دانلود کتاب Resultants and the Hermite Normal Form

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1 Introduction 1 1.1 Polynom ials .......................................................................................... 1 1.2 R esultants ............................................................................................. 3 1.3 Multivariate polynomials ................................................................. 6 1.4 Symmetric fu n ction s ........................................................................ 7 1.5 The Resultant in terms of the ro o ts ............................................ 9 1.6 Two resultant resu lts ........................................................................ 11 1.6.1 The discrim inant ................................................................ 11 1.6.2 Cyclotomic polynom ials .................................................. 13 1.7 Subresultants ...................................................................................... 17 2 Equivalence of m atrices 23 2.1 Definitions ............................................................................................. 23 2.2 One-sided equivalence ..................................................................... 25 2.3 Two-sided eq u ivalen ce ....................................................................... 28 3 The Integral polynom ial range 32 3.1 Introduction .......................................................................................... 32 3.2 Preliminaries ...................................................................................... 33 3.3 The Bigradient, Gp ............................................................................ 34 3.4 The Infinite Bigradient, G0 0 .......................................................... 39 3.5 Examples and corollaries ................................................................. 46 3.6 Monic polynomials and the resultant m a trix ............................ 51 3.7 A bound for the stability of G ^ ................................................... 59 4 R elated Topics 61 4.1 The Rational Polynomial R ange ................................................... 61 4.2 Matrix rings and multivariate polynom ials .............................. 63 Bibliography 66