integer_rational_power problems

[gerbicz]

The following answers are all wrongs/inconsistent with the documentation:

from sage.rings.rational import integer_rational_power
print integer_rational_power(-10, 1/1)
print integer_rational_power(-10, 2/2)
print integer_rational_power(-10, 4/2)
print integer_rational_power(-10, 6/3)
print integer_rational_power(0, 0/1)
print integer_rational_power(0, 1/2)
print integer_rational_power(10, 0/1)

sage gives:
None
None
None
None
0
0
1

From the first four examples it is clear that sage is unable to observe
if b evaluate as an integer when compute a^b for negative "a" value.
(the answers should be -10,-10,100,100).
The fifth example: as 0^0 is undefined it should return by None.
The sixth example: 0^(1/2)=0 is correct but shows that the documentation 
is broken, because from it: "The positive real root is taken for 
even denominators.", here 2 is even, but the result 0 is not positive.
The seventh example: 10^(0/1)=1 is correct, but from the 
documentation: "b -- a positive Rational", so change the 
documentation or return by None.}}}

[leif]

Someone^TM should check what of the above still applies.

[chapoton]

New commits:

​ff92822

trac 11228 fine details in integer_rational_power

[chapoton]

a little bit of ticket necromancy..

[tscrim]

muhahahaha

[leif]

./sage -Wunused-function?

(If you want to have further fun, perhaps take a look at rational_power_parts() in the same file, the only instance in the Sage library where integer_rational_power() is used at all.)