Decomposing polynomial sets into simple sets over finite fields: the zero-dimensional case

DOI10.1016/j.camwa.2010.09.059zbMath1207.13017OpenAlexW2016625386MaRDI QIDQ630689

Chenqi Mou, Dongming Wang, Xiaoliang Li

Publication date: 19 March 2011

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2010.09.059

zbMATH Keywords

finite fieldsquarefree decomposition\(p\)th root extractionregular setsimple set

Mathematics Subject Classification ID

Finite fields and commutative rings (number-theoretic aspects) (11T99) Polynomials, factorization in commutative rings (13P05)

Related Items (11)

A triangular decomposition algorithm for differential polynomial systems with elementary computation complexity ⋮ Stability analysis for discrete biological models using algebraic methods ⋮ Analyzing the dual space of the saturated ideal of a regular set and the local multiplicities of its zeros ⋮ Bifurcation analysis and complex dynamics of a Kopel triopoly model ⋮ Chordal graphs in triangular decomposition in top-down style ⋮ On the efficiency of solving Boolean polynomial systems with the characteristic set method ⋮ Computing equilibria of semi-algebraic economies using triangular decomposition and real solution classification ⋮ Ritt-Wu characteristic set method for Laurent partial differential polynomial systems ⋮ Elimination theory in differential and difference algebra ⋮ Computing strong regular characteristic pairs with Gröbner bases ⋮ Computing Switching Surfaces in Optimal Control Based on Triangular Decomposition

Uses Software

• FGb
• RegularChains

Cites Work

• A characteristic set method for solving Boolean equations and applications in cryptanalysis of stream ciphers
• Basic principles of mechanical theorem proving in elementary geometries
• Elimination methods
• A new method for solving algebraic systems of positive dimension
• A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
• Decomposing polynomial systems into simple systems
• Algorithmic properties of polynomial rings
• An elimination method for polynomial systems
• Computing triangular systems and regular systems
• On the theories of triangular sets
• Square-free algorithms in positive characteristic
• Associative differential operations
• Algorithms for computing triangular decompositions of polynomial systems
• Advances in Cryptology - CRYPTO 2003
• Algebraic Statistics for Computational Biology
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Decomposing polynomial sets into simple sets over finite fields: the zero-dimensional case