id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
17160,"Finitely generated axiom for (mutiplicative) magmas, semigroups, monoids, groups",nthiery,,"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",enhancement,closed,major,sage-6.6,categories,fixed,days64,tscrim sage-combinat darij virmaux,,Nicolas M. Thiéry,Travis Scrimshaw,N/A,,19ceb8124d27ba0124fb08a232c05924bb7114b0,19ceb8124d27ba0124fb08a232c05924bb7114b0,#10668 #15852,