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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Efficient Algorithms for Computing Nœther Normalization
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In this paper, we provide first a new algorithm for testing whether a monomial ideal is in Nœther position or not,
without using its dimension
, within a complexity which is quadratic in input size. Using this algorithm, we provide also a new algorithm to put an ideal in this position within an
incremental
(one variable after the other) random linear change of the last variables without using its dimension. We describe a modular (probabilistic) version of these algorithms for any ideal using the modular method used in [2] with some modifications. These algorithms have been implemented in the distributed library noether.lib [17] of
Singular
, and we evaluate their performance via some examples.