Elimination Practice : Software Tools and Applications (With Cd-Rom).
Title:
Elimination Practice : Software Tools and Applications (With Cd-Rom).
Author:
Wang, Dongming.
ISBN:
9781848161207
Personal Author:
Physical Description:
1 online resource (233 pages)
Contents:
Contents -- 1 Polynomial Elimination at Work -- 1.1 Solving Polynomial Equations -- 1.2 Proving Geometric Theorems -- 1.3 Locating Singular Points -- 1.4 Decomposing Algebraic Curves -- 2 The Epsilon Library -- 2.1 What Is EPSILON and What It Does -- 2.2 Design and Implementation -- 2.3 EPSILON Functions -- 2.4 Some Experiments -- 2.5 Interface Availability and Installation -- 3 The CharSets Package -- 3.1 Introduction -- 3.2 CharSets Functions -- 3.3 Differential Module -- 3.4 Implementation Strategies -- 3.5 Experiments and Remarks -- 4 The TriSys and SiSys Modules -- 4.1 Introduction -- 4.2 TriSys Functions -- 4.3 Differential Triangular Series -- 4.4 SiSys Functions -- 4.5 Implementation Issues and Comparisons -- 5 The GEOTHER Environment -- 5.1 Specification of Geometric Theorems -- 5.2 Basic Translations -- 5.3 Proving Geometric Theorems Automatically -- 5.4 Automated Generation of Diagrams and Documents -- 5.5 Nondegeneracy Conditions and Miscellaneous Functions -- 5.6 Implementation Strategies -- 5.7 Experiments with Algebraic Provers -- 6 Relevant Elimination Tools -- 6.1 Implementations of Triangular Sets -- 6.2 Grobner Bases Packages -- 6.3 Computing Resultants and Subresultants -- 6.4 Miscellaneous Functions -- 7 Solving Polynomial Systems -- 7.1 General Principles -- 7.2 Solving Zero-dimensional Systems -- 7.3 Solving Systems of Positive Dimension -- 7.4 Solving Parametric Systems -- 8 Automated Theorem Proving and Discovering in Geometry -- 8.1 A Simple Algebraic Approach -- 8.2 Proving Theorems via Zero Decomposition -- 8.3 Illustration with Examples -- 8.4 Discovering Geometric Theorems -- 9 Symbolic Geometric Computation -- 9.1 Deriving Locus Equations -- 9.2 Implicitizing Parametric Objects -- 9.3 Computing Offsets -- 9.4 Blending Algebraic Surfaces -- 9.5 Decomposing Algebraic Varieties.
10 Selected Problems in Computer Mathematics -- 10.1 Computation with Polynomial Ideals -- 10.2 Factorization of Polynomials -- 10.3 Qualitative Study of Differential Equations -- 10.4 Automated Reasoning in Differential Geometry -- Appendix A Polynomial Systems: 50 Test Examples -- Appendix B Algebraic Factorization: 55 Examples -- References -- Index.
Abstract:
With a software library included, this book provides an elementary introduction to polynomial elimination in practice. The library Epsilon, implemented in Maple and Java, contains more than 70 well-documented functions for symbolic elimination and decomposition with polynomial systems and geometric reasoning. The book presents the functionality, implementation, and performance of Epsilon and demonstrates the usefulness of the elimination tool by a number of selected applications, together with many examples and illustrations. The reader will find Epsilon an efficient tool, applicable to a wide range of problems in science, engineering, and industry, and this book an accessible exposition and a valuable reference for elimination theory, methods, and practice. Contents: Polynomial Elimination at Work; The Epsilon Library; The CharSets Package; The TriSys and SiSys Modules; The GEOTHER Environment; Relevant Elimination Tools; Solving Polynomial Systems; Automated Theorem Proving and Discovering in Geometry; Symbolic Geometric Computation; Selected Problems in Computer Mathematics. Readership: Researchers and graduate students in symbolic mathematical computation, geometric reasoning and modeling, as well as mathematical software engineers.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Genre:
Electronic Access:
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