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Modular Algorithms in Symbolic Summation and Symbolic Integration / by Jürgen Gerhard
(Lecture Notes in Computer Science. ISSN:16113349 ; 3218)

データ種別	電子ブック
版	1st ed. 2005.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2005
大きさ	XVI, 228 p : online resource
著者標目	*Gerhard, Jürgen author SpringerLink (Online service)

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URL	巻　次	配架場所	請求記号	登録番号	コメント	刷　年	状　態	利用注記	ISBN	予約	請求メモ
URL		射水-電子	007	EB0001934	Computer Scinece R0 2005-6,2022-3				9783540301370

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一般注記	1. Introduction -- 2. Overview -- 3. Technical Prerequisites -- 4. Change of Basis -- 5. Modular Squarefree and Greatest Factorial Factorization -- 6. Modular Hermite Integration -- 7. Computing All Integral Roots of the Resultant -- 8. Modular Algorithms for the Gosper-Petkovšek Form -- 9. Polynomial Solutions of Linear First Order Equations -- 10. Modular Gosper and Almkvist & Zeilberger Algorithms This work brings together two streams in computer algebra: symbolic integration and summation on the one hand, and fast algorithmics on the other hand. In many algorithmically oriented areas of computer science, theanalysisof- gorithms–placedintothe limelightbyDonKnuth’stalkat the 1970ICM –provides a crystal-clear criterion for success. The researcher who designs an algorithmthat is faster (asymptotically, in the worst case) than any previous method receives instant grati?cation: her result will be recognized as valuable. Alas, the downside is that such results come along quite infrequently, despite our best efforts. An alternative evaluation method is to run a new algorithm on examples; this has its obvious problems, but is sometimes the best we can do. George Collins, one of the fathers of computer algebra and a great experimenter,wrote in 1969: “I think this demonstrates again that a simple analysis is often more revealing than a ream of empirical data (although both are important). ” Within computer algebra, some areas have traditionally followed the former methodology, notably some parts of polynomial algebra and linear algebra. Other areas, such as polynomial system solving, have not yet been amenable to this - proach. The usual “input size” parameters of computer science seem inadequate, and although some natural “geometric” parameters have been identi?ed (solution dimension, regularity), not all (potential) major progress can be expressed in this framework. Symbolic integration and summation have been in a similar state HTTP:URL=https://doi.org/10.1007/b104035
件　名	LCSH:Algorithms LCSH:Numerical analysis LCSH:Computer science -- Mathematics 全ての件名で検索 LCSH:Mathematics -- Data processing 全ての件名で検索 FREE:Algorithms FREE:Numerical Analysis FREE:Symbolic and Algebraic Manipulation FREE:Computational Science and Engineering
分　類	LCC:QA76.9.A43 DC23:518.1
書誌ID	EB00001322
ISBN	9783540301370