GSoC 2012 Rough Interface

"""This is a tentative interface for the Group theory module which I plan to make as a part of GSOC 2012

I have made this interface for the abelian group of U9 """

>>>G.Group([1,2,4,5,7,8],‘%9’)

>>>G.is_abelian()
True

>>>G.identity()
1

>>>G.order_group()
6

>>>G.inverse(4)
7

>>>G.order_element(1)
1

>>>G.order_element(2)
6

>>>G.generators()
2

>>>H=[1,4,7]

>>>H.is_subgroup(G)
True

>>>H.is_normal(G)
True

>>>H.coset(8)
[8,5,2]

>>>K.Group([1,5,7,11,13,17],‘%18’])

>>>f=dict(zip(G,K))

>>>f
{1:1 , 2:5 , 4:7 , 5:11 , 7:13 , 8:17}

>>>f.is_homomorphism()
True

>>>f.kernel()
¹

>>>f.isomorphism()
True

>>>f.range(H)
[1,7,13]