about the
implementation of its elements (we can even imagine that RR is not a
parent anymore), it is about having a home for the abstraction of the
real field, in the mathematical sense. Its elements can not have an
exact representation anyway (if only for a cardinality reason). So, it
is not to replace an implementation with another, but to have something
that covers all existing representations.

Currently, we have the following behaviours:

sage: oo in RR
True

sage: NaN in RR
True

sage: RIF(0,1) in RR
False

and while i have no problem to see such behaviour for, say, RDF, i would
like RR to be, among other features to be discussed, a generic container
that will tell whether some Sage object represents a real number or not.

I have a pretty long list of doctests (and implementation) that an
abstraction of the genuine real field, as a container, should satisfy,
and the previous examples will not hold. However,

sage: RDF(1.1) in RR
True

will still hold, no worry about that !

Ciao,
Thierry


> Leave the default values of RR and CC to what they are until it's clear 
> that there's a uniformly better default for them.
> 
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