Burchberger Winkler, Burchberger / Winkler

Grobner Bases and Applications

Herausgeber: Buchberger, Bruno

• Broschiertes Buch

Produktbeschreibung

The theory of Grobner bases is a general method by which 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. An appendix contains the English translations of the original German papers of Bruno Buchberger in which Grobner bases were introduced.

Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 564
• Erscheinungstermin: 1. Dezember 1998
• Englisch
• Abmessung: 229mm x 152mm x 33mm
• Gewicht: 905g
• ISBN-13: 9780521632980
• ISBN-10: 0521632986
• Artikelnr.: 21951530

Inhaltsangabe

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.