Doctest for: Positive raised by a positive power is not known to be real

[pelegm]

But it is known to be positive...

See the following code:

sage: assume(x>0)
sage: x.is_real()
True
sage: x.is_positive()
True
sage: (x**x).is_positive()
True
sage: (x**x).is_real()
False

For comparison, this is how SymPy handles this:

In [2]: x = Symbol('x', positive=True)

In [3]: x.is_positive
Out[3]: True

In [4]: x.is_real
Out[4]: True

In [5]: (x**x).is_positive
Out[5]: True

In [6]: (x**x).is_real
Out[6]: True

Depends on #21963

CC: @rwst

Component: symbolics

Keywords: is_real, days79

Author: Peleg Michaeli, Ralf Stephan

Branch/Commit: c883299

Reviewer: Ralf Stephan, Peleg Michaeli

Issue created by migration from https://trac.sagemath.org/ticket/21940

[rwst]

comment:3

What Sage version is this? With Sage-7.5beta3 I get:

sage: assume(x>0)
sage: x.is_real()
True
sage: (x*x).is_real()
True

[pelegm]

comment:4

Replying to @rwst:

What Sage version is this? With Sage-7.5beta3 I get:

sage: assume(x>0)
sage: x.is_real()
True
sage: (x*x).is_real()
True

Hi,

This was tested on 7.5beta3. You've checked x*x, and I have checked x**x.

[rwst]

comment:5

Fixed in pynac git master, see pynac/pynac@e5c6cd2

Please add a doctest to Expression.is_real() in symbolic/expression.pyx

[rwst]

Dependencies: pynac-0.7.2

[pelegm]

Commit: 65e6c10

[pelegm]

New commits:

65e6c10

positive ** positive = real (doctest only) #21940

[pelegm]

Branch: u/pelegm/21940

[pelegm]

Author: Peleg Michaeli

[rwst]

comment:7

Maybe interesting in this regard that fixing this allows Sage to simplify some apparently complex expressions, e.g.

Before:
sqrt(abs(1/25*(3*(2*sqrt(3)*sqrt(2) - 3)*(sqrt(6) - 2) + 16*sqrt(3)*sqrt(2) +
5*sqrt(6) - 54)^2 + 1/25*(3*(sqrt(6) - 2)*(sqrt(6) - 4) + 14*sqrt(3)*sqrt(2) +
4*sqrt(6) - 42)^2 + 144/25*(sqrt(3)*sqrt(2) - sqrt(6))^2))

After:
sqrt(1/25*(3*(2*sqrt(3)*sqrt(2) - 3)*(sqrt(6) - 2) + 16*sqrt(3)*sqrt(2) +
5*sqrt(6) - 54)^2 + 1/25*(3*(sqrt(6) - 2)*(sqrt(6) - 4) + 14*sqrt(3)*sqrt(2) +
4*sqrt(6) - 42)^2 + 144/25*(sqrt(3)*sqrt(2) - sqrt(6))^2)

(from a doctest in matrix_symbolic_dense.pyx)

[pelegm]

Description changed: