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A.2.2 Groebner basis conversionThe performance of Buchberger's algorithm is sensitive to the chosen monomial order. A Groebner basis computation with respect to a less favorable order such as the lexicographic ordering may easily run out of time or memory even in cases where a Groebner basis computation with respect to a more efficient order such as the degree reverse lexicographic ordering is very well feasible. Groebner basis conversion algorithms and the Hilbert-driven Buchberger algorithm are based on this observation:
SINGULAR provides implementations for the FGLM conversion algorithm
(which applies to zero-dimensional ideals only, see stdfglm) and
variants of the Groebner walk conversion algorithm (which works for
arbitrary ideals, See frwalk, grwalk_lib).
An implementation of the Hilbert-driven Buchberger
algorithm is accessible via the
For the ideal below,
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