Monoids

class sage.monoids.monoid.Monoid_class(names)

Bases: Parent

EXAMPLES:

sage: from sage.monoids.monoid import Monoid_class
sage: Monoid_class(('a','b'))
<sage.monoids.monoid.Monoid_class_with_category object at ...>

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 type Monoid_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