Advances in the Design of Symbolic Computation Systems

1. Front Matter

   Pages i-x

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2. State of the art and motivations

   1. Front Matter

      Pages 1-1

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   2. Mathematica: doing mathematics by computer?

      • B. Buchberger

      Pages 2-20

   3. An overview of the TASSO project

      • A. Miola

      Pages 21-29

3. Mathematical objects

   1. Front Matter

      Pages 31-31

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   2. The uniform representation of mathematical objects by truncated power series

      • C. Limongelli, M. Temperini

      Pages 32-52

   3. p-adic arithmetic: a tool for error-free computations

      • A. Colagrossi, C. Limongelli, A. Miola

      Pages 53-67

   4. Exact solution of computational problems via parallel truncated p-adic Arithmetic

      • C. Limongelli

      Pages 68-83

   5. A canonical form guide to symbolic summation

      • P. Paule, I. Nemes

      Pages 84-110

   6. Indexes in sums and series: from formal definition to object-oriented implementation

      • O. Caprotti

      Pages 111-123

4. Programming methodologies

   1. Front Matter

      Pages 125-125

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   2. Equational specifications: design, implementation, and reasoning

      • S. Antoy, P. Forcheri, J. Gannon, M. T. Molfino

      Pages 126-144

   3. On the algebraic specification of classes and inheritance in object-oriented programming

      • F. Parisi-Presicce, A. Pierantonio

      Pages 145-163

   4. On subtyping in languages for symbolic computation systems

      • P. Di Blasio, M. Temperini

      Pages 164-178

   5. Enhanced strict inheritance in TASSO-L

      • P. Di Blasio, M. Temperini, P. Terlizzi

      Pages 179-195

5. Reasoning capabilities

   1. Front Matter

      Pages 197-197

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   2. Deduction and abduction using a sequent calculus

      • G. Cioni, A. Colagrossi, A. Miola

      Pages 198-216

   3. A sequent calculus machine for symbolic computation systems

      • P. Bertoli, G. Cioni, A. Colagrossi, P. Terlizzi

      Pages 217-229

   4. Automated deduction by connection method in an object-oriented environment

      • G. Cioni, G. Patrizi, M. Temperini

      Pages 230-244

   5. A general reasoning apparatus for intelligent tutoring systems in mathematics

      • A. Colagrossi, A. Micarelli

      Pages 245-256

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.

• Action
• Natural
• algorithm
• algorithms
• classification
• design
• programming

• Dipartimento di Informatica e Automazione, Università degli Studi di Roma Tre, Rome, Italy

  Alfonso Miola

• Dipartimento di Informatica e Sistemistica, Università degli Studi di Roma “La Sapienza”, Rome, Italy

  Marco Temperini

Policies and ethics