Improving DISPGB Algorithm Using the Discriminant Ideal

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dc.creatorManubens, Montserrat
dc.creatorMontes, Antonio
dc.date2006-01-31
dc.date.accessioned2026-07-07T07:51:22Z
dc.date.available2026-07-07T07:51:22Z
dc.descriptionIn 1992, V. Weispfenning proved the existence of Comprehensive Groebner Bases (CGB) and gave an algorithm to compute one. That algorithm was not very efficient and not canonical. Using his suggestions, A. Montes obtained in 2002 a more efficient algorithm (DISPGB) for Discussing Parametric Groebner Bases. Inspired in its philosophy, V. Weispfenning defined, in 2002, how to obtain a Canonical Comprehensive Groebner Basis (CCGB) for parametric polynomial ideals, and provided a constructive method. In this paper we use Weispfenning's CCGB ideas to make substantial improvements on Montes DISPGB algorithm. It now includes rewriting of the discussion tree using the Discriminant Ideal and provides a compact and effective discussion. We also describe the new algorithms in the DPGB library containing the improved DISPGB as well as new routines to check whether a given basis is a CGB or not, and to obtain a CGB. Examples and tests are also provided.
dc.description21 pages, see also http://www-ma2.upc.edu/~montes/
dc.identifierhttps://arxiv.org/abs/math/0601763
dc.identifierhttp://arxiv.org/abs/math/0601763
dc.identifierJournal of Symbolic Computation 41 (2006) 1245-1263
dc.identifierdoi:10.1016/j.jsc.2005.09.013
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125484
dc.subjectCommutative Algebra
dc.subject68W30; 13P10; 13F10
dc.titleImproving DISPGB Algorithm Using the Discriminant Ideal
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