problem with the is_principal method for fractional ideals in a number field. #487
Description
The Problem has been reported by Kevin McGown at http://groups.google.com/group/sage-forum/t/a8a6efc565e36339
In SAGE 2.8 it seems there is a problem with the is_principal method
for fractional ideals in a number field. In the code below I create
the same ideal in two different ways and obtain two different answers
from is_principal (True and False).
sage: K = QuadraticField(-119,'a')
sage: P2 = K.ideal([2]).factor()[0][0]
sage: I = P2^5
sage: a = K.0
sage: J = K.ideal([1/2*a+3/2])
sage: I==J
True
sage: I.is_principal()
False
sage: J.is_principal()
True
Kevin also suggested a fix:
I believe the problem is with the following line in the is_principal()
method:
if len (self.gens()) <= 1:
Instead it should read:
if len (self.gens_reduced()) <= 1:
Not 100% sure, but I thought I would bring it to your attention.
- Kevin
Cheers,
Michael
Component: algebraic geometry
Issue created by migration from https://trac.sagemath.org/ticket/487