47 citations · 161 across the 20 of their papers we have counts for
5 papers · 1 filter
Computing error bounds for asymptotic expansions of regular P-recursive sequences
Ruiwen Dong, Stephen Melczer, Marc Mezzarobba
Over the last several decades, improvements in the fields of analytic combinatorics and computer algebra have made determining the asymptotic behaviour of sequences satisfying line…
Change of basis for m-primary ideals in one and two variables
Seung Gyu Hyun, Stephen Melczer, Éric Schost +1
Following recent work by van der Hoeven and Lecerf (ISSAC 2017), we discuss the complexity of linear mappings, called untangling and tangling by those authors, that arise in the co…
Effective Coefficient Asymptotics of Multivariate Rational Functions via Semi-Numerical Algorithms for Polynomial Systems
Stephen Melczer, Bruno Salvy
The coefficient sequences of multivariate rational functions appear in many areas of combinatorics. Their diagonal coefficient sequences enjoy nice arithmetic and asymptotic proper…
A fast algorithm for solving linearly recurrent sequences
Seung Gyu Hyun, Stephen Melczer, Catherine St-Pierre
We present an algorithm which computes the term of a sequence satisfying a linear recurrence relation of order over a field in $O( \mathsf{M}(\bar d)\log(D) + \mat…
Symbolic-Numeric Tools for Analytic Combinatorics in Several Variables
Stephen Melczer, Bruno Salvy
Analytic combinatorics studies the asymptotic behaviour of sequences through the analytic properties of their generating functions. This article provides effective algorithms requi…