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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.
See Press Release: A collection of practical algorithms for polynomial inequality proving and discovering
Basics of Elimination Method
Zero Decomposition of Polynomial System
Triangularization of Semi-Algebraic System
Real Root Counting
Real Root Isolation
Real Root Classification
Open Weak CAD
Successive Difference Substitution
Proving Inequalities Beyond the Tarski Model
Readership: Researchers and graduate students in computational real algebraic geometry, optimization and artificial intelligence.
A series of practical algorithms for automated polynomial inequality proving and discovering
Lots of detailed demos on how to use the tools based on our algorithms
Applications to other fields such as polynomial optimization, algebraic biology, and program verification