#17160: Finitely generated axiom for (mutiplicative) magmas, semigroups,
monoids,
groups
-------------------------------------+-------------------------------------
Reporter: nthiery | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: categories | Resolution:
Keywords: | Merged in:
Authors: Nicolas M. Thiéry | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/nthiery/categories/finitely- | 4b3d74c41cfec35c35ab2262d6dc17dd90ef3472
generated-magmas-17160 | Stopgaps:
Dependencies: #10668 |
-------------------------------------+-------------------------------------
Description changed by nthiery:
Old description:
> This introduce an axiom FinitelyGeneratedAsMagma, as well as related
> categories with axioms for magmas, semigroups and groups::
> {{{
> sage: Groups().FinitelyGeneratedAsMagma()
> Category of finitely generated groups
> }}}
> For ease of notations, when there is no ambiguity, one can do::
> {{{
> sage: Groups().FinitelyGenerated()
> Category of finitely generated groups
> }}}
>
> One motivation for this change (for #8678) is that finite semigroups
> in Sage used to be automatically endowed with an `EnumeratedSets`
> structure; the default enumeration is then obtained by iteratively
> multiplying the semigroup generators. This forced any finite semigroup
> to either implement an enumeration, or provide semigroup generators;
> this was often inconvenient.
>
> Instead, finite semigroups that provide a distinguished finite set of
> generators with `semigroup_generators` should now explicitly declare
> themselves in the category of `FinitelyGeneratedSemigroups`:
> {{{
> sage: Semigroups().FinitelyGenerated()
> Category of finitely generated semigroups
> }}}
> This is a backward incompatible change.
New description:
This introduce an axiom FinitelyGeneratedAsMagma, as well as related
categories with axioms for magmas, semigroups and groups::
{{{
sage: Groups().FinitelyGeneratedAsMagma()
Category of finitely generated groups
}}}
For ease of notations, when there is no ambiguity, one can do::
{{{
sage: Groups().FinitelyGenerated()
Category of finitely generated groups
}}}
One motivation for this change (for #8678) is that finite semigroups
in Sage used to be automatically endowed with an `EnumeratedSets`
structure; the default enumeration is then obtained by iteratively
multiplying the semigroup generators. This forced any finite semigroup
to either implement an enumeration, or provide semigroup generators;
this was often inconvenient.
Instead, finite semigroups that provide a distinguished finite set of
generators with `semigroup_generators` should now explicitly declare
themselves in the category of `FinitelyGeneratedSemigroups`:
{{{
sage: Semigroups().FinitelyGenerated()
Category of finitely generated semigroups
}}}
This is a backward incompatible change.
TODO:
- Use the occasion to migrate TransitiveIdeal to RecursivelyEnumeratedSet
--
--
Ticket URL: <http://trac.sagemath.org/ticket/17160#comment:18>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
