Méthodes d'élimination avec applications
Résumé
This book provides a systematic and uniform presentation of elimination methods for zero decomposition of polynomial systems. These methods can decompose any system of multivariate polynomials into triangular systems, regular systems, simple systems, triangular systems with the projection property, and irreducible triangular systems. The various triangularized systems differ in terms of theoretical properties, computational difficulties, and practical applicabilities. The book also covers the theory and techniques of resultants and Gröbner bases, addresses unmixed and irreducible decomposition of algebraic varieties and primary decomposition of polynomial ideals, and presents several applications of symbolic elimination methods, such as solving polynomial systems, proving geometric theorems, factorizing polynomials, and qualitative study of differential equations. Suitable as a text for a graduate or advanced undergraduate course in mathematics or computer science, this book offers an indispensable reference for students, researchers, and engineers interested in mathematical computation, computer algebra (software), and systems of algebraic equations.