#4612: [with patch, needs work] is_perfect_power for rationals
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Reporter: robertwb | Owner: somebody
Type: defect | Status: new
Priority: major | Milestone: sage-3.4
Component: basic arithmetic | Resolution:
Keywords: |
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Comment (by cremona):
It won't be trivial to fix since the gmp function only returns whether or
not the argument is a perfect power, not what the root or exponents are.
I suggest that we implement something involving the factorizations.
Assuming that both numerator and denonimator are perfect powers, compute
(where the input is r = +-n/d)
{{{
gcd(gcd([e for p,e in n.factor()]), gcd([e for p,e in d.factor()]))
}}}
If that is 1 return 1. If it is e>1 then return e if r is positive or if
e is odd and r is negative, otherwise (e even, r<0) return
e.prime_to_m_part(2), i.e. the odd part of e. This will return the
largest e such that r is an e'th power.
I don't see what else we can do unless gmp has a better function.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4612#comment:4>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
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