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020 _a9783540301370
_9978-3-540-30137-0
024 7 _a10.1007/b104035
_2doi
050 4 _aQA76.9.A43
072 7 _aUMB
_2bicssc
072 7 _aCOM051300
_2bisacsh
072 7 _aUMB
_2thema
082 0 4 _a518.1
_223
100 1 _aGerhard, Jürgen.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aModular Algorithms in Symbolic Summation and Symbolic Integration
_h[electronic resource] /
_cby Jürgen Gerhard.
250 _a1st ed. 2005.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2005.
300 _aXVI, 228 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Computer Science,
_x1611-3349 ;
_v3218
505 0 _a1. 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.
520 _aThis 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.
650 0 _aAlgorithms.
650 0 _aNumerical analysis.
650 0 _aComputer science
_xMathematics.
650 0 _aMathematics
_xData processing.
650 1 4 _aAlgorithms.
650 2 4 _aNumerical Analysis.
650 2 4 _aSymbolic and Algebraic Manipulation.
650 2 4 _aComputational Science and Engineering.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783540240617
776 0 8 _iPrinted edition:
_z9783540805977
830 0 _aLecture Notes in Computer Science,
_x1611-3349 ;
_v3218
856 4 0 _uhttps://doi.org/10.1007/b104035
912 _aZDB-2-SCS
912 _aZDB-2-SXCS
912 _aZDB-2-LNC
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999 _c175043
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