Efficient Algorithms for Computing Nœther Normalization

Authors:
Amir Hashemi
Affiliations:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran 84156-83111 and Inria-Salsa project/ Lip6-Spiral team, Paris, France 75016
Venue:
Computer Mathematics
Year:
2008

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Abstract

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.