Monoids

class sage.monoids.monoid.Monoid_class(names)

Bases: Parent

EXAMPLES:

Sage

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

Python

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

gens()

Return the generators for self.

EXAMPLES:

Sage

sage: F.<a,b,c,d,e> = FreeMonoid(5)
sage: F.gens()
(a, b, c, d, e)

Python

>>> from sage.all import *
>>> F = FreeMonoid(Integer(5), names=('a', 'b', 'c', 'd', 'e',)); (a, b, c, d, e,) = F._first_ngens(5)
>>> F.gens()
(a, b, c, d, e)

monoid_generators()

Return the generators for self.

EXAMPLES:

Sage

sage: F.<a,b,c,d,e> = FreeMonoid(5)
sage: F.monoid_generators()
Family (a, b, c, d, e)

Python

>>> from sage.all import *
>>> F = FreeMonoid(Integer(5), names=('a', 'b', 'c', 'd', 'e',)); (a, b, c, d, e,) = F._first_ngens(5)
>>> F.monoid_generators()
Family (a, b, c, d, e)

sage.monoids.monoid.is_Monoid(x)

Return True if x is of type Monoid_class.

EXAMPLES:

Sage

sage: from sage.monoids.monoid import is_Monoid
sage: is_Monoid(0)
doctest:warning...
DeprecationWarning: the function is_Monoid is deprecated;
use 'isinstance(..., Monoid_class)' instead
See https://github.com/sagemath/sage/issues/37897 for details.
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

Python

>>> from sage.all import *
>>> from sage.monoids.monoid import is_Monoid
>>> is_Monoid(Integer(0))
doctest:warning...
DeprecationWarning: the function is_Monoid is deprecated;
use 'isinstance(..., Monoid_class)' instead
See https://github.com/sagemath/sage/issues/37897 for details.
False
>>> 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
>>> is_Monoid(sage.monoids.monoid.Monoid_class(('a','b')))
True
>>> F = FreeMonoid(Integer(5), names=('a', 'b', 'c', 'd', 'e',)); (a, b, c, d, e,) = F._first_ngens(5)
>>> is_Monoid(F)
True