Free abelian groups

A representation of a free abelian group over an alphabet a.

The intuition here is group elements correspond with their positive or negative multiplicities, and as such are simplified by construction.

Examples:

>>> let single a = MkFreeAbelianGroup $ Map.singleton a 1
>>> a = single 'a'
>>> b = single 'b'
>>> a
FreeAbelianGroup $ fromList [('a',1)]
>>> a <> b
FreeAbelianGroup $ fromList [('a',1),('b',1)]
>>> a <> b == b <> a
True
>>> invert a
FreeAbelianGroup $ fromList [('a',-1)]
>>> a <> b <> invert a
FreeAbelianGroup $ fromList [('b',1)]
>>> gtimes 5 (a <> b)
FreeAbelianGroup $ fromList [('a',5),('b',5)]