Module dual_abelian_group_element

Elements (characters) of the dual group of a finite Abelian group.

AUTHORS:
    - David Joyner (2006-07); based on abelian_group_element.py.
    - David Joyner (2006-10); modifications suggested by William Stein.

EXAMPLES:
    sage: F = AbelianGroup(5,[2, 3, 5, 7, 8], names="abcde")
    sage: a,b,c,d,e = F.gens()
    sage: Fd = DualAbelianGroup(F, names = "ABCDE")
    sage: A,B,C,D,E = Fd.gens()
    sage: A*B^2*D^7
    A*B^2
    sage: A(a)    ## random last few digits
    -1.0000000000000000 + 0.00000000000000013834419720915037*I
    sage: B(b)
    -0.500000000000000 + 0.866025403784439*I
    sage: A(a*b)    ## random last few digits
    -1.0000000000000000 + 0.00000000000000013834419720915037*I
    sage: (A*B*C^2*D^20*E^65).list()
    [1, 1, 2, 6, 1]
    sage: B^(-1)
    B^2

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 = A*B*C^2*D^2*E^-6
    sage: X.list()
    [1, 1, 2, 2, 2]
    sage: X.list()[1] = -1
    sage: X
    A*B^-1*C^2*D^2*E^2

This was in sage.misc.misc but commented out. Needed to add
lists of strings in the word_problem method below.

Return the sum of the elements of x.  If x is empty,
return z.

INPUT:
    x -- iterable
    z -- the "0" that will be returned if x is empty.
    
OUTPUT:
    object