Download Advances in the Design of Symbolic Computation Systems by B. Buchberger (auth.), Dr. Alfonso Miola, Dr. Marco PDF

By B. Buchberger (auth.), Dr. Alfonso Miola, Dr. Marco Temperini (eds.)

New methodological features concerning layout and implementation of symbolic computation platforms are thought of during this quantity aiming at integrating such features right into a homogeneous software program surroundings for medical computation. The proposed method relies on a mixture of alternative strategies: algebraic specification via modular process and finishing touch algorithms, approximated and certain algebraic computing tools, object-oriented programming paradigm, automatic theorem proving via tools ? l. a. Hilbert and strategies of traditional deduction. particularly the proposed therapy of mathematical items, through thoughts for approach abstraction, buildings category, and detailed illustration, the programming method which helps the layout and implementation matters, and reasoning functions supported by means of the entire framework are defined.

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Temperini 1 Introduction Systems for symbolic mathematics are based on the availability of powerful methods and techniques, which have been developed for numeric computation, symbolic and algebraic computation and automated deduction. But those different computing paradigms really work independently in such systems. Each of them represents an individual computing environment, while they are not integrated to support a uniform environment for computation. The problem of the integration of numeric and symbolic computation is still open (Caviness 1986, Limongelli and Miola 1990, Mascari and Miola 1986).

In: Shriver, B. D. ): Proceedings 23rd Hawaii International Conference on System Sciences, vol. II, software. IEEE Computer Society Press, Los Alamitos, pp. 165173. Bibel, W. (1987): Automated theorem proving. F. Vieweg und Sohn, Wiesbaden. , Cioni, G. (1988): Embedding flexible control strategies into object oriented languages. In: Mora, T. ): Applied algebra, algebraic algorithms and error- 28 A. Miola correcting codes. Springer, Berlin Heidelberg New York Tokyo, pp. 454-457 (Lecture notes in computer science, vol.

We have seen that a unified representation can be obtained when numbers and functions are represented by power series and p-adic analysis offers an appropriate mathematical settlement to handle with power series. Limongelli and Temperini (1997) show how it is possible to treat numbers by truncated power series, as well as the most general p-adic construction methods in an integrated computing environment. 2. p-adic arithmetic is an exact arithmetic and the algebraic bases on which it is founded overcome the problem of the floating point arithmetic, which is essentially due to a lack of algebraic setting.

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