Symbolic-Numeric Tools for Analytic Combinatorics in Several Variables
@article{Melczer2016SymbolicNumericTF,
title={Symbolic-Numeric Tools for Analytic Combinatorics in Several Variables},
author={Stephen Melczer and B. Salvy},
journal={Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation},
year={2016}
}Analytic combinatorics studies the asymptotic behavior of sequences through the analytic properties of their generating functions. This article provides effective algorithms required for the study of analytic combinatorics in several variables, together with their complexity analyses. Given a multivariate rational function we show how to compute its smooth isolated critical points, with respect to a polynomial map encoding asymptotic behaviour, in complexity singly exponential in the degree of… CONTINUE READING
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