Doctest: Expression.is_positive/negative fixed

[rws]

The two functions that query Pynac expressions' info::flags only work with numerics and symbols with domain. The rest simply returns False:

sage: (1-pi).is_negative()
False
sage: (log(1/2)).is_negative()
False
sage: e.is_positive()
False
sage: (e+1).is_positive()
False
sage: (2*e).is_positive()
False
sage: (e^3).is_positive()
False

UPDATE: everything above but the first works now.

[rws]

Parts of this are fixed in ​https://github.com/pynac/pynac/issues/66 (will be pynac-0.3.9.1/0.4.1)

[rws]

While products are okay already, sums with negative terms are not and will not be for some time. Correct handling depends on ​https://github.com/pynac/pynac/issues/67 and ​https://github.com/pynac/pynac/issues/68 and affects #12588 too, for example.

[rws]

Since everything apart from sums works now, let's look at what is possible with sums containing exact numerics (in the Pynac sense) and constants only. The border case is if the expression is nonzero---but only at certain precision. This is impossible to handle. It is also not possible to convert to float and only check sign if the absolute result is greater some epsilon, because that could be due to precision loss in a denominator.

I'm therefore just adding the doctests here to resolve the ticket.

[rws]

New commits:

​fe039e2

18630: Doctest: Expression.is_positive/negative fixed

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​a643c39

Merge branch 'develop' into t/18630/expression_is_positive_negative_incomplete

[rws]

Docbuild error: ValueError: line 48 of the docstring for sage.symbolic.expression.Expression.is_positive has inconsistent leading whitespace: u'::'

[rws]

New commits:

​1c62b17

18630: Doctest improvements to ex.is_positive/negative

[vdelecroix]

Would be nice to also have some less trivial examples

sage: (log(1/3) * log(1/2)).is_positive()
True
sage: log((2**500+1)/2**500).is_positive()
True
sage: log(2*500/(2**500-1)).is_negative()
True

And the following are other failing examples

sage: sin(pi/37).is_positive()   # algebraic number!
False
sage: (sqrt(2)-1).is_positive()  # algebric number!
False
sage: log(pi).is_positive()
False 
sage: sin(3).is_positive()
False
sage: sin(5).is_negative()
False

[vdelecroix]

And I don't understand why the following is ok

sage: ((-pi^(1/5))^2).is_positive()
True

while not these ones

sage: (pi^2).is_positive()
False
sage: ((-pi)^2).is_positive()
False

[rws]

Replying to vdelecroix:

And the following are other failing examples

sage: sin(pi/37).is_positive()   # algebraic number!
False
sage: (sqrt(2)-1).is_positive()  # algebric number!
False
sage: log(pi).is_positive()
False 
sage: sin(3).is_positive()
False
sage: sin(5).is_negative()
False

They are not failing. The result False simply means "I don't know.".

[rws]

Replying to vdelecroix:

sage: (pi^2).is_positive()
False
sage: ((-pi)^2).is_positive()
False

One logic for b^e.is_positive() is if (e.is_even()) return b.is_real() and b.is_nonzero() but is_nonzero was not implemented for constants until now. This is fixed in ​https://github.com/pynac/pynac/commit/e92febc468800e4a1457f944bb7a45e9baf0e2f6 and will be in pynac-0.7.15. We can as well put all of these doctests in this ticket too. Thanks for the report!

[rws]

Replying to rws:

They are not failing. The result False simply means "I don't know.".

See also #22162.

[rws]

See also ​https://github.com/pynac/pynac/issues/293 for progress on what is completely implemented as internal Pynac flag.

[rws]

New commits:

​8e446e6

18630: Doctest improvements to ex.is_positive/negative

[pelegm]

Seems like the first test still fails:

sage: (1-pi).is_negative()
False

Do we want to merge it as is?

[rws]

Yes, see comment:15.