Abstract.
In this paper, we give first some non-trivial improvements of the well-known bounds of effective Nullstellensätze. Using these bounds, we show that the Gröbner basis (for any monomial ordering) of a zero–dimensional ideal may be computed within a bit complexity which is essentially polynomial in \({D^{n^{2}}}\) where n is the number of unknowns and D is the mean value of the degrees of input polynomials.
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Manuscript received 2 June 2007
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Hashemi, A. Nullstellensätze for Zero–Dimensional Gröbner Bases. comput. complex. 18, 155–168 (2009). https://doi.org/10.1007/s00037-009-0261-9
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DOI: https://doi.org/10.1007/s00037-009-0261-9