Ebook: Advances in the Design of Symbolic Computation Systems

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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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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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.
Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
Mathematica: doing mathematics by computer?....Pages 2-20
An overview of the TASSO project....Pages 21-29
Front Matter....Pages 31-31
The uniform representation of mathematical objects by truncated power series....Pages 32-52
p-adic arithmetic: a tool for error-free computations....Pages 53-67
Exact solution of computational problems via parallel truncated p-adic Arithmetic....Pages 68-83
A canonical form guide to symbolic summation....Pages 84-110
Indexes in sums and series: from formal definition to object-oriented implementation....Pages 111-123
Front Matter....Pages 125-125
Equational specifications: design, implementation, and reasoning....Pages 126-144
On the algebraic specification of classes and inheritance in object-oriented programming....Pages 145-163
On subtyping in languages for symbolic computation systems....Pages 164-178
Enhanced strict inheritance in TASSO-L....Pages 179-195
Front Matter....Pages 197-197
Deduction and abduction using a sequent calculus....Pages 198-216
A sequent calculus machine for symbolic computation systems....Pages 217-229
Automated deduction by connection method in an object-oriented environment....Pages 230-244
A general reasoning apparatus for intelligent tutoring systems in mathematics....Pages 245-256
Back Matter....Pages 257-259

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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.
Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
Mathematica: doing mathematics by computer?....Pages 2-20
An overview of the TASSO project....Pages 21-29
Front Matter....Pages 31-31
The uniform representation of mathematical objects by truncated power series....Pages 32-52
p-adic arithmetic: a tool for error-free computations....Pages 53-67
Exact solution of computational problems via parallel truncated p-adic Arithmetic....Pages 68-83
A canonical form guide to symbolic summation....Pages 84-110
Indexes in sums and series: from formal definition to object-oriented implementation....Pages 111-123
Front Matter....Pages 125-125
Equational specifications: design, implementation, and reasoning....Pages 126-144
On the algebraic specification of classes and inheritance in object-oriented programming....Pages 145-163
On subtyping in languages for symbolic computation systems....Pages 164-178
Enhanced strict inheritance in TASSO-L....Pages 179-195
Front Matter....Pages 197-197
Deduction and abduction using a sequent calculus....Pages 198-216
A sequent calculus machine for symbolic computation systems....Pages 217-229
Automated deduction by connection method in an object-oriented environment....Pages 230-244
A general reasoning apparatus for intelligent tutoring systems in mathematics....Pages 245-256
Back Matter....Pages 257-259
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