Solving polynomial equation systems I
著者
書誌事項
Solving polynomial equation systems I
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 88）
Cambridge University Press, 2003
- : hardback
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注記
Bibliography: p. 420-421
Includes index
収録内容
- The Kronecker-Duval philosophy
- Factorization
内容説明・目次
内容説明
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.
目次
- 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.
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