Dear all, vdelecroix schrieb am Freitag, 16. Oktober 2020 um 07:50:46 UTC+2:
> 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 > That's actually what I meant. We also have: sage: RR in Fields() True We could say that RR is a non-exact realization of an exact mathematical object which is a field, so that both outputs make somehow sense. But if we want it as rigorously as requested, we must as well require sage: RR in Fields() False If that is what we want, we perhaps need another category, e.g. "PseudoFields" in order to maintain most algorithms, e.g. for matrices. I'd suggest a workaround: so what about "Real Field realized by Floating-point arithmetics of precision xx" and keep the above behavior? And then similarly for interval arithmetics and ball arithmetics. Best, Michael > 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? > > > -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/5617ca3b-bc86-40e7-b313-af0cccf7f97bn%40googlegroups.com.
