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TitleNumerical algorithms for dual bases of positive-dimensional ideals.
Author(s) Krone Robert
TypeArticle in Journal
AbstractAn ideal of a local polynomial ring can be described by calculating a standard basis with respect to a local monomial ordering. However the usual standard basis algorithms are not numerically stable. A numerically stable approach to describing the ideal is by finding the space of dual functionals that annihilate it, which reduces the problem to one of linear algebra. There are several known algorithms for finding the truncated dual up to any specified degree, which is useful for describing zero-dimensional ideals. We present a stopping criterion for positive-dimensional cases based on homogenization that guarantees all generators of the initial monomial ideal are found. This has applications for calculating Hilbert functions.

KeywordsNumerical algebraic geometry; computational algebraic geometry; Hilbert function; Macaulay dual space; Macaulay2
URL http://www.worldscientific.com/doi/abs/10.1142/S0219498813500187
JournalJ. Algebra Appl.
Pages1350018, 21
PublisherWorld Scientific, Singapore
Translation No
Refereed No