On Thu, Mar 10, 2016 at 08:17:43AM +0100, Jeroen Demeyer wrote:
> On 2016-03-09 23:56, Thierry wrote:
> >Willing to
> >change the behaviour will be similar to requesting that 'NaN in RR' should
> >return False.
> Not the topic of this thread, but I really think that "NaN in RR" should
> return False. RR represents the real numbers and NaN is *not a number*.

RR does *not* correspond to the real numbers, at least not in the way that
NN, ZZ, QQ, AA, QQbar do. RR is just a MPFR representation of numbers,
among various other representations, such as RDF, RIF, RBF,...  The
particular RR name is ill-chosen, but RR is nothing but a slower
implementation of RDF, whose second letter clearly insist on the
representation (an information that is missing for RR). The benefit of
MPFR over CPU-floats is when we use more than 53 bits of precision. The
focus on MPFR among other representations is imho a mistake.

See http://trac.sagemath.org/ticket/17713#comment:3

> Note that Sage usually defines "x in P" as "P(x) == x" which would
> actually give False for NaN since NaN != NaN.

The NaN in the namespace is from SR, so the equality RR(NaN)==NaN is
coerced in SR, in which NaN equals NaN.

Ciao,
Thierry


> Whether Infinity should be in RR is a more borderline question, but I don't
> mind that RR(1)/RR(0) gives Infinity.
> 
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