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

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.

Mots clés: the Scalar-FGLM algorithm; The BMS algorithm; Gröbner basis computation; multidimensional linear recurrent sequence; algorithms comparison

Domaines: Calcul formel [cs.SC]

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⟩