Gröbner Bases and Applications,9780521632980

Gröbner Bases and Applications

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ISBN13: 9780521632980
ISBN10: 0521632986
Format: Paperback
Pub. Date: 1998-03-28
Publisher(s): Cambridge University Press
List Price: $123.00

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Summary

The theory of Gröbner bases, invented by Bruno Buchberger, is a general method by which many fundamental problems in various branches of mathematics and engineering can be solved by structurally simple algorithms. The method is now available in all major mathematical software systems. This book provides a short and easy-to-read account of the theory of Gröbner bases and its applications. It is in two parts, the first consisting of tutorial lectures, beginning with a general introduction. The subject is then developed in a further twelve tutorials, written by leading experts, on the application of Gröbner bases in various fields of mathematics. In the second part are seventeen original research papers on Gröbner bases. An appendix contains the English translations of the original German papers of Bruno Buchberger in which Gröbner bases were introduced.

Table of Contents

Preface vii(1)
Programme Committee viii
Tutorials 3(302)
B. Buchberger
Introduction to Grobner Bases
3(29)
F. Chyzak
Grobner Bases, Symbolic Summation and Symbolic Integration
32(29)
W. Decker
T. de Jong
Grobner Bases and Invariant Theory
61(29)
M. Green
M. Stillman
A Tutorial on Generic Initial Ideals
90(19)
G.M. Greuel
G. Pfister
Grobner Bases and Algebraic Geometry
109(35)
S. Hosten
R. Thomas
Grobner Bases and Integer Programming
144(15)
H.M. Moller
Grobner Bases and Numerical Analysis
159(20)
L. Robbiano
Grobner Bases and Statistics
179(26)
S. Sakata
Grobner Bases and Coding Theory
205(16)
F. Schwarz
Janet Bases for Symmetry Groups
221(14)
D. Struppa
Grobner Bases in Partial Differential Equations
235(11)
B. Sturmfels
N. Takayama
Grobner Bases and Hypergeometric Functions
246(13)
V. Ufnarovski
Introduction to Noncommutative Grobner Bases Theory
259(22)
D. Wang
Grobner Bases Applied to Geometric Theorem Proving and Discovering
281(24)
Research Papers 305(230)
B. Amrhein
O. Gloor
The Fractal Walk
305(18)
M.A. Borges
M. Borges
Grobner Bases Property on Elimination Ideal in the Noncommutative Case
323(15)
A. Capani
G. Niesi
The CoCoA 3 Framework for a Family of Buchberger-like Algorithms
338(13)
M.-J. Gonzalez-Lopez
L. Gonzalez-Vega
Newton Identities in the Multivariate Case: Pham Systems
351(16)
M. Insa
F. Pauer
Grobner Bases in Rings of Differential Operators
367(14)
J.B. Little
Canonical Curves and the Petri Scheme
381(12)
H. Lombardi
H. Perdry
The Buchberger Algorithm as a Tool for Ideal Theory of Polynomial Rings in Constructive Mathematics
393(15)
K. Madlener
B. Reinert
Grobner Bases in Non-Commutative Reduction Rings
408(13)
J.L. Miller
Effective Algorithms for Intrinsically Computing SAGBI-Grobner Bases in a Polynomial Ring over a Field
421(13)
F. Mora
De Nugis Groebnerialium 1: Eagon, Northcott, Grobner
434(14)
J. Muller-Quade
R. Steinwandt
T. Beth
An Application of Grobner Bases to the Decomposition of Rational Mappings
448(15)
P. Nordbeck
On some Basic Applications of Grobner Bases in Non-commutative Polynomial Rings
463(10)
L. Robbiano
M.P. Rogantin
Full Factorial Designs and Distracted Fractions
473(10)
T. Sauer
Polynomial Interpolation of Minimal Degree and Grobner Bases
483(12)
J. Schicho
Inversion of Birational Maps with Grobner Bases
495(9)
J. Snellman
Reverse Lexicographic Initial Ideals of Generic Ideals are Finitely Generated
504(15)
Tran Q.-N.
Parallel Computation and Grobner Bases: An Application for Converting Bases with the Grobner Walk
519(16)
B. Buchberger
Michael Abramson
Robert Lumbert
Appendix An Algorithmic Criterion for the Solvability of a System of Algebraic Equations 535(11)
Index of Tutorials 546

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