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The growing demand of speed, accuracy, and reliability in scientific and engineering computing has been accelerating the merging of symbolic and numeric computations, two types of computation coexisting in mathematics yet separated in traditional research of mathematical computation. This book with 23 chapters presents original research and tutorial survey on the integration and interaction of symbolic and numeric computations. It represents the current state of the art and will serve as a valuable reference on the development of algorithms and software packages for hybrid symbolic-numeric computation. The book highlights the interaction between symbolic and numeric computations. It contains tutorial surveys by distinguished experts, covers recent advances on key topics, and provides effective methods illustrated with applications.

Computable functions --- Numerical analysis --- Logic, Symbolic and mathematical --- Data processing --- Computability theory --- Functions, Computable --- Partial recursive functions --- Recursive functions, Partial --- Constructive mathematics --- Decidability (Mathematical logic) --- Numerical analysis. --- Numerical Analysis. --- Mathematical analysis

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The International Symposium on Symbolic and Algebraic Computation (ISSAC) is the premier conference for research in symbolic computation and computer algebra. ISSAC is the continuation of conferences with the names SYMSAC, EUROCAL, EUROSAM, and EUROCAM, which have alternated between North America and Europe before merging into ISSAC. The whole series started in 1966 with the first ACM Symposium on Symbolic and Algebraic Manipulation, and it has been held annually since 1981. The conference typically presents a range of invited talks, tutorials, poster sessions, software demonstrations, and vendor exhibits, with its center-piece being peer-reviewed contributed research papers.

Computer science.

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The ISSAC meeting is a showcase for original research contributions on all aspects of computer algebra and symbolic mathematical computation, including: Algorithmic aspects: •Exact and symbolic linear, polynomial and differential algebra •Symbolic-numeric, homotopy, perturbation and series methods •Computational algebraic geometry, group theory and number theory, quantifier elimination and logic •Computer arithmetic •Summation, recurrence equations, integration, solution of ODEs & PDEs •Symbolic methods in other areas of pure and applied mathematics •Complexity of algebraic algorithms and algebraic complexity Software aspects: •Design of symbolic computation packages and systems •Language design and type systems for symbolic computation •Data representation •Considerations for modern hardware •Algorithm implementation and performance tuning •Mathematical user interfaces •Use with systems for, e.g., digital libraries, course-ware, simulation and optimization, automated theoremproving, computer-aided design, and automatic differentiation Application aspects: •Applications that stretch the current limits of computer algebra algorithms or systems, use computer algebra in new areas or new ways, or apply it in situations with broad impact.

Computer algorithms.