inverse() method for permutation group elements

[rbeezer]

Patch aims to resolve the following inconsistency, by providing a .inverse() method for permutation group elements.

sage: S = SymmetricGroup(4)
sage: s = S("(1,2,3)")
sage: type(s)
<type
'sage.groups.perm_gps.permgroup_element.PermutationGroupElement'>
sage: s^-1
(1,3,2)
sage: s.inverse()
(1,3,2)

sage: A = AlternatingGroup(4)
sage: a = A("(1,2,3)")
sage: type(a)
<type
'sage.groups.perm_gps.permgroup_element.PermutationGroupElement'>
sage: a^-1
(1,3,2)
sage: a.inverse()
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
<snip>
AttributeError:
'sage.groups.perm_gps.permgroup_element.PermutationGroupElement' object has no attribute 'inverse' 

Some discussion at ​http://groups.google.com/group/sage-devel/browse_thread/thread/683315261a6c6def

Apply trac_10911-inverses-permutation-group-v2.patch

[robertwb]

Calling self.__invert__() is slow, use ~self instead. Other than that, looks good.

[rbeezer]

Replying to robertwb:

Calling self.__invert__() is slow, use ~self instead.

Thanks, Robert. v2 patch has the suggested change.

Rob

[robertwb]

Looks good to me.