#12466: test whether a polynomial is cyclotomic
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Reporter: sstarosta | Owner: sstarosta
Type: task | Status: needs_review
Priority: major | Milestone: sage-5.0
Component: number theory | Resolution:
Keywords: Cernay2012 | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Comment (by davidloeffler):
This will do some strange things if the base ring is a finite field. For
instance it will say that the mod p reduction of the nth cyclotomic
polynomial is cyclotomic for some values of p, and non-cyclotomic for
others (because it will depend whether the reduction mod p is irreducible
or not).
Moreover, if the base ring is a characteristic 0 ring bigger than ZZ, you
will get some strange behaviour in case 3 because you call "f1.factor()"
and the factorization over {{{ self.base_ring() }}} won't generally be the
same as over ZZ; indeed you might even get errors at this point if the
base ring is one where Sage doesn't know how to factor polynomials.
I suggest you change the type-check
{{{
#!python
try:
self.change_ring(ZZ)
except TypeError:
return False
}}}
to something a bit more cautious like
{{{
#!python
if self.base_ring().characteristic() != 0:
return False
if self.base_ring() != ZZ:
try:
f = self.change_ring(ZZ)
return f.is_cyclotomic()
except TypeError,ValueError:
return False
}}}
(or raise a !ValueError, if you prefer). Then you can continue with your
algorithm in the confidence that the base ring is ZZ.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12466#comment:5>
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