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Solving polynomial equation systems II: Macaulay's Paradigm and Groebner Techology
No full textThe second volume of this comprehensive treatise focusses on Buchberger theory and its application to the algorithmic view of commutative algebra. In distinction to other works, the presentation here is based on the intrinsic linear algebra structure of Groebner bases, and thus elementary considerations lead easily to the state-of-the-art in issues of implementation. The same language describes the applications of Groebner technology to the central problems of commutative algebra. The book can be also used as a reference on elementary ideal theory and a source for the state-of-the-art in its algorithmization. Aiming to provide a complete survey on Groebner bases and their applications, the author also includes advanced aspects of Buchberger theory, such as the complexity of the algorithm, Galligo's theorem, the optimality of degrevlex, the Gianni-Kalkbrener theorem, the FGLM algorithm, and so on. Thus it will be essential for all workers in commutative algebra, computational algebra and algebraic geometry
A primer on ideal theoretical operation in non-commutative polynomial rings
No full textBuchberger Theory provides, for commutative polynomial rings, computational
tools allowing to perform ideal theoretical operations. Such
techniques are easily adapted to deal similar problems in the non-commutative
setting. I give here an elementary prime
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