#17160: Finitely generated axiom for (mutiplicative) magmas, semigroups,
monoids,
groups
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Reporter: nthiery | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: categories | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by nthiery:
Old description:
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.
--
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Ticket URL: <http://trac.sagemath.org/ticket/17160#comment:2>
Sage <http://www.sagemath.org>
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