Grbner Bases and Applications

'This book provides a short and easy-to-read account of the theory of Grbner bases and its applications.' L'Enseignment Mathmatique

'The book is warmly recommended ...' European Mathematical Society

Preface; 1. Programme committee; Introduction to Grbner bases B. Buchberger; 2. Grbner bases, symbolic summation and symbolic integration F. Chyzak; 3. Grbner bases and invariant theory W. Decker and T. de Jong; 4. Grbner bases and generic monomial ideals M. Green and M. Stillman; 5. Grbner bases and algebraic geometry G. M. Greuel; 6. Grbner bases and integer programming S. Hosten and R. Thomas; 7. Grbner bases and numerical analysis H. M. Mller; 8. Grbner bases and statistics L. Robbiano; 9. Grbner bases and coding theory S. Sakata; 10. Janet bases for symmetry groups F. Schwarz; 11. Grbner bases in partial differential equations D. Struppa; 12. Grbner bases and hypergeometric functions B. Sturmfels and N. Takayama; 13. Introduction to noncommutative Grbner bases theory V. Ufnarovski; 14. Grbner bases applied to geometric theorem proving and discovering D. Wang; 15. The fractal walk B. Amrhein and O. Gloor; 16. Grbner 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. Gonzlez-Lpez and L. Gonzlez-Vega; 19. Grbner 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. Grbner bases in non-commutative reduction rings K. Madlener and B. Reinert; 23. Effective algorithms for intrinsically computing SAGBI-Grbner bases in a polynomial ring over a field J. L. Miller; 24. De Nugis Groebnerialium 1: Eagon, Northcott, Grbner F. Mora; 25. An application of Grbner bases to the decomposition of rational mappings J. Mller-Quade, R. Steinwandt and T. Beth; 26. On some basic applications of Grbner 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 Grbner bases T. Sauer; 29. Inversion of birational maps with Grbner bases J. Schicho; 30. Reverse lexicographic initial ideas of generic ideals are finitely generated J. Snellman; 31. Parallel computation and Grbner bases: an application for converting bases with the Grbner walk Q.-N. Trn; 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.