Anzeige
Erschienen in:
2014 | OriginalPaper | Buchkapitel
An Algorithm for Computing Standard Bases by Change of Ordering via Algebraic Local Cohomology
verfasst von : Katsusuke Nabeshima, Shinichi Tajima
Erschienen in: Mathematical Software – ICMS 2014
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
An algorithm is introduced for transforming a standard basis of a zero-dimensional ideal, in the formal power series ring, into another standard basis with respect to any given local ordering. The key ingredient of the proposed algorithm is an efficient method for solving membership problems for Jacobi ideals in local rings, that utilizes the Grothendieck local duality theorem. Namely, a new algorithm for computing a standard basis of a given zero-dimensional ideal with respect to any given local ordering, is derived by using algebraic local cohomology. Its implementation is introduced, too.