Symbolic Rewriting Techniques

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Manuel Bronstein, Johannes Grabmeier, Volker Weispfenning
Springer Science & Business Media, 1998 - Computers - 288 pages
Symbolic rewriting techniques are methods for deriving consequences from systems of equations, and are of great use when investigating the structure of the solutions. Such techniques appear in many important areas of research within computer algebra: • the Knuth-Bendix completion for groups, monoids and general term-rewriting systems, • the Buchberger algorithm for Gröbner bases, • the Ritt-Wu characteristic set method for ordinary differential equations, and • the Riquier-Janet method for partial differential equations. This volume contains invited and contributed papers to the Symbolic Rewriting Techniques workshop, which was held at the Centro Stefano Franscini in Ascona, Switzerland, from April 30 to May 4, 1995. That workshop brought together 40 researchers from various areas of rewriting techniques, the main goal being the investigation of common threads and methods. Following the workshops, each contribution was formally refereed and 14 papers were selected for publication.
 

Contents

Parallel Completion Techniques
1
The Computation of Gröbner Bases Using an Alternative Algorithm
35
Symmetrization Based Completion
47
On the Reduction of Ginvariant Polynomials for Arbitrary Permutation Groups G
71
The NonCommutative Gröbner Freaks
93
Alternatives in Implementing Noncommutative Gröbner Basis Systems
105
String Rewriting and Gröbner Bases A General Approach to Monoid and Group Rings
125
Gröbner Fans and Projective Schemes
179
A Unified View of KnuthBendix Completion and Gröbner Bases Computation
191
New Directions for Syntactic Termination
207
Twosided Gröbner Bases in Iterated Ore Extensions
223
Computing the Torsion Group of Elliptic Curves by the Method of Gröbner Bases
242
Finding a Finite Group Presentation Using Rewriting
263
Deciding DegreeFourIdentities for Alternative Rings by Rewriting
273
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