Nils Bruin wrote:
> Here is something I think is really a bug:
> 
> sage: parent(RealField(200)(1) + 1e-20)
> Real Field with 53 bits of precision

Yes. And I'd say the behavior of RealField(200)(RR(1e-20))) is a bug as 
well (the same bug in fact).

So I think there are two different issues here:

1. Real literals are elements of RR. IMO this is a bug that needs to be
   fixed. However, Jeroen disagreed in the ticket where this discussion
   originated[1], so I would like to hear other people's opinion. In my
   view, literals such as 1e-20 could be preparsed to Python floating-
   point decimals, rationals, elements of CLF... but certainly not
   elements of RR.

   [1] http://trac.sagemath.org/ticket/15542

2. Should real literals exist in the first place? I personally agree
   with Paul that they do more harm than good (they add a gratuitous
   difference between Sage and most languages, including Python, and
   they do not fit too well in Sage's floating-point arithmetic model).
   But having them in Sage is not an unreasonable design choice either.
   And of course getting rid of them entirely would break compatibility
   with earlier versions of Sage.

-- 
Marc

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