A Geometric Approach to Cylindrical Algebraic Decomposition

Autor:	Chen, Rizeng
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Geometry Computer Science - Symbolic Computation Mathematics - Commutative Algebra 14Q30 (Primary) 14P10 14Q20 68W30 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Cylindrical algebraic decomposition is a classical construction in real algebraic geometry. Although there are many algorithms to compute a cylindrical algebraic decomposition, their practical performance is still very limited. In this paper, we revisit this problem from a more geometric perspective, where the construction of cylindrical algebraic decomposition is related to the study of morphisms between real varieties. It is showed that the geometric fiber cardinality (geometric property) decides the existence of semi-algebraic continuous sections (semi-algebraic property). As a result, all equations can be systematically exploited in the projection phase, leading to a new simple algorithm whose efficiency is demonstrated by experimental results. Comment: Rewrite the introduction, hopefully the last version!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.10515 Zobrazit plný text záznamu View this record from Arxiv