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Titlebook: Computer Algebra; Symbolic and Algebra Bruno Buchberger,George Edwin Collins,Rüdiger Loos Book 19821st edition Springer-Verlag Wien 1982 al

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发表于 2025-3-21 19:21:07 | 显示全部楼层 |阅读模式
书目名称Computer Algebra
副标题Symbolic and Algebra
编辑Bruno Buchberger,George Edwin Collins,Rüdiger Loos
视频video
丛书名称Computing Supplementa
图书封面Titlebook: Computer Algebra; Symbolic and Algebra Bruno Buchberger,George Edwin Collins,Rüdiger Loos Book 19821st edition Springer-Verlag Wien 1982 al
描述The journal Computing has established a series of supplement volumes the fourth of which appears this year. Its purpose is to provide a coherent presentation of a new topic in a single volume. The previous subjects were Computer Arithmetic 1977, Fundamentals of Numerical Computation 1980, and Parallel Processes and Related Automata 1981; the topic of this 1982 Supplementum to Computing is Computer Algebra. This subject, which emerged in the early nineteen sixties, has also been referred to as "symbolic and algebraic computation" or "formula manipulation". Algebraic algorithms have been receiving increasing interest as a result of the recognition of the central role of algorithms in computer science. They can be easily specified in a formal and rigorous way and provide solutions to problems known and studied for a long time. Whereas traditional algebra is concerned with constructive methods, computer algebra is furthermore interested in efficiency, in implementation, and in hardware and software aspects of the algorithms. It develops that in deciding effectiveness and determining efficiency of algebraic methods many other tools - recursion theory, logic, analysis and combinatorics,
出版日期Book 19821st edition
关键词algebra; computer algebra; computeralgebra
版次1
doihttps://doi.org/10.1007/978-3-7091-3406-1
isbn_ebook978-3-7091-3406-1Series ISSN 0344-8029
issn_series 0344-8029
copyrightSpringer-Verlag Wien 1982
The information of publication is updating

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发表于 2025-3-21 20:17:46 | 显示全部楼层
Pamela A. Fenning,Leah M. Nellisthe minimum root separation, Sturm’s algorithm, an algorithm based on Rolle’s theorem due to Collins and Loos and the modified Uspensky algorithm due to Collins and Aritas. For the last algorithm a recursive version with correctness proof is given which appears in print for the first time.
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https://doi.org/10.1007/978-3-031-21381-6ree decomposition algorithms and Hensel lifting techniques are analyzed. An attempt is made to establish a complete historic trace for today’s methods. The exponential worst case complexity nature of these algorithms receives attention.
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Supporting Human Activities by Obstruction,wo polynomials. We study the primitive, the reduced and the improved subresultant p.r.s. algorithm of Brown and Collins as basis for computing polynomial greatest common divisors, resultants or Sturm sequences. Habicht’s subresultant theorem allows new and simple proofs of many results and algorithms found in different ways in computer algebra.
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Generalized Polynomial Remainder Sequences,wo polynomials. We study the primitive, the reduced and the improved subresultant p.r.s. algorithm of Brown and Collins as basis for computing polynomial greatest common divisors, resultants or Sturm sequences. Habicht’s subresultant theorem allows new and simple proofs of many results and algorithms found in different ways in computer algebra.
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An ethical approach: socio-technical design,on. After introducing Zassenhaus’ quadratic lifting construction, again, the case of . and ., . [.] and . [.1,…., .r] is considered. For both techniques, chinese remaindering as well as the lifting algorithms, a complete computational example is presented and the most frequent applications are discussed.
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