Abelian Monoid Elements

AUTHORS:

• David Kohel (2005-09)

EXAMPLES:

Recall the example from abelian monoids:

Sage

sage: F = FreeAbelianMonoid(5,names = list("abcde"))
sage: (a,b,c,d,e) = F.gens()
sage: a*b^2*e*d
a*b^2*d*e
sage: x = b^2*e*d*a^7
sage: x
a^7*b^2*d*e
sage: x.list()
[7, 2, 0, 1, 1]

Python

>>> from sage.all import *
>>> F = FreeAbelianMonoid(Integer(5),names = list("abcde"))
>>> (a,b,c,d,e) = F.gens()
>>> a*b**Integer(2)*e*d
a*b^2*d*e
>>> x = b**Integer(2)*e*d*a**Integer(7)
>>> x
a^7*b^2*d*e
>>> x.list()
[7, 2, 0, 1, 1]

The list is a copy, so changing the list does not change the element:

Sage

sage: x.list()[0] = 0
sage: x
a^7*b^2*d*e

Python

>>> from sage.all import *
>>> x.list()[Integer(0)] = Integer(0)
>>> x
a^7*b^2*d*e

class sage.monoids.free_abelian_monoid_element.FreeAbelianMonoidElement

Bases: MonoidElement

Create the element x of the FreeAbelianMonoid parent.

EXAMPLES:

Sage

sage: F = FreeAbelianMonoid(5, 'abcde')
sage: F
Free abelian monoid on 5 generators (a, b, c, d, e)
sage: F(1)
1
sage: F(2)
Traceback (most recent call last):
...
TypeError: argument x (= 2) is of the wrong type
sage: F(int(1))
1
sage: a, b, c, d, e = F.gens()
sage: a^2 * b^3 * a^2 * b^4
a^4*b^7
sage: F = FreeAbelianMonoid(5, 'abcde')
sage: a, b, c, d, e = F.gens()
sage: a in F
True
sage: a*b in F
True

Python

>>> from sage.all import *
>>> F = FreeAbelianMonoid(Integer(5), 'abcde')
>>> F
Free abelian monoid on 5 generators (a, b, c, d, e)
>>> F(Integer(1))
1
>>> F(Integer(2))
Traceback (most recent call last):
...
TypeError: argument x (= 2) is of the wrong type
>>> F(int(Integer(1)))
1
>>> a, b, c, d, e = F.gens()
>>> a**Integer(2) * b**Integer(3) * a**Integer(2) * b**Integer(4)
a^4*b^7
>>> F = FreeAbelianMonoid(Integer(5), 'abcde')
>>> a, b, c, d, e = F.gens()
>>> a in F
True
>>> a*b in F
True

list()

Return the underlying list used to represent self.

If this is a monoid in an abelian monoid on \(n\) generators, then this is a list of nonnegative integers of length \(n\).

EXAMPLES:

Sage

sage: F = FreeAbelianMonoid(5, 'abcde')
sage: (a, b, c, d, e) = F.gens()
sage: a.list()
[1, 0, 0, 0, 0]

Python

>>> from sage.all import *
>>> F = FreeAbelianMonoid(Integer(5), 'abcde')
>>> (a, b, c, d, e) = F.gens()
>>> a.list()
[1, 0, 0, 0, 0]

sage.monoids.free_abelian_monoid_element.is_FreeAbelianMonoidElement(x)

Queries whether x is an object of type FreeAbelianMonoidElement.

INPUT:

• x – an object

OUTPUT:

• True if x is an object of type FreeAbelianMonoidElement; False otherwise.