Towards a deductive database for small simple groups
Abstract
This particular study investigates the application of Prolog and the associated technology of deductive databases to the realm of modern algebra. A relatively small, yet diverse, collection of information was chosen for the feasibility study. The 56 non-abelian simple groups of order less than one million have been studied in depth. In print are several tables of information such as minimal generating pairs, presentations, character tables, and maximal subgroups. The information is very heterogeneous in nature, involving formulae, tables, lists, arbitrary precision integers, character strings, irrational numbers, and rules for deducing information from the given facts.While very much a feasibility study, the work to date demonstrates that the Prolog deductive database technology is appropriate. More primitive data types, such as irrational numbers, infinite precision numbers, and tables would improve the efficiency of Prolog in this domain. More work categorizing user queries and incorporating the necessary facts and rules to answer them is required.
References
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J. McKay, and K. Young, The non-abelian simple groups G, | G | &lt;10<sup>6</sup> - minimal generating pairs, Mathematics of Computation 33 (1979) 812--814.
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- Towards a deductive database for small simple groups
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Copyright © 1991 Authors.
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Association for Computing Machinery
New York, NY, United States
Publication History
Published: 01 October 1991
Published in SIGSAM Volume 25, Issue 4
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