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Titlebook: Algorithmic Algebra and Number Theory; Selected Papers From B. Heinrich Matzat,Gert-Martin Greuel,Gerhard Hiss Conference proceedings 1999

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期刊全称Algorithmic Algebra and Number Theory
期刊简称Selected Papers From
影响因子2023B. Heinrich Matzat,Gert-Martin Greuel,Gerhard Hiss
视频videohttp://file.papertrans.cn/153/152881/152881.mp4
发行地址The book contains contributions by many top class researchers in algorithmic number theory.
图书封面Titlebook: Algorithmic Algebra and Number Theory; Selected Papers From B. Heinrich Matzat,Gert-Martin Greuel,Gerhard Hiss Conference proceedings 1999
影响因子This book contains 22 lectures presented at the final conference of the Ger­ man research program (Schwerpunktprogramm) Algorithmic Number The­ ory and Algebra 1991-1997, sponsored by the Deutsche Forschungsgemein­ schaft. The purpose of this research program and of the meeting was to bring together developers of computer algebra software and researchers using com­ putational methods to gain insight into experimental problems and theoret­ ical questions in algebra and number theory. The book gives an overview on algorithmic methods and on results ob­ tained during this period. This includes survey articles on the main research projects within the program: • algorithmic number theory emphasizing class field theory, constructive Galois theory, computational aspects of modular forms and of Drinfeld modules • computational algebraic geometry including real quantifier elimination and real algebraic geometry, and invariant theory of finite groups • computational aspects of presentations and representations of groups, especially finite groups of Lie type and their Heeke algebras, and of the isomorphism problem in group theory. Some of the articles illustrate the current state of computer
Pindex Conference proceedings 1999
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Techniques for the Computation of Galois Groupsis of interest not only from the point of view of number theory (for example see the article [.] in this volume), but leads to many questions in other areas of mathematics. An example is its application in computer algebra when simplifying radical expressions [.].
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On the Real Nullstellensatzerms, and a combination of Grabner basis computations with multivariate real root counting. We examine the scope of these implementations for applications in various fields of science, engineering, and economics.
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https://doi.org/10.1007/978-3-8350-5468-4ents realize the following main ideas: 1. Minimization of resolutions are integrated as much as possible into the standard basis algorithm. 2. Hilbert functions are used to avoid reductions of useless pairs. 3. Special orderings and strategies are used to increase the computational efficiency.
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https://doi.org/10.1007/978-3-8350-5468-4present some basic results obtained in recent years, explain the ideas behind them, and give lots of examples; proofs are usually omitted but we provide explicit references to an extensive bibliography.
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