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Published in:
2014 | OriginalPaper | Chapter
Deterministically Computing Reduction Numbers of Polynomial Ideals
Authors : Amir Hashemi, Michael Schweinfurter, Werner M. Seiler
Published in: Computer Algebra in Scientific Computing
Publisher: Springer International Publishing
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We discuss the problem of determining reduction numbers of a polynomial ideal
$\mathcal{I}$
in
n
variables. We present two algorithms based on parametric computations. The first one determines the absolute reduction number of
$\mathcal{I}$
and requires computations in a polynomial ring with (
n
–dim
$\mathcal{I}$
)dim
$\mathcal{I}$
parameters and
n
–dim
$\mathcal{I}$
variables. The second one computes via a Gröbner system the set of all reduction numbers of the ideal
$\mathcal{I}$
and thus in particular also its big reduction number. However, it requires computations in a ring with
n
dim
$\mathcal{I}$
parameters and
n
variables.