Work

Projective Delineability for Single Cell Construction

Year: 2025

Type: conference-paper

Abstract: The cylindrical algebraic decomposition (CAD) is the only complete method used in practice for solving problems like quantifier elimination or SMT solving related to real algebra, despite its doubly exponential complexity. Recent exploration-guided algorithms like NLSAT, NuCAD, and CAlC rely on CAD technology but reduce the computational effort heuristically. Single cell construction is a paradigm that is used in each of these algorithms. The central property on which the CAD algorithm is based is called delineability. Recently, we introduced a weaker notion called projective delineability which can require fewer computations to guarantee, but needs to be applied carefully. This paper adapts the single cell construction for exploiting projective delineability and reports on experimental results.

Source: Pure (Coventry University)

DOI: 10.48550/arxiv.2508.00512

Authors: Nalbach, Jasper, Michel, Lucas, Ábrahám, Erika, Brown, Christopher W., Davenport, James H., England, Matthew, Mathonet, Pierre, Zénaïdi, Naïm

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4416551447

FWCI:

Cites:

Cited by:

Related to: