Finitely generated magmas#

class sage.categories.finitely_generated_magmas.FinitelyGeneratedMagmas(base_category)[source]#

Bases: CategoryWithAxiom_singleton

The category of finitely generated (multiplicative) magmas.

See Magmas.SubcategoryMethods.FinitelyGeneratedAsMagma() for details.

EXAMPLES:

Sage

sage: C = Magmas().FinitelyGeneratedAsMagma(); C
Category of finitely generated magmas
sage: C.super_categories()
[Category of magmas]
sage: sorted(C.axioms())
['FinitelyGeneratedAsMagma']

Python

>>> from sage.all import *
>>> C = Magmas().FinitelyGeneratedAsMagma(); C
Category of finitely generated magmas
>>> C.super_categories()
[Category of magmas]
>>> sorted(C.axioms())
['FinitelyGeneratedAsMagma']

class ParentMethods[source]#

Bases: object

magma_generators()[source]#

Return distinguished magma generators for self.

OUTPUT: a finite family

This method should be implemented by all finitely generated magmas.

EXAMPLES:

Sage

sage: S = FiniteSemigroups().example()
sage: S.magma_generators()
Family ('a', 'b', 'c', 'd')

Python

>>> from sage.all import *
>>> S = FiniteSemigroups().example()
>>> S.magma_generators()
Family ('a', 'b', 'c', 'd')