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Solving Polynomial Equation Systems IV: Volume 4, Buchberger Theory and Beyond
Teo Mora
出版Cambridge University Press, 2016-04-05
主題Mathematics / Algebra / GeneralMathematics / Number TheoryMathematics / GeneralMathematics / Discrete Mathematics
ISBN13162719009781316271902
URLhttp://books.google.com.hk/books?id=04DojwEACAAJ&hl=&source=gbs_api
註釋In this fourth and final volume the author extends Buchberger's Algorithm in three different directions. First, he extends the theory to group rings and other Ore-like extensions, and provides an operative scheme that allows one to set a Buchberger theory over any effective associative ring. Second, he covers similar extensions as tools for discussing parametric polynomial systems, the notion of SAGBI-bases, Gröbner bases over invariant rings and Hironaka's theory. Finally, Mora shows how Hilbert's followers - notably Janet, Gunther and Macaulay - anticipated Buchberger's ideas and discusses the most promising recent alternatives by Gerdt (involutive bases) and Faugère (F4 and F5). This comprehensive treatment in four volumes is a significant contribution to algorithmic commutative algebra that will be essential reading for algebraists and algebraic geometers.