I agree that these are not fields in the mathematical sense. And Sage
knows about it
sage: RR.is_exact()
False
sage: QQ.is_exact()
True
However, they are much more than sets as they come with approximations
of the field operations (+, x, ^-1). Maybe a reasonable terminology
would be "numerical field"? And in this regard, RealFloatingPointField
perfectly make sense. I am against RealFloats.
Le 15/10/2020 à 11:24, Samuel Lelievre a écrit :
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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