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Gröbner bases. Statistics and software systems. Transl. from the Japanese. (English) Zbl 1282.13003

Tokyo: Springer (ISBN 978-4-431-54573-6/hbk; 978-4-431-54574-3/ebook). xv, 474 p. (2013).

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The articles of this volume will be reviewed individually.
Indexed articles:
Hibi, Takayuki, A quick introduction to Gröbner bases, 1-54 [Zbl 1306.13002]
Hamada, Tatsuyoshi, Warm-up drills and tips for mathematical software, 55-106 [Zbl 1306.13001]
Noro, Masayuki, Computation of Gröbner bases, 107-163 [Zbl 1306.13003]
Aoki, Satoshi; Takemura, Akimichi, Markov bases and designed experiments, 165-221 [Zbl 1306.13019]
Ohsugi, Hidefumi, Convex polytopes and Gröbner bases, 223-278 [Zbl 1306.13017]
Takayama, Nobuki, Gröbner basis for rings of differential operators and applications, 279-344 [Zbl 1306.13018]
Nakayama, Hiromasa; Nishiyama, Kenta, Examples and exercises, 345-466 [Zbl 1306.13016]

MSC:

13-06 Proceedings, conferences, collections, etc. pertaining to commutative algebra
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
13D40 Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
13P25 Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry)
12H05 Differential algebra
00B15 Collections of articles of miscellaneous specific interest
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