Grobner Bases and Applications

Grobner Bases and Applications

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The theory of Grobner 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 Grobner 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 Grobner bases in various fields of mathematics. In the second part are seventeen original research papers on Grobner bases. An appendix contains the English translations of the original German papers of Bruno Buchberger in which Grobner bases were more

Product details

  • Electronic book text
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 1139244221
  • 9781139244220

Review quote

'This book provides a short and easy-to-read account of the theory of Grobner bases and its applications.' L'Enseignment Mathematique 'The book is warmly recommended ...' European Mathematical Societyshow more

Table of contents

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