I like RealFloats (RF) and ComplexFloats (CF).  Since float is a type
in both Python and C, they seem reasonable as names for a type/class
in Sage too.  I can imagine many people wanting to predefine RR=RF and
CC=CF to make their own code backward-compatible, but it seems to be
to be a good thing to have the short names RF and CF to remind one
that we are *not* using some idealised implementation of genuine real
or complex numbers.

This is a big change, so we should make sure that many people have a
chance to give their opinion.

John

On Thu, 15 Oct 2020 at 10:24, Samuel Lelievre <samuel.lelie...@gmail.com> wrote:
>
> 2020-10-15 08:21:06 UTC, John Cremona:
> >
> > I was expecting someone more pedantic than me to point out that this set
> > is not a field in the mathematical sense. Since this is a big change anyway
> > (at least to a lot of doctest outputs) should we think more carefully about
> > what we want to call RR? Instead of "Real floating-point field with x bits
> > of precision" we could have "Real floating-point numbers with x bits of
> > precision" perhaps. (With an implied "The set of" in front).
>
> Good point!
>
> I like "Real floating-point numbers with x bits of precision"
> with short name RFN for real floating-point numbers.
>
> Or shorter: "RealFloats" -> "Real floats with x bits of precision",
> short name RF for the standard one with 53 bits of precision.
>
> Consistency would dictate to rename and change the string representation
> for all of the following:
>
> - ComplexField -> ComplexFloats
> - RealField -> RealFloats
>
> - ComplexDoubleField -> ComplexDoubleFloats
> - RealDoubleField -> RealDoubleFloats
>
> - ComplexBallField -> ComplexFloatBalls
> - ComplexBallField -> RealFloatBalls
>
> - ComplexIntervalField -> ComplexFloatIntervals
> - RealIntervalField -> RealFloatIntervals
>
> and maybe more sort-of-fields that can be listed using:
> ```
> sage: [g for g in globals() if 'ield' in g]
> ```
>
> - ComplexLazyField -> ComplexLazyFloats?
> - RealLazyField -> RealLazyFloats?
>
> - MPComplexField -> MPComplexFloats?
>
> What about pAdicField?
>
> Of course we can do things one at a time, but it's good to plan ahead
> and maybe have a meta-ticket to keep track of what is done and what
> needs to be done.
>
> Side remark: should ComplexIntervalFieldElement, FieldElement
> and NumberFieldElement be removed from the global namespace?
>
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