On Algorithmic Estimation of Analytic Complexity for Polynomial Solutions to Hypergeometric Systems

TL;DR

This paper investigates the analytic complexity of polynomial solutions to bivariate hypergeometric systems, providing estimates and algorithms for complexity measurement based on zonotopes.

Contribution

It introduces new estimates and algorithms for assessing the analytic complexity of polynomial solutions to hypergeometric systems of Horn type.

Findings

Derived bounds on the analytic complexity of solutions.

Proposed algorithms for complexity estimation.

Applicable to systems defined by zonotopes.

Abstract

The paper deals with the analytic complexity of solutions to bivariate holonomic hypergeometric systems of the Horn type. We obtain estimates on the analytic complexity of Puiseux polynomial solutions to the hypergeometric systems defined by zonotopes. We also propose algorithms of the analytic complexity estimation for polynomials.