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Counting and Gröbner Bases

✍ Scribed by K. Kalorkoti

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 239 KB
Volume: 31
Category: Article
ISSN: 0747-7171
DOI: 10.1006/jsco.2000.1575

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✦ Synopsis

We show how the complexity of counting relates to the well known phenomenon that computing Gröbner bases under a lexicographic order is generally harder than total degree orders. We give simple examples of polynomials for which it is very easy to compute their Gröbner basis using a total degree order but for which exponential time is required for a lexicographic order. It follows that conversion algorithms do not help in such cases.

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