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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