Gröbner Bases and Applications

doi:10.1017/CBO9780511565847

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.

‘This book provides a short and easy-to-read account of the theory of Gröbner bases and its applications.’

Source: L’Enseignment Mathématique

‘The book is warmly recommended …’

Source: European Mathematical Society

- Aa Reduce text
- Aa Enlarge text

View selected items
Save to my bookmarks
Export citations
Download PDF (zip)
Save to Kindle
Save to Dropbox
Save to Google Drive
Save content to
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to .

To save content items to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Please be advised that item(s) you selected are not available.
You are about to save
Your Kindle email address

Please provide your Kindle email.

@free.kindle.com @kindle.com (service fees apply)

By using this service, you agree that you will only keep content for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services

Page 1 of 2

First
« Prev
1
2
Next »
Last

Contents

Frontmatter
pp i-iv
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Contents
pp v-vi
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Preface
pp vii-vii
- By Bruno Buchberger, Johannes Kepler Universität Linz, Franz Winkler, Johannes Kepler Universität Linz
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Programme Committee
pp viii-viii
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Tutorials
pp 1-2
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Introduction to Gröbner Bases
pp 3-31
- By Bruno Buchberger, Research Institute for Symbolic Computation
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Gröbner Bases, Symbolic Summation and Symbolic Integration
pp 32-60
- By Frédéric Chyzak, INRIA-Rocquencourt and École polytechnique (FRANCE)
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Gröbner Bases and Invariant Theory
pp 61-89
- By Wolfram Decker, Universität des Saarlandes, Saarbrücken, Theo de Jong, Universität des Saarlandes, Saarbrücken
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

A Tutorial on Generic Initial Ideals
pp 90-108
- By Mark Green, UCLA, USA, Michael Stillman, Cornell University, USA
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Gröbner Bases and Algebraic Geometry
pp 109-143
- By Gert-Martin Greuel, Universität Kaiserslautern, Fachbereich Mathematik, Gerhard Pfister, Universität Kaiserslautern, Fachbereich Mathematik
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Gröbner Bases and Integer Programming
pp 144-158
- By Serkan Hoşten, George Mason University, Fairfax, USA, Rekha Thomas, Texas A & M University, Texas, USA
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Gröbner Bases and Numerical Analysis
pp 159-178
- By H. Michael Möller, Universität Dortmund, Germany
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Gröbner Bases and Statistics
pp 179-204
- By Lorenzo Robbiano, Università di Genova, Italy
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Gröbner Bases and Coding Theory
pp 205-220
- By Shojiro Sakata, The University of Electro-Communications
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Janet Bases for Symmetry Groups
pp 221-234
- By Fritz Schwarz
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Gröbner Bases in Partial Differential Equations
pp 235-245
- By Daniele C. Struppa, George Mason University
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Gröbner Bases and Hypergeometric Functions
pp 246-258
- By Bernd Sturmfels, Kyoto University, Japan and University of California, Berkeley, Nobuki Takayama, Kobe University, Japan
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Introduction to Noncommutative Gröbner Bases Theory
pp 259-280
- By V. Ufnarovski, Matematiska institutonen
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Gröbner Bases Applied to Geometric Theorem Proving and Discovering
pp 281-302
- By Dongming Wang, Leibniz–Imag
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Research Papers
pp 303-304
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

The Fractal Walk
pp 305-322
- By Beatrice Amrhein, Software-Schule Schweiz, Bern, Switzerland, Oliver Gloor, University of Tën, Germany
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Gröbner Bases Property on Elimination Ideal in the Noncommutative Case
pp 323-337
- By Miguel Angel Borges, University of Oriente, Mijail Borges, University of Oriente
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

17 - The CoCoA 3 Framework for a Family of Buchberger-like Algorithms
pp 338-350
- By Antonio Capani, Univ. di Genova, Italy, Gianfranco Niesi, Univ. di Genova, Italy
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

18 - Newton Identities in the Multivariate Case: Pham Systems
pp 351-366
- By María-José González-López, Universidad de Cantabria, Laureano González-Vega, Universidad de Cantabria
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

19 - Gröbner Bases in Rings of Differential Operators
pp 367-380
- By Mariano Insa, Universität Innsbruck, Franz Pauer, Universität Innsbruck
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

20 - Canonical Curves and the Petri Scheme
pp 381-392
- By John B. Little, College of Holy Cross, Worcester, USA
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

21 - The Buchberger Algorithm as a Tool for Ideal Theory of Polynomial Rings in Constructive Mathematics
pp 393-407
- By Henri Lombardi, Université de Franch-Comté, Hervé Perdry, Université de Franch-Comté
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

22 - Gröbner Bases in Non-Commutative Reduction Rings
pp 408-420
- By Klaus Madlener, Universität Kaiserslautern, Birgit Reinert, Universität Kaiserslautern
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

23 - Effective Algorithms for Intrinsically Computing SAGBI-Gröbner Bases in a Polynomial Ring over a Field
pp 421-433
- By J. Lyn Miller, Western Kentucky University
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

24 - De Nugis Groebnerialium 1: Eagon, Northcott, Gröbner
pp 434-447
- By Ferdinando Mora, Univ. Genova, Genova, Italy
- - Get access
    
    Check if you have access via personal or institutional login
    
    Log in Register
- Export citation

Page 1 of 2

First
« Prev
1
2
Next »
Last

Metrics

Altmetric attention score

Total number of HTML views: 0

Total number of PDF views: 0 *

Loading metrics...

Total views: 0 *

Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

Why this information is here

This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

Accessibility Information

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.

Gröbner Bases and Applications

Book description

Reviews

Refine List

Actions for selected content:

Save Search

Contents

Metrics

Altmetric attention score

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information