#4536: [with patch, needs further work] Various number field order and ideal
utilities
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Reporter: cremona | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.2.1
Component: number theory | Resolution:
Keywords: number fields, orders, ideals |
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Changes (by davidloeffler):
* summary: [with patch, needs review] Various number field order and
ideal utilities => [with patch, needs further
work] Various number field order and ideal
utilities
Comment:
Patches install and compile fine under 3.2, and all doctests in
sage/rings/number_field pass.
But I'm not happy with the is_coprime() method for fractional ideals. I
thought the outcome of the discussion on the sage-nt list was that coprime
for fractional ideals means disjoint supports, but I got this:
{{{
sage: E.<a> = NumberField(x^5 + 7*x^4 + 18*x^2 + x - 3)
sage: OE = E.ring_of_integers()
sage: i,j,k = [u[0] for u in factor(3*OE)] # three distinct prime ideals
of degrees 3,1,1
sage: (i/j).is_coprime(j/k)
True
sage: (j/k).is_coprime(j/k)
True
}}}
The problem here is that the fractional ideal j/k has norm 1, and the code
falsely assumes that if norm(i) and norm(j) are coprime, then i and j must
be coprime. Thus the code will say that j/k is coprime to everything
(including itself).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4536#comment:7>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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