Description
Book SynopsisThis is the first book that focuses on practical algorithms for polynomial inequality proving and discovering. It is a summary of the work by the authors and their collaborators on automated inequality proving and discovering in recent years. Besides brief introduction to some classical results and related work in corresponding chapters, the book mainly focuses on the algorithms initiated by the authors and their collaborators, such as real root counting, real root classification, improved CAD projection, dimension-decreasing algorithm, difference substitution, and so on. All the algorithms were rigorously proved and the implementations are demonstrated by lots of examples in various backgrounds such as algebra, geometry, biological science, and computer science.See Press Release: A collection of practical algorithms for polynomial inequality proving and discovering
Table of ContentsIntroduction; Basics of Elimination Method; Zero Decomposition for Polynomial System; Triangularization of Semi-Algebraic System; Real Root Counting; Real Root Isolation; Real Root Classification; Polynomial Optimization Based on Improved CAD Projection; Dimension-Decreasing Algorithm; Difference Substitution; SOS Decomposition; Inequality Proving Beyond the Tarski Model;
