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The FGLM Problem and Möller’s Algorithm on Zero-dimensional Ideals

In: Gröbner Bases, Coding, and Cryptography

Author

Listed:
  • Teo Mora

    (Università di Genova, DIMA and DISI)

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).

Suggested Citation

  • Teo Mora, 2009. "The FGLM Problem and Möller’s Algorithm on Zero-dimensional Ideals," Springer Books, in: Massimiliano Sala & Shojiro Sakata & Teo Mora & Carlo Traverso & Ludovic Perret (ed.), Gröbner Bases, Coding, and Cryptography, pages 27-45, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-93806-4_3
    DOI: 10.1007/978-3-540-93806-4_3
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