Elimination Methods
By: by Dongming Wang
Series: Texts and Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes-Kepler-University, Linz, Austria, 0943-853X; Texts and Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes-Kepler-University, Linz, Austria
Publisher: Springer Vienna; Imprint; Springer
Published: 2001
Place of publication: Vienna
Language: eng
Format: [electronic resource] /
Number of pages: 244
ISBN-13: 9783709162026
Description: 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 Gröbner 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 applicable to many other problems. Suitable as a graduate text, this book offers an indispensable reference for everyone interested in mathematical computation, computer algebra (software), and systems of algebraic equations.
Table of contents: title: List of Symbols; title: Polynomial arithmetic and zeros: Polynomials; Greatest common divisor, pseudo-division, and polynomial remainder sequences; Resultants and subresultants; Field extension and factorization; Zeros and ideals; Hilbert's Nullstellensatz; title: Zero decomposition of polynomial systems: Triangular systems; Characteristic-set-based algorithm; Seidenberg's algorithm refined; Subresultant-based algorithm; title: Projection and simple systems: Projection; Zero decomposition with projection; Decomposition into simple systems; Properties of simple systems; title: Irreducible zero decomposition: Irreducibility of triangular sets; Decomposition into irreducible triangular systems; Properties of irreducible triangular systems; Irreducible simple systems; title: Various elimination algorithms: Regular systems; Canonical triangular sets; Gröbner bases; Resultant elimination; title: Computational algebraic geometry and polynomial-ideal theory: Dimension; Decomposition of algebraic varieties; Ideal and radical ideal membership; Primary decomposition of ideals; title: Applications: Solving polynomial systems; Automated geometry theorem proving; Automatic derivation of unknown relations; Other geometric applications; Algebraic factorization; Center conditions for certain differential systems; title: Bibiographic notes; title: References; title: Subject index.