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Effective Polynomial Computation

  • Richard Zippel

Table of contents

  1. Front Matter
    Pages i-xi
  2. Richard Zippel
    Pages 1-10
  3. Richard Zippel
    Pages 11-39
  4. Richard Zippel
    Pages 41-55
  5. Richard Zippel
    Pages 57-72
  6. Richard Zippel
    Pages 73-84
  7. Richard Zippel
    Pages 85-106
  8. Richard Zippel
    Pages 107-124
  9. Richard Zippel
    Pages 125-136
  10. Richard Zippel
    Pages 137-156
  11. Richard Zippel
    Pages 157-172
  12. Richard Zippel
    Pages 173-187
  13. Richard Zippel
    Pages 189-206
  14. Richard Zippel
    Pages 207-229
  15. Richard Zippel
    Pages 231-246
  16. Richard Zippel
    Pages 247-259
  17. Richard Zippel
    Pages 261-283
  18. Richard Zippel
    Pages 285-291
  19. Richard Zippel
    Pages 293-302
  20. Richard Zippel
    Pages 303-319
  21. Richard Zippel
    Pages 321-327
  22. Richard Zippel
    Pages 329-340
  23. Back Matter
    Pages 341-363

About this book

Introduction

Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained.
Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth.
Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers).
Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed.

Keywords

Approximation Diophantine approximation Interpolation Mathematica algebra algorithms computer computer algebra finite field number theory

Authors and affiliations

  • Richard Zippel
    • 1
  1. 1.Cornell UniversityUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-3188-3
  • Copyright Information Kluwer Academic Publishers 1993
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-6398-9
  • Online ISBN 978-1-4615-3188-3
  • Series Print ISSN 0893-3405
  • Buy this book on publisher's site