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Mathematics for Computer Algebra

  • Maurice Mignotte

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Maurice Mignotte
    Pages 1-52
  3. Maurice Mignotte
    Pages 53-83
  4. Maurice Mignotte
    Pages 85-140
  5. Maurice Mignotte
    Pages 141-185
  6. Maurice Mignotte
    Pages 187-228
  7. Maurice Mignotte
    Pages 229-288
  8. Maurice Mignotte
    Pages 289-322
  9. Back Matter
    Pages 323-346

About this book

Introduction

This book corresponds to a mathematical course given in 1986/87 at the University Louis Pasteur, Strasbourg. This work is primarily intended for graduate students. The following are necessary prerequisites : a few standard definitions in set theory, the definition of rational integers, some elementary facts in Combinatorics (maybe only Newton's binomial formula), some theorems of Analysis at the level of high schools, and some elementary Algebra (basic results about groups, rings, fields and linear algebra). An important place is given to exercises. These exercises are only rarely direct applications of the course. More often, they constitute complements to the text. Mostly, hints or references are given so that the reader should be able to find solutions. Chapters one and two deal with elementary results of Number Theory, for example : the euclidean algorithm, the Chinese remainder theorem and Fermat's little theorem. These results are useful by themselves, but they also constitute a concrete introduction to some notions in abstract algebra (for example, euclidean rings, principal rings ... ). Algorithms are given for arithmetical operations with long integers. The rest of the book, chapters 3 through 7, deals with polynomials. We give general results on polynomials over arbitrary rings. Then polynomials with complex coefficients are studied in chapter 4, including many estimates on the complex roots of polynomials. Some of these estimates are very useful in the subsequent chapters.

Keywords

Mathematica algorithms computer algebra mathematics set theory

Authors and affiliations

  • Maurice Mignotte
    • 1
  1. 1.Départment de MathématiqueUniversité Louis PasteurStrasbourgFrance

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