PolSys seminarRSS

The Skeletons you find when you Order your Ideal's Closet

Intervenant(s) : John Perry (The University of Southern Mississippi, USA)
Most algorithms to compute a Groebner basis of a polynomial ideal are textit{static}, producing a basis with respect to a term ordering given as a parameter. We naturally prefer efficient orderings, but the choice is not usually obvious.
Enter the textit{dynamic} algorithm, which computes a basis textit{and} an ordering textit{simultaneously}, using a ``tentative'' Hilbert function to estimate efficiency. Unfortunately, record-keeping quickly grows very large, outweighing benefts even for “toy ideals”.
This talk, based on joint work with Massimo Caboara of the University of Pisa, introduces dynamic algorithms, describes two effective techniques to minimize record-keeping, and reports on experiments with other criteria for efficiency.
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