Monoids¶
-
class
sage.monoids.monoid.
Monoid_class
(names)¶ Bases:
sage.structure.parent.Parent
EXAMPLES:
sage: from sage.monoids.monoid import Monoid_class sage: Monoid_class(('a','b')) <class 'sage.monoids.monoid.Monoid_class_with_category'>
TESTS:
sage: F.<a,b,c,d,e> = FreeMonoid(5) sage: TestSuite(F).run()
-
gens
()¶ Returns the generators for
self
.EXAMPLES:
sage: F.<a,b,c,d,e> = FreeMonoid(5) sage: F.gens() (a, b, c, d, e)
-
monoid_generators
()¶ Returns the generators for
self
.EXAMPLES:
sage: F.<a,b,c,d,e> = FreeMonoid(5) sage: F.monoid_generators() Family (a, b, c, d, e)
-
-
sage.monoids.monoid.
is_Monoid
(x)¶ Returns True if
x
is of typeMonoid_class
.EXAMPLES:
sage: from sage.monoids.monoid import is_Monoid sage: is_Monoid(0) False sage: is_Monoid(ZZ) # The technical math meaning of monoid has ... # no bearing whatsoever on the result: it's ... # a typecheck which is not satisfied by ZZ ... # since it does not inherit from Monoid_class. False sage: is_Monoid(sage.monoids.monoid.Monoid_class(('a','b'))) True sage: F.<a,b,c,d,e> = FreeMonoid(5) sage: is_Monoid(F) True