LEADER 05542nam 2200685Ia 450 001 9910784833703321 005 20230721031011.0 010 $a1-281-93008-3 010 $a9786611930080 010 $a981-277-885-3 035 $a(CKB)1000000000406644 035 $a(EBL)1193445 035 $a(SSID)ssj0000292355 035 $a(PQKBManifestationID)11212706 035 $a(PQKBTitleCode)TC0000292355 035 $a(PQKBWorkID)10269178 035 $a(PQKB)10579578 035 $a(WSP)00006289 035 $a(Au-PeEL)EBL1193445 035 $a(CaPaEBR)ebr10698768 035 $a(CaONFJC)MIL193008 035 $a(OCoLC)714877399 035 $a(MiAaPQ)EBC1193445 035 $a(EXLCZ)991000000000406644 100 $a20080502d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aComputer algebra 2006$b[electronic resource] $elatest advances in symbolic algorithms : proceedings of the Waterloo Workshop in Computer Algebra 2006, Ontario, Canada, 10-12 April 2006 /$feditors, Ilias Kotsireas, Eugene Zima 210 $aSingapore ;$aHackensack, NJ $cWorld Scientific$dc2007 215 $a1 online resource (220 p.) 300 $a"The Waterloo Workshop on Computer Algebra (WWCA-2006) was held on April 10-12, 2006 at Wilfrid Laurier University (Waterloo, Ontario, Canada)."--P. v. 300 $aWorkshop dedicated to the 60th birthday of Sergei Abramov. 311 $a981-270-200-8 320 $aIncludes bibliographical references and index. 327 $aCONTENTS; Preface; Hypergeometric Summation Revisited S. A. Abramov, M. Petkovsek; 1. Introduction; 2. Validity conditions of the discrete Newton-Leibniz formula; 2.1. A criterion; 2.2. Summation of proper hypergeometric sequences; 2.3. When the interval I contains no leading integer singularity of L; 3. The spaces VI(L) and WI(R(k), L); 3.1. The structure of WI(R(k), L); 3.2. When a rational solution of Gosper's equation is not unique; 3.3. If Gosper's equation has a rational solution R(k) then WI(R, L) = 0; References 327 $aFive Applications of Wilf-Zeilberger Theory to Enumeration and Probability M. Apagodu, D. ZeilbergerExplicit Formulas vs. Algorithms; The Holonomic Ansatz; Why this Paper?; The Maple packages AppsWZ and AppsWZmulti; Asymptotics; First Application: Rolling a Die; Second Application: How many ways to have r people chip in to pay a bill of n cents; Third Application: Hidden Markov Models; Fourth Application: Lattice Paths Counting; References; Factoring Systems of Linear Functional Equations Using Eigenrings M. A. Barkatou; 1. Introduction and notations; 2. Preliminaries 327 $a3. Eigenrings and reduction of pseudo-linear equationsMaximal Decompsition; 4. Spaces of homomorphisms and factorization; Appendix A. K[X; ?, ?].modules and matrix pseudo-linear equations; Appendix A.1. Pseudo-linear operators; Appendix A.2. Similarity, reducibility, decomposability and complete reducibility; Appendix A.3. The ring of endomorphisms of a pseudo-linear operator; References; Modular Computation for Matrices of Ore Polynomials H. Cheng, G. Labahn; 1. Introduction; 2. Preliminaries; 2.1. Notation; 2.2. Definitions; 2.3. The FFreduce Elimination Algorithm 327 $a3. Linear Algebra Formulation4. Reduction to Zp[t][Z]; 4.1. Lucky Homomorphisms; 4.2. Termination; 5. Reduction to Zp; 5.1. Applying Evaluation Homomorphisms and Computation in Zp; 5.2. Lucky Homomorphisms and Termination; 6. Complexity Analysis; 7. Implementation Considerations and Experimental Results; 8. Concluding Remarks; References; Beta-Expansions of Pisot and Salem Numbers K. G. Hare; 1. Introduction and History; 2. Univoque Pisot Numbers; 3. Algorithms and Implementation Issues; 4. Conclusions and Open Questions; References 327 $aLogarithmic Functional and the Weil Reciprocity Law A. Khovanskii1. Introduction; 1.1. The Weil reciprocity law; 1.2. Topological explanation of the reciprocity law over the field C; 1.3. Multi-dimensional reciprocity laws; 1.4. The logarithmic functional; 1.5. Organization of material; 2. Formulation of the Weil reciprocity law; 3. LB-functional of the pair of complex valued functions of the segment on real variable; 4. LB-functional of the pair of complex valued functions and one-dimensional cycle on real manifold; 5. Topological proof of the Weil reciprocity law 327 $a6. Generalized LB-functional 330 $aWritten by world-renowned experts, the book is a collection of tutorial presentations and research papers catering to the latest advances in symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. The papers were presented at a workshop celebrating the 60th birthday of Sergei Abramov (Russia), whose highly influential contributions to symbolic methods are adopted in many leading computer algebra systems. 606 $aAlgebra$xData processing$vCongresses 606 $aComputer algorithms$vCongresses 615 0$aAlgebra$xData processing 615 0$aComputer algorithms 676 $a005.1 701 $aKotsireas$b Ilias$0950774 701 $aZima$b E. V$g(Evgenii Viktorovich)$01512950 701 $aAbramov$b S. A$01512951 712 12$aWaterloo Workshop in Computer Algebra$f(2006 :$eWilfrid Laurier University) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910784833703321 996 $aComputer algebra 2006$93747166 997 $aUNINA