Camac2: A portable system for combinatorial and algebraic computation
| Autor: | Jeffrey S. Leon |
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| Rok vydání: | 2005 |
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| Zdroj: | EUROSAM 84 ISBN: 354013350X EUROSAM |
| Popis: | In recent years, computers have come to play an increasingly important role in research in many fields of mathematics, including combinatorics and algebra. They have been used in constructing large combinatorial objects or in proving their nonexistence, in classifying Smaller objects up to isomorphism, and in investigating the properties (symmetry group, code weight distribution, etc.) of combinatorial objects of various sizes. Several of the sporadic simple groups were first constructed by computer, character tables of many large groups rely on machine computations, and p-groups of low order have been investigated by computer methods. Perhaps no project of this type has occupied more computer time than the effort to determine if there exists a projective plane of order 10. Many interesting problems in these areas are finite and thus, in principle, solvable by exhaustive search (testing all possibilities). However, such techniques generally require time at least exponential in the object size and thus are feasible only for very small cases. Considerably more sophisticated algorithms have been developed for a number of combinatorial and algebraic calculations. Some of these, though still exponential in the worst case, perform quite well for many interesting objects, even fairly large ones. However, most of them require a good deal of effort to program. |
| Databáze: | OpenAIRE |
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