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Solving Polynomial Equation Systems I

BuchGebunden
438 Seiten
Englisch
Cambridge University Presserschienen am17.05.2019
Polynomial equations have been long studied, both theoretically and with a view to solving them. Until recently, manual computation was the only solution method and the theory was developed to accommodate it. With the advent of computers, the situation changed dramatically. Many classical results can be more usefully recast within a different framework which in turn lends itself to further theoretical development tuned to computation. This first book in a trilogy is devoted to the new approach. It is a handbook covering the classical theory of finding roots of a univariate polynomial, emphasising computational aspects, especially the representation and manipulation of algebraic numbers, enlarged by more recent representations like the Duval Model and the Thom Codification. Mora aims to show that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.mehr
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Produkt

KlappentextPolynomial equations have been long studied, both theoretically and with a view to solving them. Until recently, manual computation was the only solution method and the theory was developed to accommodate it. With the advent of computers, the situation changed dramatically. Many classical results can be more usefully recast within a different framework which in turn lends itself to further theoretical development tuned to computation. This first book in a trilogy is devoted to the new approach. It is a handbook covering the classical theory of finding roots of a univariate polynomial, emphasising computational aspects, especially the representation and manipulation of algebraic numbers, enlarged by more recent representations like the Duval Model and the Thom Codification. Mora aims to show that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.
Details
ISBN/GTIN978-0-521-81154-5
ProduktartBuch
EinbandartGebunden
Erscheinungsjahr2019
Erscheinungsdatum17.05.2019
Seiten438 Seiten
SpracheEnglisch
MasseBreite 161 mm, Höhe 240 mm, Dicke 30 mm
Gewicht901 g
Artikel-Nr.17322459

Inhalt/Kritik

Inhaltsverzeichnis
Preface; Part I. The Kronecker-Duval Philosophy: 1. Euclid; 2. Intermezzo: Chinese remainder theorems; 3. Cardano; 4. Intermezzo: multiplicity of roots; 5. Kronecker I: Kronecker's philosophy; 6. Intermezzo: Sylvester; 7. Galois I: finite fields; 8. Kronecker II: Kronecker's model; 9. Steinitz; 10. Lagrange; 11. Duval; 12. Gauss; 13. Sturm; 14. Galois II; Part II. Factorization: 15. Ouverture; 16. Kronecker III: factorization; 17. Berlekamp; 18. Zassenhaus; 19. Fermeture; Bibliography; Index.mehr