#11304: Problems with S-class groups of number fields
-----------------------------+----------------------------------------------
Reporter: fwclarke | Owner: davidloeffler
Type: defect | Status: new
Priority: major | Milestone: sage-4.7.1
Component: number fields | Keywords: S-class groups
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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There are some serious problems at present with the code for S-class
groups. They only emerge when the class groups is non-cyclic. For
example,
{{{
sage: K.<a> = QuadraticField(-105)
sage: C = K.class_group(); C
Class group of order 8 with structure C2 x C2 x C2 of Number Field in a
with defining polynomial x^2 + 105
sage: S = (K.ideal(11, a + 7),)
sage: K.S_class_group(S)
Traceback (most recent call last):
...
IndexError: Argument length (= 3) must be 2.
}}}
This problem arises when the class group and the S-class group have
differing numbers of generators. It arises essentially because generators
of S-class groups are created as `FractionalIdealClass` elements rather
than `SFractionalIdealClass` elements.
But there is a more serious problem. The Pari data for the S-class group
which we failed to construct above can be obtained as
{{{
sage: SC_data = K._S_class_group_and_units(S)[1]; SC_data
[(Fractional ideal (10, a + 5), 2, 10), (Fractional ideal (6, a + 3), 2,
6)]
}}}
so that if
{{{
sage: P, Q = [u[0] for u in SC_data]
}}}
the S-classes of the ideals `P` and `Q` (each of order 2) generate the
S-class group. However,
{{{
sage: P._S_ideal_class_log(S)
[0, 0]
}}}
which cannot be correct.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11304>
Sage <http://www.sagemath.org>
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