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You may try the following:

a = var(",".join( "a%i" %i for i in range(0, 7)))
R.<x,y> = LaurentPolynomialRing(SR,2)
f = x*y + a6*x + a4*y + x*y^-1 + x^-1*y + a3*y^-1 + a1*x^-1 + x^-1*y^-1

It gives a6 as you expect and e.g.


is equal to a4. Also you can determine the coefficient of any monomial:


is 1.