Solving Polynomial Equation Systems I: The Kronecker-Duval PhilosophyCambridge University Press, 27 mars 2003 - 423 pages With the advent of computers, theoretical studies and solution methods for polynomial equations have 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, emphasizing 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. |
Table des matières
I | xi |
II | 1 |
III | 3 |
IV | 4 |
V | 6 |
VI | 8 |
VII | 9 |
VIII | 10 |
LXIII | 168 |
LXIV | 169 |
LXVI | 170 |
LXVII | 175 |
LXIX | 176 |
LXX | 180 |
LXXI | 184 |
LXXII | 186 |
IX | 12 |
X | 16 |
XII | 18 |
XIII | 23 |
XIV | 24 |
XV | 26 |
XVI | 29 |
XVII | 32 |
XVIII | 35 |
XIX | 39 |
XX | 41 |
XXI | 47 |
XXII | 48 |
XXIII | 51 |
XXIV | 52 |
XXV | 53 |
XXVI | 54 |
XXVII | 55 |
XXVIII | 57 |
XXIX | 58 |
XXX | 62 |
XXXI | 64 |
XXXII | 68 |
XXXIII | 74 |
XXXIV | 75 |
XXXV | 76 |
XXXVI | 81 |
XXXVII | 84 |
XXXVIII | 86 |
XXXIX | 91 |
XL | 92 |
XLI | 96 |
XLII | 100 |
XLIII | 106 |
XLIV | 108 |
XLV | 112 |
XLVI | 115 |
XLVII | 119 |
XLVIII | 120 |
XLIX | 123 |
L | 125 |
LI | 127 |
LII | 133 |
LIII | 135 |
LIV | 141 |
LV | 148 |
LVI | 156 |
LVII | 159 |
LVIII | 164 |
LIX | 165 |
LXI | 167 |
LXXIII | 187 |
LXXIV | 191 |
LXXV | 192 |
LXXVI | 193 |
LXXVII | 196 |
LXXVIII | 203 |
LXXIX | 206 |
LXXX | 212 |
LXXXI | 216 |
LXXXII | 221 |
LXXXIII | 223 |
LXXXIV | 224 |
LXXXV | 228 |
LXXXVI | 232 |
LXXXVII | 237 |
LXXXVIII | 263 |
LXXXIX | 264 |
XC | 272 |
XCI | 275 |
XCII | 280 |
XCIII | 284 |
XCIV | 288 |
XCV | 290 |
XCVI | 294 |
XCVII | 297 |
XCVIII | 298 |
XCIX | 300 |
C | 305 |
CI | 314 |
CII | 318 |
CIII | 327 |
CIV | 329 |
CV | 338 |
CVI | 346 |
CVII | 347 |
CVIII | 350 |
CIX | 352 |
CX | 361 |
CXI | 369 |
CXII | 380 |
CXIII | 381 |
CXIV | 389 |
CXV | 391 |
CXVI | 395 |
CXVII | 398 |
CXVIII | 402 |
CXIX | 405 |
CXX | 415 |
CXXI | 420 |
422 | |
Autres éditions - Tout afficher
Solving Polynomial Equation Systems I: The Kronecker-Duval Philosophy Teo Mora Aucun aperçu disponible - 2003 |
Expressions et termes fréquents
algebraic closure algebraic extension b₁ basis canonical projection char(k Chinese Remainder Theorem coefficients compute conjugate construct cyclotomic deduce defined Definition deg(f deg(ƒ deg(g deg(h degree discuss divides elements Example exists Fa[X fact factorization algorithm factorization of f field extension field of f finite field Gauss gcd(f gcd(m GF q given h Corollary h₁ idempotents induction integer irreducible factor irreducible polynomial isomorphic k-isomorphism K₁ Kronecker Kronecker's Model lc(g Lemma Let f Let Kk linear factors minimal polynomial morphism multiplicity nilpotent normal extension notation nth root O₁ obtain obvious P₁ polynomial equations polynomial ƒ(X prime field primitive root principal ideal domain Proof Let Proposition prove representation result ring root of f root of unity root tower satisfies Section solving splitting field squarefree squarefree polynomial symmetric function transcendental unique