Module abelian_group_element

Abelian group elements

AUTHORS:
    - David Joyner (2006-02); based on free_abelian_monoid_element.py, written by David Kohel.
    - David Joyner (2006-05); bug fix in order
    -              (2006-08); bug fix+new method in pow for negatives+fixed corresponding examples.

EXAMPLES:
Recall an example from abelian groups.
    sage: F = AbelianGroup(5,[4,5,5,7,8],names = list("abcde"))
    sage: (a,b,c,d,e) = F.gens()
    sage: x = a*b^2*e*d^20*e^12
    sage: x
    a*b^2*d^6*e^5
    sage: x = a^10*b^12*c^13*d^20*e^12
    sage: x
    a^2*b^2*c^3*d^6*e^4
    sage: y = a^13*b^19*c^23*d^27*e^72
    sage: y
    a*b^4*c^3*d^6
    sage: x*y
    a^3*b*c*d^5*e^4
    sage: x.list()
    [2, 2, 3, 6, 4]

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] = 3
    sage: x.list()
    [3, 2, 3, 6, 4]
    sage: x
    a^3*b^2*c^3*d^6*e^4

Return true if x is an abelian group element, i.e., an element of type
AbelianGroupElement. 

EXAMPLES:
Though the integer 3 is in the integers, and the integers have an abelian
group structure, 3 is not an AbelianGroupElement:
     sage: is_AbelianGroupElement(3)
     False
     sage: F = AbelianGroup(5, [3,4,5,8,7], 'abcde')
     sage: is_AbelianGroupElement(F.0)
     True