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We present a strategy for computing asymptotics of coefficients of$d$-variate algebraic generating functions. Using known constructions, we embedthe coefficient array into an array represented by a rational generatingfunctions in $d+1$ variables, and then apply ACSV theory to analyse the latter.This method allows us to give systematic results in the multivariate case,seems more promising than trying to derive analogs of the rational ACSV theoryfor algebraic GFs, and gives the prospect of further improvements as embeddingmethods are studied in more detail.

Asymptotics of coefficients of algebraic series via embedding into rational series (extended abstract)