Wronski Pairs of Honeycomb Curves

TL;DR

This paper investigates Wronski pairs of honeycomb curves, exploring their real solutions and computational challenges using algebraic geometry algorithms, advancing understanding of polynomial systems related to convex polytope triangulations.

Contribution

It introduces a detailed study of Wronski pairs of honeycomb curves, linking algebraic geometry with computational methods to analyze real solutions of polynomial systems.

Findings

Analysis of real solutions in Wronski systems

Development of computational approaches using Gr"obner bases

Insights into algebraic and numerical methods for polynomial systems

Abstract

We study certain generic systems of real polynomial equations associated with triangulations of convex polytopes and investigate their number of real solutions. Our main focus is set on pairs of plane algebraic curves which form a so-called Wronski system. The computational tasks arising in the analysis of such Wronski pairs lead us to the frontiers of current computer algebra algorithms and their implementations, both via Gr\"obner bases and numerical algebraic geometry.