Modular Algorithms in Symbolic Summation and Symbolic Integration / by Jürgen Gerhard.

Format:

Book

Author/Creator:

Gerhard, Jürgen, 1967- author.

Contributor:

SpringerLink (Online service)

Series:

Computer Science (Springer-11645)

Lecture notes in computer science 0302-9743 ; 3218.

Lecture Notes in Computer Science, 0302-9743 ; 3218

Language:

English

Subjects (All):

Algorithms.

Numerical analysis.

Computer science--Mathematics.

Computer science.

Algorithm Analysis and Problem Complexity.

Numeric Computing.

Symbolic and Algebraic Manipulation.

Computational Science and Engineering.

Local Subjects:

Algorithm Analysis and Problem Complexity.

Numeric Computing.

Symbolic and Algebraic Manipulation.

Algorithms.

Computational Science and Engineering.

Physical Description:

1 online resource (XVI, 228 pages).

Edition:

First edition 2005.

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2005.

System Details:

text file PDF

Summary:

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.

Contents:

1. Introduction

2. Overview

3. Technical Prerequisites

4. Change of Basis

5. Modular Squarefree and Greatest Factorial Factorization

6. Modular Hermite Integration

7. Computing All Integral Roots of the Resultant

8. Modular Algorithms for the Gosper-Petkovšek Form

9. Polynomial Solutions of Linear First Order Equations

10. Modular Gosper and Almkvist and Zeilberger Algorithms.

Other Format:

Printed edition:

ISBN:

978-3-540-30137-0

9783540301370

Access Restriction:

Restricted for use by site license.