Hi!
On Wed, Mar 11, 2015 at 03:22:32PM -0700, Volker Braun wrote:
> IMHO always assume constructive unless otherwise noted if you do
> things on the computer. You can pick elements of sets, elements of
> two sets (or other structure) can actually be distinguished, etc.
> There is no need to restrict ourselves to the usual pen&paper math
> nomenclature.
Thanks Volker for the feedback!
So at this point this leans toward what's in the current
implementation:
- Groups with with a distinguished finite set of generators:
sage: Groups().FinitelyGenerated()
Category of finitely generated groups
in fact a short hand for:
sage: Groups().FinitelyGeneratedAsMagma()
Category of finitely generated groups
- Finite groups with a distinguished finite set of generators (which
is different from just finite groups):
sage: Groups().Finite().FinitelyGenerated()
Category of finite finitely generated groups
- Rings with a distinguished finite set of *multiplicative* generators:
sage: Rings().FinitelyGeneratedAsMagmas()
Category of finitely-generated-as-magma rings
Does this sound acceptable to everyone?
The plan is to finalize this ticket for the Sage days next week, so
quick feedback would be appreciated.
> Why not have an Iterable() category for everything with __iter__?
Yup; in fact we have EnumeratedSets for parents with a distinguished
enumeration (implemented by __iter__ / rank / list)
A few more minor design points:
- All the finite permutation groups implemented in Sage come endowed
with a distinguished set of generators. Do we want the category of
finite permutation groups to be automatically a subcategory of
finite finitely generated permutation groups? This would make the
output a bit shorter:
sage: DihedralGroup(3).category()
Category of finite permutation groups
instead of:
sage: DihedralGroup(3).category()
Category of finite finitely generated permutation groups
- As far as I know, all the finite fields implemented in Sage have
__iter__ implemented. Do we want to keep the category of finite
fields as a subcategory of EnumeratedSets()?
Or maybe a subcategory Monoids().FinitelyGenerated()? In this case,
we would need to provide multiplicative generators. Is there an easy
way to implement this generically for any finite field?
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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