### [sage-devel] Re: Bug in positivity test of a real expression

```Hi Ralf,

On 2018-02-05, Ralf Stephan  wrote:
> Argh, we cannot return Unknown from bool() because of Python. Still, we can
> avoid calling Maxima for numeric questions:
> https://trac.sagemath.org/ticket/24658
>
> This is a really tiny ticket and should be easy to review.

Thanks for opening the ticket!

Best regards,
Simon

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### [sage-devel] Re: Bug in positivity test of a real expression

```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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### [sage-devel] Re: Bug in positivity test of a real expression

```Argh, we cannot return Unknown from bool() because of Python. Still, we can
avoid calling Maxima for numeric questions:
https://trac.sagemath.org/ticket/24658

This is a really tiny ticket and should be easy to review.

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### [sage-devel] Re: Bug in positivity test of a real expression

```I think we should refrain from calling Maxima with bool(...) because our
tests are good enough. Moreover with
https://trac.sagemath.org/ticket/24345
we could then simply return Unknown. Please review.

On Monday, February 5, 2018 at 8:12:49 AM UTC+1, Ralf Stephan wrote:
>
> Actually Sage's logic is fine here, the bug with bool(val>0) is in
> Maxima.The default with bool(relation) is to use RIF and at the default
> setting it cannot decide, so ultimately Maxima is called:
>
> (%i2) is (%pi-(1116521080257783321*2^(23/2))/1029347477390786609545>0);
> (%o2)true
>
> Regards,
>

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### [sage-devel] Re: Bug in positivity test of a real expression

```Actually Sage's logic is fine here, the bug with bool(val>0) is in
Maxima.The default with bool(relation) is to use RIF and at the default
setting it cannot decide, so ultimately Maxima is called:

(%i2) is (%pi-(1116521080257783321*2^(23/2))/1029347477390786609545>0);
(%o2)true

Regards,

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### Re: [sage-devel] Re: Bug in positivity test of a real expression

```
Hi Simon,

On 04/02/2018 23:59, Simon King wrote:

On 2018-02-04, Simon King  wrote:

On 2018-02-04, Thierry  wrote:

On Sun, Feb 04, 2018 at 10:24:55PM +, Simon King wrote:
What is wrong ?

val is a NEGATIVE real number converted into SR. val evaluates POSITIVE,
even though the conversion of val into RR still evaluates negative.

Ouch, sorry, when I posted I was apparently editing stuff in a wrong
way.

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.

But 182 bits is enough

sage: R = RealIntervalField(128)
sage: (R.pi() - r * R(2).sqrt()) > 0
False
sage: (R.pi() - r * R(2).sqrt()) < 0
True

Vincent

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### [sage-devel] Re: Bug in positivity test of a real expression

```Hi Ralph,

On 2018-02-05, Ralf Stephan  wrote:
> With bool(val<0) ultimately (val<0).test_relation() is called which does:
>
> sage: RIF(val)
> 0.?e-15
> sage: RIF(val) < 0
> False

I could understand if BOTH val>0 and val<0 evaluated to False, as val is
almost zero. However, if val < 0 evaluates to False then val > 0 evaluating
to True is a bug, IMHO. After all, the number *is* negative (by construction,
actually).

Best regards,
Simon

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```

### [sage-devel] Re: Bug in positivity test of a real expression

```With bool(val<0) ultimately (val<0).test_relation() is called which does:

sage: RIF(val)
0.?e-15
sage: RIF(val) < 0
False

Regards.

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```

### [sage-devel] Re: Bug in positivity test of a real expression

```On 2018-02-04, Simon King  wrote:
> On 2018-02-04, Thierry  wrote:
>> On Sun, Feb 04, 2018 at 10:24:55PM +, Simon King wrote:
>> What is wrong ?
>
> val is a NEGATIVE real number converted into SR. val evaluates POSITIVE,
> even though the conversion of val into RR still evaluates negative.

Ouch, sorry, when I posted I was apparently editing stuff in a wrong
way.

So, here is the example:
sage: val = pi - 2286635172367940241408/1029347477390786609545*sqrt(2)
sage: bool(val<0)
False
sage: bool(val>0)
True

Hence, val evaluates positive. However, it represents a negative real
number:
sage: RR(val)
-4.44089209850063e-16

Sorry, in my original post I was starting from that number and got a
couple of things wrong.

Note that evaluating val to higher precision still gives a negative
number, although a clearly different one:
sage: RR(RealField(2000)(val))
-5.68242325601396e-24

Going to even higher precision doesn't change things.

So, is that a bug, after all? val being positive, RR(val) being
negative?

Cheers,
Simon

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### [sage-devel] Re: Bug in positivity test of a real expression

```On 2018-02-04, Thierry  wrote:
> On Sun, Feb 04, 2018 at 10:24:55PM +, Simon King wrote:
> What is wrong ?

val is a NEGATIVE real number converted into SR. val evaluates POSITIVE,
even though the conversion of val into RR still evaluates negative.

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