General theory of algebraic equations / Etienne Bezout ; translated by Eric Feron.

Format:

Book

Author/Creator:

Bézout, Etienne, 1730-1783.

Contributor:

Feron, Eric, 1967-

Standardized Title:

Théorie générale des équations algébriques. English

Language:

English

Subjects (All):

Equations, Theory of.

Mathematics.

Physical Description:

1 online resource (362 p.)

Edition:

Core Textbook

Place of Publication:

Princeton : Princeton University Press, c2006.

Language Note:

English

Summary:

This book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two hundred years, the English translation of his famous mathematics textbooks. Here, Bézout presents his approach to solving systems of polynomial equations in several variables and in great detail. He introduces the revolutionary notion of the "polynomial multiplier," which greatly simplifies the problem of variable elimination by reducing it to a system of linear equations. The major result presented in this work, now known as "Bézout's theorem," is stated as follows: "The degree of the final equation resulting from an arbitrary number of complete equations containing the same number of unknowns and with arbitrary degrees is equal to the product of the exponents of the degrees of these equations." The book offers large numbers of results and insights about conditions for polynomials to share a common factor, or to share a common root. It also provides a state-of-the-art analysis of the theories of integration and differentiation of functions in the late eighteenth century, as well as one of the first uses of determinants to solve systems of linear equations. Polynomial multiplier methods have become, today, one of the most promising approaches to solving complex systems of polynomial equations or inequalities, and this translation offers a valuable historic perspective on this active research field.

Contents:

Front matter

Contents

Translator's Foreword

Dedication from the 1779 edition

Preface to the 1779 edition

Introduction

Book One

Book Two

Notes:

Description based upon print version of record.

ISBN:

9786612935428

9781282935426

1282935429

9781400826964

1400826969

OCLC:

697174426