This 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.
Contents: PrefaceBasics of Elimination MethodZero Decomposition of Polynomial SystemTriangularization of Semi-Algebraic SystemReal Root CountingReal Root IsolationReal Root ClassificationOpen Weak CADDimension-Decreasing AlgorithmSOS DecompositionSuccessive Difference SubstitutionProving Inequalities Beyond the Tarski Model
Readership: Researchers and graduate students in computational real algebraic geometry, optimization and artificial intelligence.
