The FGLM problem and Möller's algorithm on zero-dimensional ideals

Abstract

Möller's Algorithm is a procedure which, given a set of linear functionals defining a zero-dimensional polynomial ideal, allows to compute, with good complexity, a set of polynomials which are triangular/bihortogonal to the given functionals; at least a minimal polynomial which vanishes to all the given functionals; a Gröbner basis of the given ideal. As such Möller's Algorithm has applications when the functionals are point evaluation (where the only relevant informations are the bihortogonal polynomials); as an interpretation of Berlekamp-Massey Algorithm (such interpretation is due to Fitzpatrick) where the deduced minimal vanishing polynomial is the key equation; as an efficient solution of the FGLM-Problem (deduced with good complexity the lex Gröbner basis of a zero-dim. ideal given by another easy-to-be-computed Gröbner basis of the same ideal). © 2009 Springer-Verlag Berlin Heidelberg.