Performance of Buchberger's Improved Algorithm using Prime Based Ordering

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dc.creatorHoran, Peter
dc.creatorCarminati, John
dc.date2009-01-28
dc.date.accessioned2026-07-07T12:35:09Z
dc.date.available2026-07-07T12:35:09Z
dc.descriptionPrime-based ordering which is proved to be admissible, is the encoding of indeterminates in power-products with prime numbers and ordering them by using the natural number order. Using Eiffel, four versions of Buchberger's improved algorithm for obtaining Groebner Bases have been developed: two total degree versions, representing power products as strings and the other two as integers based on prime-based ordering. The versions are further distinguished by implementing coefficients as 64-bit integers and as multiple-precision integers. By using primebased power product coding, iterative or recursive operations on power products are replaced with integer operations. It is found that on a series of example polynomial sets, significant reductions in computation time of 30% or more are almost always obtained.
dc.description10 pages, 2 tables, 4 refs
dc.identifierhttps://arxiv.org/abs/0901.4404
dc.identifierhttp://arxiv.org/abs/0901.4404
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217681
dc.subjectSoftware Engineering
dc.subjectSymbolic Computation
dc.titlePerformance of Buchberger's Improved Algorithm using Prime Based Ordering
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