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© 2012

Algebra for Symbolic Computation

  • It provides a good way of revising abstract concepts learnt in algebra courses

  • It shows the algorithmic nature of many concepts and theorems

  • It allows the reader to test his/her knowledge of the computer algebra systems

Textbook

Part of the UNITEXT book series (UNITEXT)

Also part of the La Matematica per il 3+2 book sub series (UNITEXTMAT)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Antonio Machì
    Pages 39-64
  3. Antonio Machì
    Pages 65-85
  4. Antonio Machì
    Pages 87-139
  5. Antonio Machì
    Pages 141-169
  6. Back Matter
    Pages 171-180

About this book

Introduction

This book deals with several topics in algebra useful for computer science applications and the symbolic treatment of algebraic problems, pointing out and discussing their algorithmic nature. The topics covered range from classical results such as the Euclidean algorithm, the Chinese remainder theorem, and polynomial interpolation, to p-adic expansions of rational and algebraic numbers and rational functions, to reach the problem of the polynomial factorisation,  especially via Berlekamp’s method, and the discrete Fourier transform. Basic algebra concepts are revised in a form suited for implementation on a computer algebra system.

Keywords

Algebra Algorithms Computer

Authors and affiliations

  1. 1.Department of MathematicsUniversity La SapienzaRomeItaly

Bibliographic information

  • Book Title Algebra for Symbolic Computation
  • Authors Antonio Machi
  • Series Title UNITEXT
  • DOI https://doi.org/10.1007/978-88-470-2397-0
  • Copyright Information Springer-Verlag Italia Srl. 2012
  • Publisher Name Springer, Milano
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-88-470-2396-3
  • eBook ISBN 978-88-470-2397-0
  • Series ISSN 2038-5714
  • Edition Number 1
  • Number of Pages VIII, 180
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebra
  • Buy this book on publisher's site

Reviews

From the reviews:

“The contents of this book is classical. … Many examples illustrate the text and make the mathematical objects very concrete. There are also many practical exercises. … It is clear that a thorough comprehension of these subjects would be greatly simplified if it is accompanied by exercises at the computer. Many examples of algorithms are given in the text, others may be easily deduced from the theory. … this book will be very useful and is very pleasant to read.” (Maurice Mignotte, Zentralblatt MATH, Vol. 1238, 2012)