  We consider a bivariate rational generating function F(x,y) = P(x,y) / Q(x,y)
= sum_{r, s} a_{r,s} x^r y^s under the assumption that the complex algebraic
curve $\sing$ on which $Q$ vanishes is smooth. Formulae for the asymptotics of
the coefficients a_{rs} were derived by Pemantle and Wilson (2002). These
formulae are in terms of algebraic and topological invariants of the pole
variety, but up to now these invariants could be computed only under a
minimality hypothesis, namely that the dominant saddle lies on the boundary of
the domain of convergence. In the present paper, we give an effective method
for computing the topological invariants, and hence the asymptotics of the
values a_{r,s}, without the minimality assumption. This leads to a
theoretically rigorous algorithm, whose implementation is in progress at
http://www.mathemagix.org .
