Home | Quick Search | Advanced Search | Bibliography submission | Bibliography submission using bibtex | Links | Help | Internal

# Preface

This bibliography was initiated by Bruno Buchberger and is being built up under his direction. The authors of the bibliography are Bruno Buchberger and Alexander Zapletal and the managing editors are Buchberger's PhD students M.Wiesinger and H.Rahkooy.

In this bibliography, we try to collect all journal and proceeding articles, books, survey articles, technical reports, tutorials, lecture notes, slides of talks etc. on Gröbner bases theory and related topics (theory, algorithms, systems, applications).

We invite authors of written material on Gröbner bases theory and related topics to enter the material by using the bibliography submission form or the bibliography submission form for bibtex.

You can search for items in the bibliography by using the search facility or by viewing all entries and simply using the Find function of your browser.

We also refer to the following sites for searching literature on Gröbner bases theory and related topics:

CiteSeer
MathSciNet
Scirus
Zentralblatt MATH

# How to use this bibliography?

Please see the help page. There you will find details on how to browse, add and edit items.

# Early Forerunners

• Euclid
Non-linear univariate systems. Euclid's algorithm turns out to be a special case of the Gröbner bases algorithm.
• C.F. Gauss
Linear multivariate systems. Gauss's algorithm turns out to be a special case of the Gröbner bases algorithm.
• Division Process in 19th Century
A kind of division process for multivariate polynomials.
• P. Gordan, 1899
Introduced (in the language of that time) the notion of Gröbner bases (based on the division process) and showed their existence (finiteness?) but did not give an algorithm for constructing them.
• L.E. Dickson, 1913
A general lemma on the termination of certain sequences of tuples of natural numbers. From this lemma, the termination of the Gröbner bases algorithm follows easily. And, then, Hilbert's basis theorem is an easy corollary of the existence of Gröbner bases.
• M. Janet, 1920
Similar notions and methods for differential equations (viewed symbolically).
• G. Hermann, 1926
A solution of the membership problem for polynomial ideals based on linear algebra.
• W. Gröbner
• J. Ritt
Characteristic sets.
• A.I. Shirshov, 1962
Similar notion and method for Lie algebras.
• H. Hironaka, 1964
In the frame of his famous paper on the resolution of singularities: the notion of "standard bases" in the domain of formal power series, but no algorithm for their construction.

Webmaster