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Gröbner bases and applications. Based on a course for young researchers, January 1998, and the conference “33 years of Gröbner bases”, Linz, Austria, February 2–4, 1998. (English) Zbl 0883.00014
London Mathematical Society Lecture Note Series. 251. Cambridge: Cambridge University Press. viii, 552 p. (1998).

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[The articles of this volume will be reviewed individually.]
The present book contains a short introduction to the theory of Gröbner bases, tutorial papers on the interaction between Gröbner bases and various other mathematical theories, and the original research papers presented at the conference. Finally, an English translation by Michael Abramson and Robert Lumbert of the journal version of Buchberger’s Ph.D. thesis (1965) is included.
Indexed articles:
Buchberger, Bruno, Introduction to Gröbner bases, 3-31 [Zbl 0941.13017]
Chyzak, Frédéric, Gröbner bases, symbolic summation and symbolic integration, 32-60 [Zbl 0898.68040]
Decker, Wolfram; de Jong, Theo, Gröbner bases and invariant theory, 61-89 [Zbl 0908.13019]
Green, Marc; Stillman, Michael, A tutorial on generic initial ideals, 90-108 [Zbl 0919.13017]
Greuel, Gert-Martin; Pfister, Gerhard, Gröbner bases and algebraic geometry, 109-143 [Zbl 0930.13020]
Hoşten, Serkan; Thomas, Rekha, Gröbner bases and integer programming, 144-158 [Zbl 0904.90123]
Möller, H. Michael, Gröbner bases and numerical analysis, 159-178 [Zbl 0928.65058]
Robbiano, Lorenzo, Gröbner bases and statistics, 179-204 [Zbl 0907.62087]
Sakata, Shojiro, Gröbner bases and coding theory, 205-220 [Zbl 0919.94052]
Schwarz, Fritz, Janet bases for symmetry groups, 221-234 [Zbl 1024.34027]
Struppa, Daniele C., Gröbner bases in partial differential equations, 235-245 [Zbl 0990.35007]
Sturmfels, Bernd; Takayama, Nobuki, Gröbner bases and hypergeometric functions, 246-258 [Zbl 0918.33004]
Ufnarovski, V., Introduction to noncommutative Gröbner bases theory, 259-280 [Zbl 0902.16002]
Wang, Dongming, Gröbner bases applied to geometric theorem proving and discovering, 281-301 [Zbl 0898.68076]
Amrhein, Beatrice; Gloor, Oliver, The fractal walk, 305-322 [Zbl 0937.13007]
Borges, Miguel Angel; Borges, Mijail, Gröbner bases property on elimination ideal in the noncommutative case, 323-337 [Zbl 0924.16001]
Capani, Antonio; Niesi, Gianfranco, The CoCoA 3 framework for a family of Buchberger-like algorithms, 338-350 [Zbl 0898.68032]
González-López, María-José; González-Vega, Laureano, Newton identities in the multivariate case: Pham systems, 351-366 [Zbl 0902.12006]
Insa, Mariano; Pauer, Franz, Gröbner bases in rings of differential operators, 367-380 [Zbl 0945.13021]
Little, John B., Canonical curves and the Petri scheme, 381-392 [Zbl 0937.14041]
Lombardi, Henri; Perdry, Hervé, The Buchberger algorithm as a tool for ideal theory of polynomial rings in constructive mathematics, 393-407 [Zbl 0926.13016]
Madlener, Klaus; Reinert, Birgit, Gröbner bases in non-commutative reduction rings, 408-420 [Zbl 0924.16002]
Miller, J. Lyn, Effective algorithms for intrinsically computing SAGBI-Gröbner bases in a polynomial ring over a field, 421-433 [Zbl 0916.13012]
Mora, Ferdinando, On the gags of Gröbner bases. I: Eagon, Northcott, Gröbner, 434-447 [Zbl 0933.13013]
Müller-Quade, Jörn; Steinwandt, Rainer; Beth, Thomas, An application of Gröbner bases to the decomposition of rational mappings, 448-462 [Zbl 0913.14004]
Nordbeck, Patrik, On some basic applications of Gröbner bases in non-commutative polynomial rings, 463-472 [Zbl 0961.16018]
Robbiano, Lorenzo; Rogantin, Maria Piera, Full factorial designs and distracted fractions, 473-482 [Zbl 0897.62085]
Sauer, Thomas, Polynomial interpolation of minimal degree and Gröbner bases, 483-494 [Zbl 0898.41001]
Schicho, Josef, Inversion of birational maps with Gröbner bases, 495-503 [Zbl 0936.14011]
Snellman, Jan, Reverse lexicographic initial ideals of generic ideals are finitely generated, 504-518 [Zbl 0920.13016]
Trân, Quôc-Nam, Parallel computation and Gröbner bases: An application for converting bases with the Gröbner walk, 519-531 [Zbl 0901.68089]
Buchberger, Bruno, An algorithmic criterion for the solvability of a system of algebraic equations, 535-545 [Zbl 0906.13007]

MSC:
00B25 Proceedings of conferences of miscellaneous specific interest
13-06 Proceedings, conferences, collections, etc. pertaining to commutative algebra
68-06 Proceedings, conferences, collections, etc. pertaining to computer science
16-06 Proceedings, conferences, collections, etc. pertaining to associative rings and algebras
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
Software:
CoCoA
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