On 19 mai, 03:36, leif <not.rea...@online.de> wrote:
> vdelecroix wrote:
> > In an attempt to improve #14567, I found the following thing (which
> > for me is a bug). Consider the different real fields with rounding
> > RNDD or RNDU. Then -pi is systematically wrongly approximated.
>
> AFAIK that's a (probably unexpected) feature rather than a bug, because
>
> R(-pi) = R(-1)*R(pi)
>
> (since pi is a symbolic constant, hence -pi a symbolic expression).
We should not have R(-pi) = R(-1) * R(pi) with rounding mode RNDD or
RNDU because it is how it is documented and how it works for
rationals. I agree that -pi is a symbolic expression but it is not a
reason for having a wrong answer. If we want to round down the
expression "- expr" then we should round up "expr" and then take the
opposite. Note that there are more dramatic problems with the symbolic
ring due to cancellation
{{{
sage: sage: a.n(digits=8)
293.65079
sage: sage: a.n(digits=10)
292.6277805
sage: sage: a.n(digits=12)
292.634618133
sage: sage: a.n(digits=15)
292.634591053247
}}}
What is shown above is that the rounding of ``a`` is *very far* from
being the nearest element of RR...
In my first post I also mentionned that it does not work either for
number field elements
{{{
a = NumberField(x^3-2, 'a', embedding=1.25).gen()
for rnd in 'RNDD','RNDU':
R = RealField(15,rnd=rnd)
s,m,e = R(-a).sign_mantissa_exponent()
}}}
gives
{{{
RNDD 20642
RNDU 20643
}}}
instead of
{{{
RNDD 20643
RNDU 20642
}}}
Moreover, the approximation does not work as expected either (the last
digits are always False)
{{{
sage: sage: b = (76504*a - 96389) / (90325 - 71691*a)
sage: b.n(digits=5)
0.096557
sage: b.n(digits=6)
0.0965556
sage: b.n(digits=7)
0.09655549
}}}
Vincent
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