#5250: [with patch, needs review] Bug in multiplicative_generator function for
Z/NZ
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Reporter: was | Owner: davidloeffler
Type: defect | Status: assigned
Priority: major | Milestone: sage-4.0
Component: number theory | Keywords:
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Changes (by davidloeffler):
* owner: was => davidloeffler
* status: new => assigned
Comment:
This comes up whenever n is twice a power of an odd prime. In these cases,
{{{multiplicative_group_is_cyclic}}} would wrongly return False,
{{{multiplicative_generator}}} would throw an error and {{{unit_gens}}}
would return a list of length 2 one of whose elements is 1.
The attached patch fixes this. It also streamlines the code a bit by using
the is_prime_power function; this is more readable, and in theory should
be quicker than factorisation. At the moment it is actually a tiny
fraction slower, but this is a consequence of an awkward workaround for a
Pari bug (see #4777) and it will presumably be fixed in the future.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5250#comment:1>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
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