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Modern algorithmic techniques for summation, most of which were introduced in the 1990s, are developed here and carefully implemented in the computer algebra system Maple™. The algorithms of Fasenmyer, Gosper, Zeilberger, Petkovšek and van Hoeij for hypergeometric summation and recurrence equations, efficient multivariate summation as well as q-analogues of the above algorithms are covered. Similar algorithms concerning differential equations are considered. An equivalent theory of hyperexponential integration due to Almkvist and Zeilberger completes the book. The combination of these results gives orthogonal polynomials and (hypergeometric and q-hypergeometric) special functions a solid algorithmic foundation. Hence, many examples from this very active field are given. The materials covered are suitable for an introductory course on algorithmic summation and will appeal to students and researchers alike.

Mathematics. --- Differential equations. --- Special functions. --- Algorithms. --- Computer software. --- Combinatorics. --- Mathematical Software. --- Special Functions. --- Ordinary Differential Equations. --- Combinatorics --- Algebra --- Mathematical analysis --- Software, Computer --- Computer systems --- Algorism --- Arithmetic --- Special functions --- 517.91 Differential equations --- Differential equations --- Math --- Science --- Foundations --- Functions, special. --- Differential Equations. --- Hypergeometric functions.

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This book presents contributions of international and local experts from the African Institute for Mathematical Sciences (AIMS-Cameroon) and also from other local universities in the domain of orthogonal polynomials and applications. The topics addressed range from univariate to multivariate orthogonal polynomials, from multiple orthogonal polynomials and random matrices to orthogonal polynomials and Painlevé equations. The contributions are based on lectures given at the AIMS-Volkswagen Stiftung Workshop on Introduction of Orthogonal Polynomials and Applications held on October 5–12, 2018 in Douala, Cameroon. This workshop, funded within the framework of the Volkswagen Foundation Initiative "Symposia and Summer Schools", was aimed globally at promoting capacity building in terms of research and training in orthogonal polynomials and applications, discussions and development of new ideas as well as development and enhancement of networking including south-south cooperation.

Special functions. --- Special Functions. --- Orthogonal polynomials --- Special functions --- Mathematical analysis --- Fourier analysis --- Functions, Orthogonal --- Polynomials

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This book constitutes the proceedings of the 14th International Workshop on Computer Algebra in Scientific Computing, CASC 2013, held in Berlin, Germany, in September 2013. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as polynomial algebra; the solution of tropical linear systems and tropical polynomial systems; the theory of matrices; the use of computer algebra for the investigation of various mathematical and applied topics related to ordinary differential equations (ODEs); applications of symbolic computations for solving partial differential equations (PDEs) in mathematical physics; problems arising at the application of computer algebra methods for finding infinitesimal symmetries; applications of symbolic and symbolic-numeric algorithms in mechanics and physics; automatic differentiation; the application of the CAS Mathematica for the simulation of quantum error correction in quantum computing; the application of the CAS GAP for the enumeration of Schur rings over the group A5; constructive computation of zero separation bounds for arithmetic expressions; the parallel implementation of fast Fourier transforms with the aid of the Spiral library generation system; the use of object-oriented languages such as Java or Scala for implementation of categories as type classes; a survey of industrial applications of approximate computer algebra.

Engineering & Applied Sciences --- Computer Science --- Computer science. --- Arithmetic and logic units, Computer. --- Algorithms. --- Numerical analysis. --- Computer science --- Computer graphics. --- Computer Science. --- Algorithm Analysis and Problem Complexity. --- Discrete Mathematics in Computer Science. --- Symbolic and Algebraic Manipulation. --- Computer Graphics. --- Numeric Computing. --- Arithmetic and Logic Structures. --- Mathematics. --- Science --- Mathematics --- Data processing --- Computer software. --- Computational complexity. --- Algebra --- Electronic data processing. --- Data processing. --- Informatics --- ADP (Data processing) --- Automatic data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Complexity, Computational --- Machine theory --- Software, Computer --- Computer systems --- Automation --- Digital techniques --- Computer science—Mathematics. --- Arithmetic and logic units, Computer --- Computer arithmetic --- Electronic digital computers --- Mathematical analysis --- Algorism --- Arithmetic --- Circuits --- Foundations --- Discrete mathematics. --- Computer arithmetic and logic units. --- Numerical Analysis. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis

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This book constitutes the proceedings of the 19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017, held in Beijing, China, in September 2017. The 28 full papers presented in this volume were carefully reviewed and selected from 33 submissions. They deal with cutting-edge research in all major disciplines of Computer Algebra.

Computer science. --- Special purpose computers. --- Software engineering. --- Algorithms. --- Computer logic. --- Computer science --- Management information systems. --- Computer Science. --- Algorithm Analysis and Problem Complexity. --- Mathematics of Computing. --- Special Purpose and Application-Based Systems. --- Management of Computing and Information Systems. --- Software Engineering. --- Logics and Meanings of Programs. --- Mathematics. --- Computer-based information systems --- EIS (Information systems) --- Executive information systems --- MIS (Information systems) --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Computer science logic --- Algorism --- Computer software engineering --- Special purpose computers --- Informatics --- Mathematics --- Sociotechnical systems --- Information resources management --- Management --- Logic, Symbolic and mathematical --- Algebra --- Arithmetic --- Engineering --- Computers --- Science --- Communication systems --- Foundations --- Computer software. --- Information Systems. --- Logic design. --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Machine theory --- Switching theory --- Software, Computer --- Computer systems --- Computer science—Mathematics. --- Computers, Special purpose. --- Electronic data processing—Management. --- IT Operations. --- Computer Science Logic and Foundations of Programming.

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This book constitutes the proceedings of the 16th International Workshop on Computer Algebra in Scientific Computing, CASC 2014, held in Warsaw, Poland, in September 2014. The 33 full papers presented were carefully reviewed and selected for inclusion in this book. The papers address issues such as Studies in polynomial algebra are represented by contributions devoted to factoring sparse bivariate polynomials using the priority queue, the construction of irreducible polynomials by using the Newton index, real polynomial root finding by means of matrix and polynomial iterations, application of the eigenvalue method with symmetry for solving polynomial systems arising in the vibration analysis of mechanical structures with symmetry properties, application of Gröbner systems for computing the (absolute) reduction number of polynomial ideals, the application of cylindrical algebraic decomposition for solving the quantifier elimination problems, certification of approximate roots of overdetermined and singular polynomial systems via the recovery of an exact rational univariate representation from approximate numerical data, new parallel algorithms for operations on univariate polynomials (multi-point evaluation, interpolation) based on subproduct tree techniques.

Computer science. --- Arithmetic and logic units, Computer. --- Algorithms. --- Numerical analysis. --- Computer science --- Computer graphics. --- Computer Science. --- Algorithm Analysis and Problem Complexity. --- Discrete Mathematics in Computer Science. --- Symbolic and Algebraic Manipulation. --- Computer Graphics. --- Numeric Computing. --- Arithmetic and Logic Structures. --- Mathematics. --- Computer software. --- Computational complexity. --- Algebra --- Electronic data processing. --- Data processing. --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Complexity, Computational --- Electronic data processing --- Machine theory --- Software, Computer --- Computer systems --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Engineering graphics --- Image processing --- Informatics --- Science --- Automation --- Digital techniques --- Computer science—Mathematics. --- Arithmetic and logic units, Computer --- Computer arithmetic --- Electronic digital computers --- Mathematical analysis --- Algorism --- Arithmetic --- Circuits --- Foundations --- Discrete mathematics. --- Computer arithmetic and logic units. --- Numerical Analysis. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis