## Advances in the Design of Symbolic Computation SystemsNew 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. |

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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 |

257 | |

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

### Other editions - View all

Advances in the Design of Symbolic Computation Systems Alfonso Miola,Marco Temperini Limited preview - 2012 |

Advances in the Design of Symbolic Computation Systems Alfonso Miola,Marco Temperini No preview available - 1997 |

### Common terms and phrases

abstract abstract data type alg-expression algorithm application axioms Berlin Heidelberg Buchberger Cioni class specification CLOS Colagrossi computer algebra computer science consider data type deduction defined definition domain equation Euclidean domain example execution expressions Farey fraction first-order logic flist formula function given greatest common divisor Heidelberg Heidelberg New York Hensel code hypergeometric implementation induction inheritance input instance integer interface Limongelli Linz logic manipulation Mathematica matrix method invocation method lookup Miola morphism multiple inheritance natural deduction node notes in computer object-oriented programming obtained operations output p-adic arithmetic parallel parameter polynomial problem procedure programming language proof properties proving pseudo-Hensel code quantified rational number rationale recursive redefinition representation represented result s-expression Sect sequence-domain sequent calculus sequent F solution solving sort Springer steps subclass subtyping succedent sum-expression summation superclass symbolic computation systems TASSO TASSO-L Temperini theorem valid sequent variable verificative York Tokyo

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Page iv - Dipartimento di Informatica e Sistemistica, Universita degli Studi di Roma "La Sapienza", Via Solaria 113, 00198 Roma, Italy J.