In-depth comparison of the Berlekamp – Massey – Sakata and the Scalar-FGLM algorithms: the non adaptive variants

Jérémy Berthomieu 1 Jean-Charles Faugère 1
1 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria de Paris
Abstract : We compare thoroughly the Berlekamp – Massey – Sakata algorithm and the Scalar-FGLM algorithm, which compute both the ideal of relations of a multi-dimensional linear recurrent sequence. Suprisingly, their behaviors differ. We detail in which way they do and prove that it is not possible to tweak one of the algorithms in order to mimic exactly the behavior of the other.
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Submitted on : Wednesday, September 20, 2017 - 5:43:27 PM
Last modification on : Thursday, March 21, 2019 - 1:11:47 PM

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  • HAL Id : hal-01516708, version 2
  • ARXIV : 1709.07168

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Jérémy Berthomieu, Jean-Charles Faugère. In-depth comparison of the Berlekamp – Massey – Sakata and the Scalar-FGLM algorithms: the non adaptive variants. 2017. ⟨hal-01516708v2⟩

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