#4777: Sage is_prime_power is seriously buggy, because pari's ispower is BROKEN
------------------------------+---------------------------------------------
Reporter: was | Owner: somebody
Type: defect | Status: new
Priority: critical | Milestone: sage-3.2.2
Component: basic arithmetic | Keywords:
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{{{
18:18 < wstein> sage: n =
3089265681159475043336839581081873360674602365963130114355701114591322241990483812812582393906477998611814245513881
18:18 < wstein> sage: factor(n)
18:18 < wstein> 150607571^14
18:18 < wstein> sage: sage.rings.arith.is_prime_power(n)False
18:18 < wstein> sage: n.is_prime_power()
18:18 < wstein> False
18:18 < wstein> sage: is_prime(150607571)
18:18 < wstein> True
18:19 < wstein> Yep, Sage's is_prime_power function is just plain wrong.
18:19 < wstein> Great.
18:19 < wstein> I wrote that, I think... :-(
18:20 < wstein> sage: k = pari(n); k.ispower()
18:20 < wstein> (2,
1757630701017558763141032341047742794506161527817537960891)
18:20 < wstein> Oh, it's a bug in pari, actually.
18:20 < wstein> Since pari's ispower is guaranteed to give the maximal k
such that x=n^k according
18:20 < wstein> to the docs.
18:20 < wstein> But it doesn't.
}}}
Pari's docs say this:
{{{
ispower(x,{k},{&n}): true (1) if x is a k-th power, false (0) if not.
If n is
given and a k-th root was computed in the process, put that in n. If k
is
omitted, return the maximal k >= 2 such that x = n^k is a perfect
power, or 0
if no such k exist.
}}}
So this is a bug in pari. The short-term solution is to I think just
factor that damned number at the end. This obviously could be slow in
general, but at least it will be right. Plus add a note to the docs and
post a bugreport upstream (but check latest svn pari first, since we use
an ancient pari). I've reported bugs in this ispower function in pari
before, by the way, so it's a known offender.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4777>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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