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Modular Algorithms in Symbolic Summation and Symbolic Integration
Brings together two streams in computer algebra: symbolic integration and summation on the one hand, and fast algorithmics on the other hand. In many algorithmically oriented areas of computer science, the analysis of al gorithms placed into the lime light by DonKnuth’stalkat the 1970ICM –provides a crystal-clear criterion for success. The researcher who designs an algorithm that is faster (asymptotically, in the worst case) than any previous method receives instant gratification : her result will be recognized as valuable. Al as, the downside is that such results come along quite infrequently, despite our best efforts. An alternative evaluation method is to run a new algorithm on examples; this has its obvious problems, but is sometimes the best we can do. George Collins, one of the fathers of computer algebra and a great experimenter,wrote in 1969: “I think this demonstrates again that a simple analysis is often more revealing than a ream of empirical data (although both are important). ” Within computer algebra, some areas have traditionally followed the former methodology, notably some parts of polynomial algebra and linear algebra. Other areas, such as polynomial system solving, have not yet been amenable to this - proach. The usual “input size” parameters of computer science seem inadequate, and although some natural “geometric” parameters have been identified (solution dimension, regularity), not all (potential) major progress can be expressed in this framework. Symbolic integration and summation have been in a similar state.
Intelligent Computer Mathematics ; 9th International Conference, AISC 2008, 15th Symposium, Calculemus 2008, 7th International Conference, MKM 2008, Birmingham, UK, July 28 - August 1, 2008. Proceedings
This book constitutes the joint refereed proceedings of the 9th International Conference on Artificial Intelligence and Symbolic Computation, AISC 2008, the 15th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2008, and the 7th International Conference on Mathematical Knowledge Management, MKM 2008, held in Birmingham, UK, in July/August as CICM 2008, the Conferences on Intelligent Computer Mathematics.
Frontiers of combining systems ; 5th International Workshop, FroCoS 2005, Vienna, Austria, September 19-21, 2005, Proceedings
Constitutes the refereed proceedings of the 5th International Workshop on Frontiers of Combining Systems, FroCoS 2005, held in Vienna, Austria. This book includes 19 full papers that are organized in topical sections on combinations of logics, theories, and decision procedures; constraint solving and programming; and others.
Computer algebra in scientific computing ; 22nd International Workshop, CASC 2020, Linz, Austria, September 14–18, 2020, Proceedings
This book constitutes the refereed proceedings of the 22nd International Workshop on Computer Algebra in Scientific Computing, CASC 2020, held in Linz, Austria, in September 2020. The conference was held virtually due to the COVID-19 pandemic. The 34 full papers presented together with 2 invited talks were carefully reviewed and selected from 41 submissions. They deal with cutting-edge research in all major disciplines of computer algebra. The papers cover topics such as polynomial algebra, symbolic and symbolic-numerical computation, applications of symbolic computation for investigating and solving ordinary differential equations, applications of CAS in the investigation and solution of celestial mechanics problems, and in mechanics, physics, and robotics.
Computer algebra and geometric algebra with applications ; 6th International Workshop, IWMM 2004, Shanghai, China, May 19-21, 2004 and International Workshop, GIAE 2004, Xian, China, May 24-28, 2004.Revised Selected Papers
MathematicsMechanization consistsoftheory,softwareandapplicationofc- puterized mathematical activities such as computing, reasoning and discovering. ItsuniquefeaturecanbesuccinctlydescribedasAAA(Algebraization,Algori- mization, Application). The name “Mathematics Mechanization” has its origin in the work of Hao Wang (1960s), one of the pioneers in using computers to do research in mathematics, particularly in automated theorem proving. Since the 1970s, this research direction has been actively pursued and extensively dev- oped by Prof. Wen-tsun Wu and his followers. It di?ers from the closely related disciplines like Computer Mathematics, Symbolic Computation and Automated Reasoning in that its goal is to make algorithmic studies and applications of mathematics the major trend of mathematics development in the information age.
Automatic program development : A tribute to Robert Paige
This work, a tribute to renowned researcher Robert Paige, is a collection of revised papers published in his honor in the Higher-Order and Symbolic Computation Journal in 2003 and 2005. The book also includes some papers by members of the IFIP Working Group 2.1 of which Bob was an active member.
Artificial intelligence and symbolic computation ; 8th International Conference, AISC 2006, Beijing, China, September 20-22, 2006, Proceedings
This book constitutes the refereed proceedings of the 8th International Conference on Artificial Intelligence and Symbolic Computation, AISC 2006, held in Beijing, China in September 2006. The 18 revised full papers presented together with 4 invited papers were carefully reviewed and selected from 39 submissions. Based on heuristics and mathematical algorithmics, artificial intelligence and symbolic computation are two views and approaches for automating (mathematical) problem solving. The papers address all current aspects in the area of symbolic computing and AI: mathematical foundations, implementations, and applications in industry and academia. The papers are organized in topical sections on artificial intelligence and theorem proving, symbolic computation, constraint satisfaction/solving, and mathematical knowledge management.
Algorithms in Invariant Theory
The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions.
Algebraic Biology ; 3rd International Conference, AB 2008, Castle of Hagenberg, Austria, July 31-August 2, 2008 Proceedings
This book constitutes the refereed proceedings of the Third International Conference on Algebraic Biology, AB 2008, held at the Castle of Hagenberg, Austria in July 2008 as part of the RISC Summer 2008, organized by the Research Institute for Symbolic Computation.
Algebraic Biology ; 2nd International Conference, AB 2007, Castle of Hagenberg, Austria, July 2-4, 2007, Proceedings
This volume constitutes the refereed proceedings of the Second International Conference on Algebraic Biology. The conference served as an interdisciplinary forum for the presentation of research on all aspects of the application of symbolic computation in biology, including computer algebra, computational logic, and related methods.
Abstract Computing Machines : A Lambda Calculus Perspective
The book addresses ways and means of organizing computations, highlighting the relationship between algorithms and the basic mechanisms and runtime structures necessary to execute them using machines. It completely abstracts from concrete programming languages and machine architectures, taking instead the lambda calculus as the basic programming and program execution model to design various abstract machines for its correct implementation. The emphasis is on fully normalizing machines based on full-fledged beta-reductions as essential prerequisites for symbolic computations that treat functions and variables truly as first-class objects. Their weakly normalizing counterparts are shown to be functional abstract machines that sacrifice the flavors of full beta-reductions for decidedly simpler runtime structures and improved runtime efficiency. Further downgrading of the lambda calculus leads to classical imperative machines that permit side-effecting operations on the runtime environment.
