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Gröbner Bases and Applications

Gröbner Bases and Applications

$139.99

Part of London Mathematical Society Lecture Note Series

B. Buchberger, F. Chyzak, W. Decker, T. de Jong, M. Green, M. Stillman, G. M. Greuel, S. Hosten, R. Thomas, H. M. Möller, L. Robbiano, S. Sakata, F. Schwarz, D. Struppa, B. Sturmfels, N. Takayama, V. Ufnarovski, D. Wang, B. Amrhein, O. Gloor, M. A. Borges, M. Borges, A. Capani, G. Niesi, M.-J. González-López, L. González-Vega, M. Insa, F. Pauer, J. B. Little, H. Lombardi, H. Perdry, K. Madlener, B. Reinert, J. L. Miller, F. Mora, J. Müller-Quade, R. Steinwandt, T. Beth, P. Nordbeck, M. P. Rogantin, T. Sauer, J. Schicho, J. Snellman, Q.-N. Trân
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  • Date Published: March 1998
  • availability: Available
  • format: Paperback
  • isbn: 9780521632980

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  • 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 there 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.

    • First time a book has a comprehensive tutorial treatment of all known application areas of Gröbner bases
    • Edited by the inventor of the method
    • Contains tutorial, research and historical material
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    Product details

    • Date Published: March 1998
    • format: Paperback
    • isbn: 9780521632980
    • length: 564 pages
    • dimensions: 229 x 152 x 32 mm
    • weight: 0.82kg
    • availability: Available
  • Table of Contents

    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.

  • Editors

    Bruno Buchberger, Johannes Kepler Universität Linz

    Franz Winkler, Johannes Kepler Universität Linz

    Contributors

    B. Buchberger, F. Chyzak, W. Decker, T. de Jong, M. Green, M. Stillman, G. M. Greuel, S. Hosten, R. Thomas, H. M. Möller, L. Robbiano, S. Sakata, F. Schwarz, D. Struppa, B. Sturmfels, N. Takayama, V. Ufnarovski, D. Wang, B. Amrhein, O. Gloor, M. A. Borges, M. Borges, A. Capani, G. Niesi, M.-J. González-López, L. González-Vega, M. Insa, F. Pauer, J. B. Little, H. Lombardi, H. Perdry, K. Madlener, B. Reinert, J. L. Miller, F. Mora, J. Müller-Quade, R. Steinwandt, T. Beth, P. Nordbeck, M. P. Rogantin, T. Sauer, J. Schicho, J. Snellman, Q.-N. Trân

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