Hi Vincent,

On 2018-02-05, Vincent Delecroix <20100.delecr...@gmail.com> wrote:
>> So, here is the example:
>>   sage: val = pi - 2286635172367940241408/1029347477390786609545*sqrt(2)
>>   sage: bool(val<0)
>>   False
>>   sage: bool(val>0)
>>   True
> >
> > [SNIP]
> >
>> So, is that a bug, after all? val being positive, RR(val) being
>> negative?
>
> This is example is definitely a bug. In order to test
> positivity/negativity of a real number you would better use interval
> field to get provent result such as the following. With the default
> precision of 53 bits it fails
>
> sage: r = 2286635172367940241408/1029347477390786609545
>
> sage: R = RIF
> sage: (R.pi() - r * R(2).sqrt()) > 0
> False
> sage: (R.pi() - r * R(2).sqrt()) < 0
> False
>
> Note that in the above example R here is consistent with comparison: it
> does not know and answers False everywhere.

As I said, it'd be OK to answer False in both cases. OK, since you
confirm it is a bug, I should soonish open a ticket (although TB pointed
me off-list (why?) to #19162, but I think #19162 is just a meta-ticket
and thus shouldn't prevent to create a regular ticket).

Cheers,
Simon

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