05542nam 2200685Ia 450 991078483370332120230721031011.01-281-93008-39786611930080981-277-885-3(CKB)1000000000406644(EBL)1193445(SSID)ssj0000292355(PQKBManifestationID)11212706(PQKBTitleCode)TC0000292355(PQKBWorkID)10269178(PQKB)10579578(WSP)00006289(Au-PeEL)EBL1193445(CaPaEBR)ebr10698768(CaONFJC)MIL193008(OCoLC)714877399(MiAaPQ)EBC1193445(EXLCZ)99100000000040664420080502d2007 uy 0engur|n|---|||||txtccrComputer algebra 2006[electronic resource] latest advances in symbolic algorithms : proceedings of the Waterloo Workshop in Computer Algebra 2006, Ontario, Canada, 10-12 April 2006 /editors, Ilias Kotsireas, Eugene ZimaSingapore ;Hackensack, NJ World Scientificc20071 online resource (220 p.)"The Waterloo Workshop on Computer Algebra (WWCA-2006) was held on April 10-12, 2006 at Wilfrid Laurier University (Waterloo, Ontario, Canada)."--P. v.Workshop dedicated to the 60th birthday of Sergei Abramov.981-270-200-8 Includes bibliographical references and index.CONTENTS; 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; ReferencesFive 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. Preliminaries3. Eigenrings and reduction of pseudo-linear equationsMaximal Decompsition; 4. Spaces of homomorphisms and factorization; Appendix A. K[X; φ, δ].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 Algorithm3. 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; ReferencesLogarithmic 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 law6. Generalized LB-functionalWritten 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.AlgebraData processingCongressesComputer algorithmsCongressesAlgebraData processingComputer algorithms005.1Kotsireas Ilias950774Zima E. V(Evgenii Viktorovich)1512950Abramov S. A1512951Waterloo Workshop in Computer Algebra(2006 :Wilfrid Laurier University)MiAaPQMiAaPQMiAaPQBOOK9910784833703321Computer algebra 20063747166UNINA