Cylindrical Algebraic Decomposition Using Local Projections

TL;DR

This paper introduces a novel algorithm for cylindrical algebraic decomposition that uses local projections for each cell, reducing complexity and improving efficiency compared to traditional methods.

Contribution

The paper proposes a new local projection-based algorithm for CAD, which decreases the number of cells by computing smaller, cell-specific projection sets.

Findings

Empirical results show fewer cells generated with the new method.

The local projection approach reduces computational complexity.

Compared to classical CAD, the new algorithm is more efficient in practice.

Abstract

We present an algorithm which computes a cylindrical algebraic decomposition of a semialgebraic set using projection sets computed for each cell separately. Such local projection sets can be significantly smaller than the global projection set used by the Cylindrical Algebraic Decomposition (CAD) algorithm. This leads to reduction in the number of cells the algorithm needs to construct. We give an empirical comparison of our algorithm and the classical CAD algorithm.