Hi John,
On Mon, May 18, 2009 at 09:25:56PM -0700, John H Palmieri wrote:
>
> On May 18, 8:43 pm, wkehowski <wkehow...@cox.net> wrote:
> > What about matrix rings over ZZ?
>
> No, but they're not supposed to be.
>
>
> > On May 18, 7:03 pm, John H Palmieri <jhpalmier...@gmail.com> wrote:
> >
> > > On May 18, 2:44 pm, benjamin antieau <d.ben.anti...@gmail.com> wrote:
> >
> > > > Oh, and this is also the case over other base rings, like over GF(p).
> >
> > > > On May 18, 2:43 pm, benjamin antieau <d.ben.anti...@gmail.com> wrote:
> >
> > > > > I noticed the following incorrect behavior.
> >
> > > > > sage: C=simplicial_complexes.ChessboardComplex(3,3).chain_complex()
> > > > > sage: C.category()
> > > > > Category of chain complexes over Integer Ring
> > > > > sage: A=C.category()
> > > > > sage: A.is_abelian()
> > > > > False
> >
> > > > > As far as I can tell ChainComplexes inherits is_abelian from
> > > > > AbelianCategory, so I don't know what the problem is.
> >
> > > > > class ChainComplexes(Category_module):
> > > > > class Category_module(Category_over_base_ring, AbelianCategory):
> > > > > class AbelianCategory:
> > > > > def is_abelian(self):
> > > > > return True
> >
> > > The problem is not just chain complexes:
> >
> > > sage: RingModules(ZZ).is_abelian()
> > > False
>
> See <http://trac.sagemath.org/sage_trac/ticket/6081> for a patch.
To avoid a conflict, I will integrate this into the category patch.
Now, I'd like to make sure we have the samething in mind: currently in
my patch an AbelianCategory is a category with a direct sum operation
on the objects. Does this match with what you have in mind? Which
categories should be abelian?
Note about the patch: to avoid dependencies on the inheritance order
between the bases, wouldn't it be more natural to have the default
definition of is_abelian in Category?
Best,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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