Doctest: Numerics in nested symbolic powers not combined

[rwst]

Numerics in power towers are not combined if nonnumerics present:

sage: ((x^(1/2) + 1)^2).expand()
x + 2*sqrt(x) + 1
sage: ((x^(x/2) + 1)^2).expand()
(x^(1/2*x))^2 + 2*x^(1/2*x) + 1
sage: ((x^(1/2*x))^2).expand()
(x^(1/2*x))^2

Also in GiNaC:

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Type ?? for a list of help topics.
> expand((x^(x/2)+1)^2);
1+2*x^(1/2*x)+(x^(1/2*x))^2
> expand((x^(x/2))^2);
(x^(1/2*x))^2

Sympy does it as expected:

In [5]: ((x**(x/2) + 1)**2).expand()
Out[5]:
   x
   ─
   2    x
2⋅x  + x  + 1

In [1]: ((x**(x/2))**2).expand()
Out[1]:
 x
x

Component: symbolics

Author: Ralf Stephan

Branch/Commit: c4f4952

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/21360

[rwst]

comment:1

The ticket is questioning this GiNaC code snippet (power.cpp:566):

        // Turn (x^c)^d into x^(c*d) in the case that x is positive and c is real.
        if (is_exactly_a<power>(ebasis) && ebasis.op(0).info(info_flags::positive) && ebasis.op(1).info(info_flags::real))
                return power(ebasis.op(0), ebasis.op(1) * eexponent);

[rwst]

comment:2

Note there are two parts to this. If the outer exponent is a fraction then branches play a role and the discussion in #14305, which makes the GiNaC code in this case correct. This does not apply to the sqrt(x)^2 case and even less to:

sage: ((x^(2*x))^2)
(x^(2*x))^2

[rwst]

comment:3

This is now implemented in Pynac for the outer exponent a positive integer.

[rwst]

Branch: u/rws/numerics_in_nested_symbolic_powers_not_combined

[sagetrac-git]

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

c4f4952

Merge branch 'develop' into t/21360/numerics_in_nested_symbolic_powers_not_combined

[sagetrac-git]

Commit: c4f4952

[fchapoton]

comment:7

looks good. Please fill the Author field

[fchapoton]

Reviewer: Frédéric Chapoton

[rwst]

comment:8

Thanks.

[rwst]

Author: Ralf Stephan

[vbraun]

Changed branch from u/rws/numerics_in_nested_symbolic_powers_not_combined to c4f4952