#5535: is_primitive is computes integer prime factorization on every call
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Reporter: rhinton | Owner: tbd
Type: enhancement | Status: new
Priority: major | Milestone:
Component: algebra | Keywords:
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The current (generic) code for is_primitive in
rings/polynomial/polynomial_element.pyx is
{{{
if not self.is_irreducible():
return False
p = self.parent().characteristic()
n = p ** self.degree() - 1
y = self.parent().quo(self).gen()
for d in n.prime_divisors():
if ( y ** (n//d) ) == 1:
return False
return True
}}}
Note that the integer n and its prime divisors are calculated as part of
the algorithm. This calculation can be lengthy for large n, and can
dominate the running time of the algorithm.
The proposed patch adds optional arguments to is_primitive to provide the
results of these calculations -- useful for is_primitive tests for
multiple polynomials of the same degree.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5535>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
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