Modular Algorithms in Symbolic Summation and Symbolic Integration

• Main Author: Gerhard, Jürgen (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.
• Series: Lecture Notes in Computer Science, 3218
• Subjects: Computer science.; Algorithms.; Numerical analysis.; Computer science > Mathematics.; Computer mathematics.; Computer Science.; Algorithm Analysis and Problem Complexity.; Numeric Computing.; Symbolic and Algebraic Manipulation.; Computational Science and Engineering.

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...

Table of 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 & Zeilberger Algorithms.