Intervals, Syzygies, Numerical Gröbner Bases: A Mixed Study

  • Marco Bodrato
  • Alberto Zanoni
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4194)

Abstract

In Gröbner bases computation, as in other algorithms in commutative algebra, a general open question is how to guide the calculations coping with numerical coefficients and/or not exact input data. It often happens that, due to error accumulation and/or insufficient working precision, the obtained result is not one expects from a theoretical derivation. The resulting basis may have more or less polynomials, a different number of solution, roots with different multiplicity, another Hilbert function, and so on. Augmenting precision we may overcome algorithmic errors, but one does not know in advance how much this precision should be, and a trial–and–error approach is often the only way to follow. Coping with initial errors is an even more difficult task. In this experimental work we propose the combined use of syzygies and interval arithmetic to decide what to do at each critical point of the algorithm.

AMS Subject Classification: 13P10, 65H10, 90C31.

Keywords and phrases

Gröbner bases numerical coefficients syzygies 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marco Bodrato
    • 1
  • Alberto Zanoni
    • 1
  1. 1.Dipartimento di Matematica “Leonida Tonelli”Università di PisaPisaItaly

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