CONTRIBUTIONS TO MECHANICAL MATHEMATICS

We describe the experience relating to the design of a programming language, Formula Algol, which is suitable for describing algorithms that mechanize some mathematical tasks. We develop a theory that yields results from which we can prove the termination of some Markov algorithms that perform algeb...

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Bibliographic Details
Main Author: Iturriaga,Renato
Format: Report
Language:English
Subjects:
ADAPTIVE SYSTEMS
ALGEBRA
ALGORITHMS
Computer Hardware
Computer Programming and Software
COMPUTERS
DIFFERENTIAL EQUATIONS
INEQUALITIES
ITERATIONS
METAMATHEMATICS
PROBLEM SOLVING
SEQUENCES(MATHEMATICS)
TAYLORS SERIES
Theoretical Mathematics
THESES
TRANSFORMATIONS(MATHEMATICS)
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Summary:We describe the experience relating to the design of a programming language, Formula Algol, which is suitable for describing algorithms that mechanize some mathematical tasks. We develop a theory that yields results from which we can prove the termination of some Markov algorithms that perform algebraic transformations. Using these results, we also can characterize the classes of formulae that constitute the input and output for such algorithms. Next, we discuss in some detail the various problems related to the mechanization of limiting processes and inequalities. Twenty-five appendices--with running programs--illustrate the various points made during our presentation. (Author)