Advertisement

Elimination Methods

  • Dongming Wang

Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Dongming Wang
    Pages 1-20
  3. Dongming Wang
    Pages 21-51
  4. Dongming Wang
    Pages 52-83
  5. Dongming Wang
    Pages 84-106
  6. Dongming Wang
    Pages 107-150
  7. Dongming Wang
    Pages 178-231
  8. Back Matter
    Pages 232-244

About this book

Introduction

The development of polynomial-elimination techniques from classical theory to modern algorithms has undergone a tortuous and rugged path. This can be observed L. van der Waerden's elimination of the "elimination theory" chapter from from B. his classic Modern Algebra in later editions, A. Weil's hope to eliminate "from algebraic geometry the last traces of elimination theory," and S. Abhyankar's sug­ gestion to "eliminate the eliminators of elimination theory. " The renaissance and recognition of polynomial elimination owe much to the advent and advance of mod­ ern computing technology, based on which effective algorithms are implemented and applied to diverse problems in science and engineering. In the last decade, both theorists and practitioners have more and more realized the significance and power of elimination methods and their underlying theories. Active and extensive research has contributed a great deal of new developments on algorithms and soft­ ware tools to the subject, that have been widely acknowledged. Their applications have taken place from pure and applied mathematics to geometric modeling and robotics, and to artificial neural networks. This book provides a systematic and uniform treatment of elimination algo­ rithms that compute various zero decompositions for systems of multivariate poly­ nomials. The central concepts are triangular sets and systems of different kinds, in terms of which the decompositions are represented. The prerequisites for the concepts and algorithms are results from basic algebra and some knowledge of algorithmic mathematics.

Keywords

algebra algebraic geometry algorithms ants automated theorem proving computer algebra derivation mathematical computation proving

Authors and affiliations

  • Dongming Wang
    • 1
  1. 1.Laboratoire d’Informatique de Paris 6Université Pierre et Marie CurieParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-7091-6202-6
  • Copyright Information Springer-Verlag/Wien 2001
  • Publisher Name Springer, Vienna
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-211-83241-7
  • Online ISBN 978-3-7091-6202-6
  • Series Print ISSN 0943-853X
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking
Telecommunications