Symbolic Computation Group

The field of Analytic Combinatorics in Several Variables (ACSV) uses techniques from complex analysis and algebraic geometry to determine the asymptotic behaviour of sequences through their multivariate generating functions. When the generating function is rational, its set of singularities is an algebraic variety, and the geometry of this singular variety heavily influences asymptotics. Under a set of verifiable conditions, asymptotic behaviour for a wide class of sequences with rational generating functions can be determined. The SageMath package sage-acsv is the first software package to rigorously compute asymptotics for sequences with rational generating functions. I will talk about the algorithms and computational techniques used to develop the package, and how it showcases a powerful application of computer algebra in an adjacent mathematical field. This talk is based on joint work with Steve Melczer, Eric Schost, and Benjamin Hackl.