inconsistent powers of symbolic sums

[rwst]

Pynac immediately factors out the positive content of a sum raised to an integer number:

sage: (5*cos(x) + 5)^2
25*(cos(x) + 1)^2
sage: (5*cos(x) + 5)^-3
1/125/(cos(x) + 1)^3

sage: (-5*x + 5)^-3
-1/125/(x - 1)^3

The last example shows how the leading coefficient is forced to be positive. This is not consistent with other CAS and considered a typical Sage quirk.

Also, the content of rational powers is usually extracted but we only do this if there is a rational power part!

sage: sqrt(5*cos(x) + 5)
sqrt(5*cos(x) + 5)
sage: sqrt(8*x + 8)
2*sqrt(2)*sqrt(x + 1)

Component: symbolics

Issue created by migration from https://trac.sagemath.org/ticket/25639

[rwst]

comment:1

See pynac/pynac@4ef83c3

[rwst]

Description changed:

--- 
+++ 
@@ -11,9 +11,11 @@
 ```
 The last example shows how the leading coefficient is forced to be positive. This is not consistent with other CAS and considered a typical Sage quirk.
 
-Also, the content of rational powers is usually extracted but we don't do this:
+Also, the content of rational powers is usually extracted but we only  do this if there is a rational power part!
 
 ```
 sage: sqrt(5*cos(x) + 5)
 sqrt(5*cos(x) + 5)
+sage: sqrt(8*x + 8)
+2*sqrt(2)*sqrt(x + 1)
 ```

[rwst]

comment:3

The pynac commit given above contains the code for the change but it is not called because many doctests would have to change. If you want to review nevertheless, then please voice your intention here.