Details:
Title  Introduction to Gröbner Bases  Author(s)  Bruno Buchberger  Text  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 easytoread 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.  Type  Book, Chapter in Book, Conference Proceeding  Abstract  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 Buchbergerlike algorithms A. Capani and G. Niesi;
18. Newton identities in the multivariate case: Pham systems, M.J. GonzálezLópez and L. GonzálezVega;
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 noncommutative reduction rings, K. Madlener and B. Reinert;
23. Effective algorithms for intrinsically computing SAGBIGröbner 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. MüllerQuade, 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.  Length  29  ISBN  0521632986 
File 
 Language  English  Series  London Mathematical Society Lectures Notes Series 251  Pages  3  31  Publisher  Cambridge University Press  Year  1998  Month  April  Editor  B. Buchberger, F. Winkler  Translation 
No  Refereed 
Yes  Book  Gröbner Bases and Applications  Organization 
Johannes Kepler University Linz  Institution 
RISC (Research Institute for Symbolic Computation) 
