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Elimination Methods

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ISBN-10: 3211832416

ISBN-13: 9783211832417

Edition: 2001

Authors: D. Wang

List price: $109.99
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This book provides a systematic and uniform presentation of elimination methods and the underlying theories, along the central line of decomposing arbitrary systems of polynomials into triangular systems of various kinds. Highlighting methods based on triangular sets, the book also covers the theory and techniques of resultants and Grbner bases. The methods and their efficiency are illustrated by fully worked out examples and their applications to selected problems such as from polynomial ideal theory, automated theorem proving in geometry and the qualitative study of differential equations. The reader will find the formally described algorithms ready for immediate implementation and…    
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Book details

List price: $109.99
Copyright year: 2001
Publisher: Springer
Publication date: 11/30/2000
Binding: Paperback
Pages: 244
Size: 6.69" wide x 9.61" long x 0.17" tall
Weight: 1.144

List of symbols
Polynomial arithmetic and zeros
Greatest common divisor, pseudo-division, and polynomi remainder sequences
Resultants and subresultants
Field extension and factorization
Zeros and ideals
Hilbert's Nullstellensatz
Zero decomposition of polynomial systems
Triangular systems
Characteristic-set-based algorithm
Seidenberg's algorithm refined
Subresultant-based algorithm
Projection and simple systems
Zero decomposition with projection
Decomposition into simple systems
Properties of simple systems
Irreducible zero decomposition
Irreducibility of triangular sets
Decomposition into irreducible triangular systems
Properties of irreducible triangular systems
Irreducible simple systems
Various elimination algorithms
Regular systems
Canonical triangular sets
Grobner bases
Resultant elimination
Computational algebraic geometry and polynomial-ideal theory
Decomposition of algebraic varieties
Ideal and radical ideal membership
Primary decomposition of ideals
Solving polynomial systems
Automated geometry theorem proving
Automatic derivation of unknown relations
Other geometric applications
Algebraic factorization
Center conditions for certain differential systems
Bibliographic notes
Subject index