21.4 Abelian monoid elements

Module: sage.monoids.free_abelian_monoid_element

Abelian monoid elements

Author: - David Kohel (2005-09)

Recall the example from abelian monoids.

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]

It is important to note that lists are mutable and the returned list is not a copy. As a result, reassignment of an element of the list changes the object.

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

Module-level Functions

is_FreeAbelianMonoidElement( x)

Class: FreeAbelianMonoidElement

class FreeAbelianMonoidElement

FreeAbelianMonoidElement( self, F, x)

Create the element x of the FreeAbelianMonoid F.

sage: F = FreeAbelianMonoid(5, 'abcde')
sage: F
Free abelian monoid on 5 generators (a, b, c, d, e)
sage: F(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

Functions: list

list( self)

Return (a reference to) the underlying list used to represent this element. If this is a monoid in an abelian monoid on generators, then this is a list of nonnegative integers of length .

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

Special Functions: __init__, $\,$ __mul__, $\,$ __pow__, $\,$ __repr__

__pow__( self, n)

Raises self to the power of n.

Author: - Tom Boothby (2007-08) Replaced O(log n) time, O(n) space algorithm with O(1) time and space "algorithm".

sage: F = FreeAbelianMonoid(5,names = list("abcde"))
sage: (a,b,c,d,e) = F.gens()
sage: x = a*b^2*e*d; x
a*b^2*d*e
sage: x^3
a^3*b^6*d^3*e^3
sage: x^0
1

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