id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
11304,Problems with S-class groups of number fields,fwclarke,davidloeffler,"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. = 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.",defect,closed,major,sage-4.7.2,number fields,fixed,S-class groups,jdemeyer cremona rlm,sage-4.7.2.alpha1,Francis Clarke,John Cremona,N/A,,,,,