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

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25 - An application of Gröbner Bases to the Decomposition of Rational Mappings
pp 448-462
- By Jörn Müller-Quade, Universität Karlsruhe, Rainer Steinwandt, Universität Karlsruhe, Thomas Beth, Universität Karlsruhe
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26 - On some Basic Applications of Gröbner Bases in Non-commutative Polynomial Rings
pp 463-472
- By Patrik Nordbeck, Lund Institute of Technology
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27 - Full Factorial Designs and Distracted Fractions
pp 473-482
- By Lorenzo Robbiano, Università di Genova, Italy, Maria Piera Rogantin, Università di Genova, Italy
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28 - Polynomial interpolation of Minimal Degree and Gröbner Bases
pp 483-494
- By Thomas Sauer, Universität Erlangen
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29 - Inversion of Birational Maps with Gröbner Bases
pp 495-503
- By Josef Schicho, Johannes Kepler University
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30 - Reverse Lexicographic Initial Ideals of Generic Ideals are Finitely Generated
pp 504-518
- By Jan Snellman, Stockholm University
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31 - Parallel Computation and Gröbner Bases: An Application for Converting Bases with the Gröbner Walk
pp 519-532
- By Quôc-Nam Trân, Johannes Kepler University
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Appendix - An Algorithmic Criterion for the Solvability of a System of Algebraic Equations (translated by Michael Abramson and Robert Lumbert)
pp 533-545
- By Bruno Buchberger, Universität Innsbruck
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Index of Tutorials
pp 546-552
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Contents

25 - An application of Gröbner Bases to the Decomposition of Rational Mappings
pp 448-462

26 - On some Basic Applications of Gröbner Bases in Non-commutative Polynomial Rings
pp 463-472

27 - Full Factorial Designs and Distracted Fractions
pp 473-482

28 - Polynomial interpolation of Minimal Degree and Gröbner Bases
pp 483-494

29 - Inversion of Birational Maps with Gröbner Bases
pp 495-503

30 - Reverse Lexicographic Initial Ideals of Generic Ideals are Finitely Generated
pp 504-518

31 - Parallel Computation and Gröbner Bases: An Application for Converting Bases with the Gröbner Walk
pp 519-532

Appendix - An Algorithmic Criterion for the Solvability of a System of Algebraic Equations (translated by Michael Abramson and Robert Lumbert)
pp 533-545

Index of Tutorials
pp 546-552

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