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Algebra for Symbolic Computation

  • Textbook
  • © 2012

Overview

Authors:
  1. Antonio Machì

    1. Department of Mathematics, University La Sapienza, Rome, Italy

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  • 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
  • Includes supplementary material: sn.pub/extras

Part of the book series: UNITEXT (UNITEXT)

Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-VIII
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  2. The Euclidean algorithm, the Chinese remainder theorem and interpolation

    • Antonio Machì
    Pages 1-38

  3. p-adic Series Expansions

    • Antonio Machì
    Pages 39-64

  4. The resultant

    • Antonio Machì
    Pages 65-85

  5. Factoring polynomials

    • Antonio Machì
    Pages 87-139

  6. The discrete Fourier transform

    • Antonio Machì
    Pages 141-169

  7. Back Matter

    Pages 171-180
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Keywords

About this book

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.

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)

Authors and Affiliations

  • Department of Mathematics, University La Sapienza, Rome, Italy

    Antonio Machì

Bibliographic Information

  • Book Title: Algebra for Symbolic Computation

  • Authors: Antonio Machì

  • Series Title: UNITEXT

  • DOI: https://doi.org/10.1007/978-88-470-2397-0

  • Publisher: Springer Milano

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Italia Srl. 2012

  • Softcover ISBN: 978-88-470-2396-3Published: 16 March 2012

  • eBook ISBN: 978-88-470-2397-0Published: 10 July 2012

  • Series ISSN: 2038-5714

  • Series E-ISSN: 2532-3318

  • Edition Number: 1

  • Number of Pages: VIII, 180

  • Topics: Algebra

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