Gröbner Bases and Applications

Comprehensive account of theory and applications of Gröbner bases, co-edited by the subject's inventor.

Bruno Buchberger (Edited by), Franz Winkler (Edited by)

9780521632980, Cambridge University Press

Paperback, published 26 February 1998

564 pages
22.4 x 15.3 x 3.5 cm, 0.82 kg

'The book is warmly recommended …' European Mathematical Society

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.

Preface
1. Programme committee
Introduction to Gröbner bases B. Buchberger
2. Gröbner bases, symbolic summation and symbolic integration F. Chyzak
3. Gröbner bases and invariant theory W. Decker and T. de Jong
4. Gröbner bases and generic monomial ideals M. Green and M. Stillman
5. Gröbner bases and algebraic geometry G. M. Greuel
6. Gröbner bases and integer programming S. Hosten and R. Thomas
7. Gröbner bases and numerical analysis H. M. Möller
8. Gröbner bases and statistics L. Robbiano
9. Gröbner bases and coding theory S. Sakata
10. Janet bases for symmetry groups F. Schwarz
11. Gröbner bases in partial differential equations D. Struppa
12. Gröbner bases and hypergeometric functions B. Sturmfels and N. Takayama
13. Introduction to noncommutative Gröbner bases theory V. Ufnarovski
14. Gröbner bases applied to geometric theorem proving and discovering D. Wang
15. The fractal walk B. Amrhein and O. Gloor
16. Gröbner bases property on elimination ideal in the noncommutative case M. A. Borges and M. Borges
17. The CoCoA 3 framework for a family of Buchberger-like algorithms A. Capani and G. Niesi
18. Newton identities in the multivariate case: Pham systems M.-J. González-López and L. González-Vega
19. Gröbner bases in rings of differential operators M. Insa and F. Pauer
20. Canonical curves and the Petri scheme J. B. Little
21. The Buchberger algorithm as a tool for ideal theory of polynomial rings in constructive mathematics H. Lombardi and H. Perdry
22. Gröbner bases in non-commutative reduction rings K. Madlener and B. Reinert
23. Effective algorithms for intrinsically computing SAGBI-Gröbner bases in a polynomial ring over a field J. L. Miller
24. De Nugis Groebnerialium 1: Eagon, Northcott, Gröbner F. Mora
25. An application of Gröbner bases to the decomposition of rational mappings J. Müller-Quade, R. Steinwandt and T. Beth
26. On some basic applications of Gröbner bases in noncommutative polynomial rings P. Nordbeck
27. Full factorial designs and distracted fractions L. Robbiano and M. P. Rogantin
28. Polynomial interpolation of minimal degree and Gröbner bases T. Sauer
29. Inversion of birational maps with Gröbner bases J. Schicho
30. Reverse lexicographic initial ideas of generic ideals are finitely generated J. Snellman
31. Parallel computation and Gröbner bases: an application for converting bases with the Gröbner walk Q.-N. Trân
32. Appendix. an algorithmic criterion for the solvability of a system of algebraic equations B. Buchberger (translated by M. Abramson and R. Lumbert)
Index of Tutorials.

Subject Areas: Algebraic geometry [PBMW]