BibTeX
@MISC{Pritchard01walkingthrough,
author = {David Pritchard},
title = {Walking Through The Gröbner Fan},
year = {2001}
}
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Abstract
Abstract. The Gröbner Walk is an algorithm that transforms a polynomial ideal’s Gröbner basis under one term order into a basis under another order. Although we could always directly compute such a basis using Buchberger’s algorithm, the Gröbner Walk is of special interest because, in many cases, it is much more efficient to convert a basis using this algorithm than to compute it directly. We first discuss matrix-defined term orderings, and introduce the Gröbner Fan of an ideal, an object that allows us to explore all of an ideal’s bases at once. Finally, we present the Walk.
