Solving polynomial systems over semialgebraic sets represented by cylindrical algebraic formulas

Autor:	Adam Strzebonski
Rok vydání:	2012
Předmět:	Algebra Polynomial ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Real algebraic geometry System of polynomial equations Algebraic function Dimension of an algebraic variety Disjoint sets Algebraic element Cylindrical algebraic decomposition Mathematics
Zdroj:	ISSAC
DOI:	10.1145/2442829.2442877
Popis:	Cylindrical algebraic formulas are an explicit representation of semialgebraic sets as finite unions of cylindrically arranged disjoint cells bounded by graphs of algebraic functions. We present a version of the Cylindrical Algebraic Decomposition (CAD) algorithm customized for solving systems of polynomial equations and inequalities over semialgebraic sets given in this representation. The algorithm can also be used to solve conjunctions of polynomial conditions in an incremental manner. We show application examples and give an empirical comparison of incremental and direct CAD computation.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::00127d12d2004940b8e3d308718b0c0c https://doi.org/10.1145/2442829.2442877 Zobrazit plný text záznamu