Computer Algebra and Polynomials

Applications of Algebra and Number Theory

  • Jaime Gutierrez
  • Josef Schicho
  • Martin Weimann

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8942)

Also part of the Theoretical Computer Science and General Issues book sub series (LNTCS, volume 8942)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Joachim von zur Gathen, Konstantin Ziegler
    Pages 50-75
  3. Willem A. de Graaf
    Pages 76-93
  4. Georg Grasegger, Franz Winkler
    Pages 94-104
  5. Manuel Kauers, Maximilian Jaroschek, Fredrik Johansson
    Pages 105-125
  6. Zoltán Kovács, Bernard Parisse
    Pages 126-138
  7. Ragni Piene
    Pages 139-150
  8. Cristian-Silviu Radu
    Pages 151-156
  9. J. Rafael Sendra, David Sevilla, Carlos Villarino
    Pages 192-203
  10. Back Matter
    Pages 213-213

About this book

Introduction

Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life.

This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects.

The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.

Keywords

algebra computational geometry computations on polynomials computing methodologies mathematical analysis number theory numerical analysis randomness, geometry and discrete structures symbolic and algebraic manipulation

Editors and affiliations

  • Jaime Gutierrez
    • 1
  • Josef Schicho
    • 2
  • Martin Weimann
    • 3
  1. 1.University of CantabriaSantanderSpain
  2. 2.Ricam LinzLinzAustria
  3. 3.University of CaenCaenFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-15081-9
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-15080-2
  • Online ISBN 978-3-319-15081-9
  • Series Print ISSN 0302-9743
  • Series Online ISSN 1611-3349
  • About this book