On Thu, Mar 13, 2014 at 01:02:09PM +0100, Vincent Delecroix wrote:
> Nope, too confusing... the bars in QQbar and RRbar have two different 
> meanings.

Well, i agree that QQ.bar() and RR.bar() will be confusing, because they
do not correspond to the same operations (algebraic_closure, vs 2-point
compactification). But QQbar and RRbar (as a single string) both come
from very standard mathematical notations. I am not sure someone ever
confused QQbar as a compactification of QQ or RRbar as the algebraic
closure of RR (and if this happens, perhaps could Sage be helping such
people to learn some mathematics in using those notations). Such a
parent could help in dealing with InfinityRing coercions issues.

sage: PolynomialRing(QQ, 1, 'x').quotient(x^2).an_element()
xbar

To summarize, i would 
- use a homogeneous notation for genuine mathematical objects,
  e.g. NN, ZZ, QQ, AA, RR, RRbar, QQbar, CC.
- use a homogeneous notation for the various computer approximations,
  e.g. RDF, RIF, RFF, RLF, RSF, CDF, CIF, CFF, CLF, CSF.

I think such naming scheme could help a lot in making Sage easier to
grasp for newcommers, and is the one that requires the less changes in
Sage existing notations.

Ciao,
Thierry

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