#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 robertwb):
A new patch is up. If n/d is a not perfect power, it is usually cheaper to
check min(n,d) for being a perfect power first, but that is redundant if
n/d is in fact a perfect power. I added an extra parameter to handle that,
let me know if you think it's a good idea or excessive.
It is more work to figure out the maximal exponent a number can be
expressed with than it is to detect whether it can be expressed with any
exponent. For example, consider $p^(2r) / q^(2s)$. It is easy to detect
that both are perfect squares, but finding r and s is more work.
Clearly, the optimal solution would look something like gmp's
mpz_perfect_power_p done in parallel on the numerator and denominator.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4612#comment:8>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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