We have a *new* problem here :
-
Sage’s NN, ZZ and QQ are :
- mathematically corect representations of [image: \mathbb{N}], [image:
\mathbb{Z}] and [image: \mathbb{Q}] respectively, *and*
- provide acceptable implementations of their arithmetics.
-
The algebraic sets AA and QQbar provide both an acceptable (one could
say miraculous) representation of the (real or not) algebraics and an
implementation of their respective arithmetics modulo some conventions on
representations.
We know that neither [image: \mathbb{R}] nor [image: \mathbb{C}] can have
an acceptable representation in machine. So we created *approximate*
representation(s) (RR, RDF und so weiter…) of (parts of) these sets, and,
until now, refrained to create objects representing the general (abstract)
properties of the (mathematical) reals (resp. complexes).
Unfortunately, we used the “easy” names RR and CC for our approximate
representations. So, our alternative is:
- keep the “easy” names for the implementations, create new names for
the “abstracts” sets (if and when implemented) ; to be consistent, we
should also create new names for the “abstract sets representing the
naturals, integerts, fractions and algebraics, even if simple synonyms of
the implementations.
- keep the “easy” names for the abstract sets and create names for the
implementations ; this would introduce a big (?) backward compatibility
problem,
Since Sage’s target is mathematicians, I *think* that they may think first
in terms of mathematical properties, the implementation being only a
secondary concern. Is that “mathematical ease of use” worth the
backward-compatibility problem ?
Until I hear more about this tradeoff, I’ll abstain from voting.
One more question : how easy (or difficult) would it be to “trap”
operations on reals (resp complexes) needing an implementation to raise a
warning (or an exception) (or potentially a silent substitution) if called
inadvertently on a member of an “abstract” set ?
Le mercredi 21 octobre 2020 à 10:10:40 UTC+2, chris wuthrich a écrit :
>
> +1 for changing printing of RR to something like John Cremona or others
> have suggested
> -1 for changing RR or RealField at this stage. (It is not "progress" to
> change a name, so does not vouch for breaking backwards compatibility; I
> may change when and if another serious candidate for RR it is here, but
> probably not even then.)
>
> Chris
>
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