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Computing the Radical of an Ideal in Positive Characteristic

✍ Scribed by Ryutaroh Matsumoto

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 294 KB
Volume: 32
Category: Article
ISSN: 0747-7171
DOI: 10.1006/jsco.2001.0446

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✦ Synopsis

We propose a method for computing the radical of an arbitrary ideal in the polynomial ring in n variables over a perfect field of characteristic p > 0. In our method Buchberger's algorithm is performed once in n variables and a Gröbner basis conversion algorithm is performed at most n log p d times in 2n variables, where d is the maximum of total degrees of generators of the ideal and 3. Next we explain how to compute radicals over a finitely generated coefficient field over a field K, when we have a radical computation method over the field K. Thus we can compute radicals over any finitely generated field over a perfect field.

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