General Theory of Algebraic Equations

Nonfiction, Science & Nature, Mathematics, Algebra
Cover of the book General Theory of Algebraic Equations by Etienne Bézout, Princeton University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Etienne Bézout ISBN: 9781400826964
Publisher: Princeton University Press Publication: January 10, 2009
Imprint: Princeton University Press Language: English
Author: Etienne Bézout
ISBN: 9781400826964
Publisher: Princeton University Press
Publication: January 10, 2009
Imprint: Princeton University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Princeton University Press

Cover of the book Arendt and Heidegger by Etienne Bézout
Cover of the book American Jesuits and the World by Etienne Bézout
Cover of the book Why Stock Markets Crash by Etienne Bézout
Cover of the book Iraq by Etienne Bézout
Cover of the book All the Missing Souls by Etienne Bézout
Cover of the book Dynamic Models in Biology by Etienne Bézout
Cover of the book The Extreme Life of the Sea by Etienne Bézout
Cover of the book Mimesis by Etienne Bézout
Cover of the book Nuclear Logics by Etienne Bézout
Cover of the book The Flame of Eternity by Etienne Bézout
Cover of the book Regulating Aversion by Etienne Bézout
Cover of the book Law, Politics, and Morality in Judaism by Etienne Bézout
Cover of the book The Gamble: The Hand You're Dealt by Etienne Bézout
Cover of the book Outside Ethics by Etienne Bézout
Cover of the book Nation Building by Etienne Bézout
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy