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I have the abelian group (let's say, $Z_5^2$). I want to represent its Cayley graph as a grid, in which the element $a^i b^j$ occupies the $[i,j]$ position in the plane. For that, I need would need a method .pos(). which did the following.

A = groups.presentation.FGAbelian([n,n]);
e=A[2]

-->e=aba^-1

e.pos()

--> [0,1]

How can I create something like that?