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

New methodological facets regarding layout and implementation of symbolic computation structures are thought of during this quantity aiming at integrating such facets right into a homogeneous software program setting for clinical computation. The proposed method is predicated on a mixture of other suggestions: algebraic specification via modular technique and crowning glory algorithms, approximated and detailed algebraic computing tools, object-oriented programming paradigm, automatic theorem proving via tools ? los angeles Hilbert and techniques of ordinary deduction. particularly the proposed therapy of mathematical items, through recommendations for approach abstraction, buildings category, and specified illustration, the programming technique which helps the layout and implementation matters, and reasoning features supported by way of the complete framework are defined.

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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. 357). , Collins, G. , Loos, R. ) (1983): Computer algebra, symbolic and algebraic computation, 2nd edn. Springer, Wien New York. Caviness, B. (1986): Computer algebra: past and future. J. Symb. Comput. 2: 217-236. , Miola, A. (1995): A sequent calculus for symbolic computation systems.

From the previous description we can see that the Hensel method takes polynomials as input and returns either a truncated power series or a Hensel code. It applies the EEA (in SOLVE, in order to solve either the Diophantine equation or the modular equation). It should be located where all the properties of a Euclidean domain are available (see Fig. 6). Hence the Euclidean domain is the structure of highest level of abstraction, where the Hensel method can be defined. Let us note that, in this case, the algorithm is not a characterizing attribute of the abstract structure of Euclidean domain; in fact, it is added to the definition, just enriching it.

104: 89-107. , Mele, M. , Temperini, M. (1990): Abstract specification of mathematical structures and methods. In: Miola, A. ): Design and implementation of symbolic computation systems. Springer, Berlin Heidelberg New York Tokyo, pp. 61-70 (Lecture notes in computer science, vol. 429). Meyer, B. (1992): Eiffel: the language, 2nd edn. Prentice Hall, Englewood Cliffs. Overview 29 Miola, A. ) (1 990a): Computing tools for scientific problems solving. Academic Press, London. Miola, A. ) (1990b): Design and implementation of symbolic computation systems.

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