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Paper   IPM / M / 16379
School of Mathematics
  Title:   Intrinsic complexity for constructing zero-dimensional Grobner bases
  Author(s):  Amir Hashemi (Joint with J. Heintz, L. M. Pardo, and P. Solerno)
  Status:   Published
  Journal: LNCS
  Vol.:  12291
  Year:  2020
  Pages:   245-265
  Supported by:  IPM
  Abstract:
In this paper, we give a thorough revision of Lakshman's paper by fixing some serious flaws in his approach. Furthermore, following this analysis, an intrinsic complexity bound for the construction of zero-dimensional Grobner bases is given. Our complexity bound is in terms of the degree of the input ideal as well as the degrees of its generators. Finally, as an application of the presented method, we exhibit and analyze a (Monte Carlo) probabilistic algorithm to compute the degree of an equi-dimensional ideal.


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