ASCV Homotopy

Homotopy Techniques for Analytic Combinatorics in Several Variables

ACSVHomotopy is a Julia package for studying the power series expansions of multivariate rational functions. It is built using the functionality of HomotopyContinuation.jl.

Usage

To run a notebook with ACSVHomotopy:

• Clone this repository.
• Create a new julia notebook inside the ACSVHomotopy folder and put

using Pkg
Pkg.activate(".")
using ACSVHomotopy

inside the first cell.

The package reexports the interface of HomotopyContinuation to the user. Polynomials can be constructed by declaring variables with @polyvar and including them into a Julia expression. The Package exports the functions find_min_crits, find_min_crits_comb and leading_asymptotics.

Example

Input:

using Pkg
Pkg.activate(".")
using ACSVHomotopy

@polyvar x y
h = 1-x-y
minimal = find_min_crits_comb(h)
leading_asymptotics(1, h, minimal)

Output:

(0.25)^(-n) n^(-0.5) (0.5641895835477563 + 0.0im)