Computing Arrangements of Hypersurfaces

TL;DR

This paper introduces a Julia software package designed to compute all connected components in the complement of arrangements of real algebraic hypersurfaces in Euclidean space.

Contribution

The paper presents a new computational tool that efficiently analyzes the topology of hypersurface arrangements in real algebraic geometry.

Findings

Successfully computes connected components in various hypersurface arrangements.

Provides a practical implementation for topological analysis in real algebraic geometry.

Enhances existing methods with a Julia package for better performance and usability.

Abstract

We present a Julia package HypersurfaceRegions.jl for computing all connected components in the complement of an arrangement of real algebraic hypersurfaces in $\mathbb{R}^n$.