Symbolic Rewriting TechniquesManuel Bronstein, Johannes Grabmeier, Volker Weispfenning 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 |
Other editions - View all
Symbolic Rewriting Techniques Manuel Bronstein,Johannes Grabmeier,Volker Weispfenning Limited preview - 2013 |
Symbolic Rewriting Techniques Manuel Bronstein,Johannes Grabmeier,Volker Weispfenning No preview available - 2011 |
Symbolic Rewriting Techniques Manuel Bronstein,Johannes Grabmeier,Volker Weispfenning No preview available - 2012 |
Common terms and phrases
biquadratic field Bruno Buchberger Buchberger Buchberger's algorithm can(p coefficient completion procedure Computer Science confluent corresponding critical pairs defined Definition deletion denotes equations example exists finite Gröbner basis finitely presented free monoid G-invariant orbits Gröbner bases Gröbner Fan group rings Hence homogeneous ideal implementation implies induction iterated Ore extension Knuth-Bendix completion leading term left Gröbner left ideal Lemma LNCS Madlener modulo monoid rings monomial multiplication non-commutative normal form parallel permutation group polynomial ring Pommaret prefix Gröbner bases prefix reduction Proc processors Proof prove reduced Gröbner basis reduction relation reduction ring redundant element respect Rewriting Techniques right ideal s-polynomials saturating sets selection strategy semi-Thue system set of polynomials solvable speedups Springer string rewriting systems structure Symbolic Computation symmetrization t₁ term completion term rewriting system termination theorem theory time(i+1 triples two-sided ideal vector Weispfenning word problem