Ebook: Symbolic Rewriting Techniques

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.

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Content:
Front Matter....Pages i-vii
Parallel Completion Techniques....Pages 1-34
The Computation of Gr?bner Bases Using an Alternative Algorithm....Pages 35-45
Symmetrization Based Completion....Pages 47-70
On the Reduction of G-invariant Polynomials for Arbitrary Permutation Groups G ....Pages 71-92
The Non-Commutative Gr?bner Freaks....Pages 93-104
Alternatives in Implementing Noncommutative Gr?bner Basis Systems....Pages 105-126
String Rewriting and Gr?bner Bases — A General Approach to Monoid and Group Rings....Pages 127-180
Gr?bner Fans and Projective Schemes....Pages 181-191
Normalized Rewriting: A Unified View of Knuth-Bendix Completion and Gr?bner Bases Computation....Pages 193-208
New Directions for Syntactic Termination Orderings....Pages 209-224
Two-sided Gr?bner Bases in Iterated Ore Extensions....Pages 225-243
Computing the Torsion Group of Elliptic Curves by the Method of Gr?bner Bases....Pages 245-265
Finding a Finite Group Presentation Using Rewriting....Pages 267-276
Deciding Degree-Four-Identities for Alternative Rings by Rewriting....Pages 277-288

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Content:
Front Matter....Pages i-vii
Parallel Completion Techniques....Pages 1-34
The Computation of Gr?bner Bases Using an Alternative Algorithm....Pages 35-45
Symmetrization Based Completion....Pages 47-70
On the Reduction of G-invariant Polynomials for Arbitrary Permutation Groups G ....Pages 71-92
The Non-Commutative Gr?bner Freaks....Pages 93-104
Alternatives in Implementing Noncommutative Gr?bner Basis Systems....Pages 105-126
String Rewriting and Gr?bner Bases — A General Approach to Monoid and Group Rings....Pages 127-180
Gr?bner Fans and Projective Schemes....Pages 181-191
Normalized Rewriting: A Unified View of Knuth-Bendix Completion and Gr?bner Bases Computation....Pages 193-208
New Directions for Syntactic Termination Orderings....Pages 209-224
Two-sided Gr?bner Bases in Iterated Ore Extensions....Pages 225-243
Computing the Torsion Group of Elliptic Curves by the Method of Gr?bner Bases....Pages 245-265
Finding a Finite Group Presentation Using Rewriting....Pages 267-276
Deciding Degree-Four-Identities for Alternative Rings by Rewriting....Pages 277-288
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