Computer 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 Zima

• Record Nr.: UNINA9910784833703321
• Pubbl/distr/stampa: Singapore ; ; Hackensack, NJ, : World Scientific, c2007
• ISBN: 1-281-93008-3; 9786611930080; 981-277-885-3
• Descrizione fisica: 1 online resource (220 p.)
• Altri autori (Persone): KotsireasIlias; ZimaE. V (Evgenii Viktorovich); AbramovS. A
• Disciplina: 005.1
• Soggetti: Algebra - Data processing; Computer algorithms
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "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.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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; References; Five 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; 3. 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 Algorithm; 3. 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; Logarithmic 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; 6. Generalized LB-functional
• Sommario/riassunto: Written 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.