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Lecture Notes in Computer Science
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Modular Algorithms in Symbolic Summation and Symbolic Integration

Authors: Gerhard, Jürgen

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About this book

This work brings together two streams in computer algebra: symbolic integration and summation on the one hand, and fast algorithmics on the other hand. In many algorithmically oriented areas of computer science, theanalysisof- gorithms–placedintothe limelightbyDonKnuth’stalkat the 1970ICM –provides a crystal-clear criterion for success. The researcher who designs an algorithmthat is faster (asymptotically, in the worst case) than any previous method receives instant grati?cation: her result will be recognized as valuable. Alas, the downside is that such results come along quite infrequently, despite our best efforts. An alternative evaluation method is to run a new algorithm on examples; this has its obvious problems, but is sometimes the best we can do. George Collins, one of the fathers of computer algebra and a great experimenter,wrote in 1969: “I think this demonstrates again that a simple analysis is often more revealing than a ream of empirical data (although both are important). ” Within computer algebra, some areas have traditionally followed the former methodology, notably some parts of polynomial algebra and linear algebra. Other areas, such as polynomial system solving, have not yet been amenable to this - proach. The usual “input size” parameters of computer science seem inadequate, and although some natural “geometric” parameters have been identi?ed (solution dimension, regularity), not all (potential) major progress can be expressed in this framework. Symbolic integration and summation have been in a similar state.

Table of contents (10 chapters)

Table of contents (10 chapters)
  • 1. Introduction

    Pages 1-5

    Gerhard, Jürgen

  • 2. Overview

    Pages 7-25

    Gerhard, Jürgen

  • 3. Technical Prerequisites

    Pages 27-40

    Gerhard, Jürgen

  • 4. Change of Basis

    Pages 41-60

    Gerhard, Jürgen

  • 5. Modular Squarefree and Greatest Factorial Factorization

    Pages 61-77

    Gerhard, Jürgen

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-3-540-30137-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.99
price for USA in USD
  • ISBN 978-3-540-24061-7
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Modular Algorithms in Symbolic Summation and Symbolic Integration
Authors
Series Title
Lecture Notes in Computer Science
Series Volume
3218
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-30137-0
DOI
10.1007/b104035
Softcover ISBN
978-3-540-24061-7
Series ISSN
0302-9743
Edition Number
1
Number of Pages
XVI, 228
Topics

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