Advances in the Design of Symbolic Computation Systems

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Springer Science & Business Media, Mar 27, 1997 - Computers - 259 pages
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 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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Contents

doing mathematics by computer?
2
An overview of the TASSO project
21
The uniform representation of mathematical objects by truncated power series
32
a tool for errorfree computations
53
Exact solution of computational problems via parallel truncated padic arithmetic
68
A canonical form guide to symbolic summation
84
from formal definition to objectoriented implementation
111
design implementation and reasoning
126
On subtyping in languages for symbolic computation systems
164
Enhanced strict inheritance in TASSOL
179
Deduction and abduction using a sequent calculus
198
A sequent calculus machine for symbolic computation systems
217
Automated deduction by connection method in an objectoriented environment
230
A general reasoning apparatus for intelligent tutoring systems in mathematics
245
Subject index
257
Copyright

On the algebraic specification of classes and inheritance in objectoriented programming
145

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