LEADER 04747nam 22006975 450 001 996466367803316 005 20200704065306.0 010 $a3-540-30137-2 024 7 $a10.1007/b104035 035 $a(CKB)1000000000212648 035 $a(SSID)ssj0000204702 035 $a(PQKBManifestationID)11172535 035 $a(PQKBTitleCode)TC0000204702 035 $a(PQKBWorkID)10188717 035 $a(PQKB)10671856 035 $a(DE-He213)978-3-540-30137-0 035 $a(MiAaPQ)EBC3068434 035 $a(PPN)13412359X 035 $a(EXLCZ)991000000000212648 100 $a20101024d2005 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aModular Algorithms in Symbolic Summation and Symbolic Integration$b[electronic resource] /$fby Jürgen Gerhard 205 $a1st ed. 2005. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2005. 215 $a1 online resource (XVI, 228 p.) 225 1 $aLecture Notes in Computer Science,$x0302-9743 ;$v3218 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-24061-6 320 $aIncludes bibliographical references (p. [207]-216) and index. 327 $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-Petkov?ek Form -- 9. Polynomial Solutions of Linear First Order Equations -- 10. Modular Gosper and Almkvist & Zeilberger Algorithms. 330 $aThis work brings together two streams in computer algebra: symbolic integration and summation on the one hand, and fast algorithmics on the other hand. In many algorithmically oriented areas of computer science, theanalysisof- gorithms?placedintothe limelightbyDonKnuth?stalkat the 1970ICM ?provides a crystal-clear criterion for success. The researcher who designs an algorithmthat is faster (asymptotically, in the worst case) than any previous method receives instant grati?cation: her result will be recognized as valuable. Alas, the downside is that such results come along quite infrequently, despite our best efforts. An alternative evaluation method is to run a new algorithm on examples; this has its obvious problems, but is sometimes the best we can do. George Collins, one of the fathers of computer algebra and a great experimenter,wrote in 1969: ?I think this demonstrates again that a simple analysis is often more revealing than a ream of empirical data (although both are important). ? Within computer algebra, some areas have traditionally followed the former methodology, notably some parts of polynomial algebra and linear algebra. Other areas, such as polynomial system solving, have not yet been amenable to this - proach. The usual ?input size? parameters of computer science seem inadequate, and although some natural ?geometric? parameters have been identi?ed (solution dimension, regularity), not all (potential) major progress can be expressed in this framework. Symbolic integration and summation have been in a similar state. 410 0$aLecture Notes in Computer Science,$x0302-9743 ;$v3218 606 $aAlgorithms 606 $aNumerical analysis 606 $aComputer science?Mathematics 606 $aComputer mathematics 606 $aAlgorithm Analysis and Problem Complexity$3https://scigraph.springernature.com/ontologies/product-market-codes/I16021 606 $aNumeric Computing$3https://scigraph.springernature.com/ontologies/product-market-codes/I1701X 606 $aSymbolic and Algebraic Manipulation$3https://scigraph.springernature.com/ontologies/product-market-codes/I17052 606 $aAlgorithms$3https://scigraph.springernature.com/ontologies/product-market-codes/M14018 606 $aComputational Science and Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/M14026 615 0$aAlgorithms. 615 0$aNumerical analysis. 615 0$aComputer science?Mathematics. 615 0$aComputer mathematics. 615 14$aAlgorithm Analysis and Problem Complexity. 615 24$aNumeric Computing. 615 24$aSymbolic and Algebraic Manipulation. 615 24$aAlgorithms. 615 24$aComputational Science and Engineering. 676 $a005.1 686 $a54.10$2bcl 700 $aGerhard$b Jürgen$4aut$4http://id.loc.gov/vocabulary/relators/aut$0441584 906 $aBOOK 912 $a996466367803316 996 $aModular Algorithms in Symbolic Summation and Symbolic Integration$9772838 997 $aUNISA