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E-raamat: Advances in the Design of Symbolic Computation Systems

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New methodological aspects related to design and implementation of symbolic computation systems are considered in this volume aiming at integrating such aspects into a homogeneous software environment for scientific computation. The proposed methodology is based on a combination of different techniques: algebraic specification through modular approach and completion algorithms, approximated and exact algebraic computing methods, object-oriented programming paradigm, automated theorem proving through methods à la Hilbert and methods of natural deduction. In particular the proposed treatment of mathematical objects, via techniques for method abstraction, structures classification, and exact representation, the programming methodology which supports the design and implementation issues, and reasoning capabilities supported by the whole framework are described.

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List of contributors ix State of the art and motivations 2(30) B. Buchberger Mathematica: doing mathematics by computer? 2(19) A. Miola An overview of the TASSO project 21(11) Mathematical objects 32(94) C. Limongelli M. Temperini The uniform representation of mathematical objects by truncated power series 32(21) A. Colagrossi C. Limongelli A. Miola p-adic arithmetic: a tool for error-free computations 53(15) C. Limongelli Exact solution of computational problems via parallel truncated p-adic arithmetic 68(16) P. Paule I. Nemes A canonical form guide to symbolic summation 84(27) O. Caprotti Indexes in sums and series: from formal definition to object-oriented implementation 111(15) Programming methodologies 126(72) S. Antoy P. Forcheri J. Gannon M.T. Molfino Equational specifications: design, implementation, and reasoning 126(19) F. Parisi-Presicce A. Pierantonio On the algebraic specification of classes and inheritance in object-oriented programming 145(19) P. Di Blasio M. Temperini On subtyping in languages for symbolic computation systems 164(15) P. Di Blasio M. Temperini P. Terlizzi Enhanced strict inheritance in TASSO-L 179(19) Reasoning capabilities 198(59) G. Cioni A. Colagrossi A. Miola Deduction and abduction using a sequent calculus 198(19) P. Bertoli G. Cioni A. Colagrossi P. Terlizzi A sequent calculus machine for symbolic computation systems 217(13) G. Cioni G. Patrizi M. Temperini Automated deduction by connection method in an object-oriented environment 230(15) A. Colagrossi A. Micarelli A general reasoning apparatus for intelligent tutoring systems in mathematics 245(12) Subject index 257
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