problem with Abelian groups and trivial elements

[ncalexan]

This is a problem:

sage: AbelianGroup(1, [1], names='e')
Trivial Abelian Group
sage: AbelianGroup(1, [1], names='e').list()
[]

The handling of 1's in the list of element orders is a problem:

sage: AbelianGroup(3, [2, 1, 2], names=list('abc')).list()
---------------------------------------------------------------------------
<type 'exceptions.IndexError'>            Traceback (most recent call last)

/Users/ncalexan/Documents/School/MATH235/genus2cm/<ipython console> in <module>()

/Users/ncalexan/sage-2.10.3.rc3/local/lib/python2.5/site-packages/sage/groups/abelian_gps/abelian_group.py in AbelianGroup(n, invfac, names)
    304     elif len(invfac) > n:
    305         raise ValueError, "invfac (=%s) must have length n (=%s)"%(invfac, n)
--> 306     M = AbelianGroup_class(n, invfac, names)
    307     return M
    308 

/Users/ncalexan/sage-2.10.3.rc3/local/lib/python2.5/site-packages/sage/groups/abelian_gps/abelian_group.py in __init__(self, n, invfac, names)
    371         # *now* define ngens
    372         self.__ngens = len(self.__invariants)
--> 373         self._assign_names(names)
    374 
    375 

/Users/ncalexan/Documents/School/MATH235/genus2cm/parent_gens.pyx in sage.structure.parent_gens.ParentWithGens._assign_names()

/Users/ncalexan/Documents/School/MATH235/genus2cm/parent_gens.pyx in sage.structure.parent_gens.normalize_names()

<type 'exceptions.IndexError'>: the number of names must equal the number of generators

This is the cause of strange things like:

sage: x = ZZ['x'].gen()
sage: K
Number Field in a with defining polynomial x^4 + 4*x^2 + 2
sage: K = NumberField(x^4 + 4*x^2 + 2, 'a')
sage: K.class_group()
Class group of order 1 with structure  of Number Field in a with defining polynomial x^4 + 4*x^2 + 2

CC: @ncalexan

Component: group theory

Keywords: trivial abelian group class group

Issue created by migration from https://trac.sagemath.org/ticket/2574

[ncalexan]

comment:1

And also of

sage: x = ZZ['x'].gen()
sage: K
Number Field in a with defining polynomial x^4 + 4*x^2 + 2
sage: K = NumberField(x^4 + 4*x^2 + 2, 'a')
sage: K.class_group()
Class group of order 1 with structure  of Number Field in a with defining polynomial x^4 + 4*x^2 + 2
sage: K.class_group().gens()
[]

[wdjoyner]

comment:2

I don't know about the class_group code, but this patch fixes the other error mentioned:

sage: AbelianGroup(1, [1], names='e')
Multiplicative Abelian Group isomorphic to C1
sage: AbelianGroup(1, [1], names='e').gens()
(e,)
sage: AbelianGroup(1, [1], names='e').list()
[1]

[wdjoyner]

abelian group patch

[wdjoyner]

comment:3

Attachment: 8962.patch.gz

[mwhansen]

comment:4

Looks good to me.

[sagetrac-mabshoff]

comment:5

Merged in Sage 2.11.alpha0