By B. Buchberger (auth.), Dr. Alfonso Miola, Dr. Marco Temperini (eds.)
New methodological points on the topic of layout and implementation of symbolic computation structures are thought of during this quantity aiming at integrating such features right into a homogeneous software program surroundings for medical computation. The proposed technique is predicated on a mix of other strategies: algebraic specification via modular process and of entirety algorithms, approximated and certain algebraic computing tools, object-oriented programming paradigm, computerized theorem proving via equipment ? los angeles Hilbert and strategies of ordinary deduction. particularly the proposed remedy of mathematical gadgets, through concepts for technique abstraction, constructions class, and special illustration, the programming method which helps the layout and implementation matters, and reasoning features supported through the complete framework are defined.
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Extra info for Advances in the Design of Symbolic Computation Systems
Let us consider the case of the matrix structure. A general square matrix of Abstract structure plane Parametric structure plane Ring ::::::::::::::==:::::::::-----I---jL__ -----t --------::::: Commutative Integral Unit Ring Ring Ring ~t~:a: '\ Ring Formal Power Series Domain Integral Unit Domain --....... Euclidean Domain Matrix -i-t-------_ Polynomial t Field Fig. 2. Example of parametric structure Uniform representation of mathematical objects 37 order n (n is a natural number) is an element of the set where In = i E NAT: 1 :::: i :::: n and NAT is the sort of natural numbers.
Executable code is then derived from the edited specifications (Antoy et al. 1990, Antoy 1990). For the "a posteriori" verification, a completeness checker for the rewriting rules associated with the specifications is available (Forcheri and Molfino 1990). TASSO includes two main modules: TASSO-L and TASSO-D. TASSO-L is the language, based on an object-oriented paradigm, which allows the user to define objects, to instantiate abstract structures into actual computing domains, and to compute with available objects.
In this paper, a possible solution to this problem is considered, taking into account the well-known need for abstraction in the definition of mathematical data structures. Mainly we focus on the possibility of using a uniform representation of those structures and of extending the use of algebraic algorithms to numerical settings. With this aim in mind, we will present a classification of formal structures, defined in an algebraic context. In such a classification a fundamental role is played by the methods defined on algebraic structures: the algorithms for the manipulation of abstract structures can be included in the definition of the structures themselves.
Advances in the Design of Symbolic Computation Systems by B. Buchberger (auth.), Dr. Alfonso Miola, Dr. Marco Temperini (eds.)