Johannes Grabmeier – författare

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.

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.

Two ideas lie gleaming on the jeweler's velvet. The first is the calculus, the sec­ ond, the algorithm. The calculus and the rich body of mathematical analysis to which it gave rise made modern science possible; but it has been the algorithm that has made possible the modern world. -David Berlinski, The Advent of the Algorithm First there was the concept of integers, then there were symbols for integers: I, II, III, 1111, fttt (what might be called a sticks and stones representation); I, II, III, IV, V (Roman numerals); 1, 2, 3, 4, 5 (Arabic numerals), etc. Then there were other concepts with symbols for them and algorithms (sometimes) for ma­ nipulating the new symbols. Then came collections of mathematical knowledge (tables of mathematical computations, theorems of general results). Soon after algorithms came devices that provided assistancefor carryingout computations. Then mathematical knowledge was organized and structured into several related concepts (and symbols): logic, algebra, analysis, topology, algebraic geometry, number theory, combinatorics, etc. This organization and abstraction lead to new algorithms and new fields like universal algebra. But always our symbol systems reflected and influenced our thinking, our concepts, and our algorithms.

Two ideas lie gleaming on the jeweler''s velvet. The first is the calculus, the sec­ ond, the algorithm. The calculus and the rich body of mathematical analysis to which it gave rise made modern science possible; but it has been the algorithm that has made possible the modern world. -David Berlinski, The Advent of the Algorithm First there was the concept of integers, then there were symbols for integers: I, II, III, 1111, fttt (what might be called a sticks and stones representation); I, II, III, IV, V (Roman numerals); 1, 2, 3, 4, 5 (Arabic numerals), etc. Then there were other concepts with symbols for them and algorithms (sometimes) for ma­ nipulating the new symbols. Then came collections of mathematical knowledge (tables of mathematical computations, theorems of general results). Soon after algorithms came devices that provided assistancefor carryingout computations. Then mathematical knowledge was organized and structured into several related concepts (and symbols): logic, algebra, analysis, topology, algebraic geometry, number theory, combinatorics, etc. This organization and abstraction lead to new algorithms and new fields like universal algebra. But always our symbol systems reflected and influenced our thinking, our concepts, and our algorithms.

Two ideas lie gleaming on the jeweler's velvet. The first is the calculus, the sec­ ond, the algorithm. The calculus and the rich body of mathematical analysis to which it gave rise made modern science possible; but it has been the algorithm that has made possible the modern world. -David Berlinski, The Advent of the Algorithm First there was the concept of integers, then there were symbols for integers: I, II, III, 1111, fttt (what might be called a sticks and stones representation); I, II, III, IV, V (Roman numerals); 1, 2, 3, 4, 5 (Arabic numerals), etc. Then there were other concepts with symbols for them and algorithms (sometimes) for ma­ nipulating the new symbols. Then came collections of mathematical knowledge (tables of mathematical computations, theorems of general results). Soon after algorithms came devices that provided assistancefor carryingout computations. Then mathematical knowledge was organized and structured into several related concepts (and symbols): logic, algebra, analysis, topology, algebraic geometry, number theory, combinatorics, etc. This organization and abstraction lead to new algorithms and new fields like universal algebra. But always our symbol systems reflected and influenced our thinking, our concepts, and our algorithms.