Efficient Computation of Zero-Dimensional Gröbner Bases by Change of Ordering

  title={Efficient Computation of Zero-Dimensional Gr{\"o}bner Bases by Change of Ordering},
  author={J. Faug{\`e}re and P. Gianni and D. Lazard and T. Mora},
  journal={J. Symb. Comput.},
  • J. Faugère, P. Gianni, +1 author T. Mora
  • Published 1993
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • We present an efficient algorithm for the transformation of a Grobner basis of a zero-dimensional ideal with respect to any given ordering into a Grobner basis with respect to any other ordering. This algorithm is polynomial in the degree of the ideal. In particular the lexicographical Grobner basis can be obtained by applying this algorithm after a total degree Grobner basis computation: it is usually much faster to compute the basis this way than with a direct application of Buchberger's… CONTINUE READING
    624 Citations

    Topics from this paper

    Fast computation of Gröbner bases of ideals of F[x, y]
    • Yindong Chen, Y. Lu, P. Lu
    • Mathematics, Computer Science
    • 2009 IEEE International Symposium on Information Theory
    • 2009
    Changing the ordering of Gröbner bases with LLL: case of two variables
    • 17
    • PDF
    The Hilbert zonotope and a polynomial time algorithm for universal Gröbner bases
    • 36
    • PDF
    Gröbner bases of ideals defined by functionals with an application to ideals of projective points
    • 121
    Computing Gröbner Bases for Vanishing Ideals of Finite Sets of Points
    • 29
    • PDF
    Computing Gröbner Bases within Linear Algebra
    • A. Suzuki
    • Mathematics, Computer Science
    • CASC
    • 2009
    • 6
    Characterization of relative Gröbner bases
    • 5


    Gröbner Bases and Primary Decomposition of Polynomial Ideals
    • 425
    • PDF
    Solving Zero-Dimensional Algebraic Systems
    • D. Lazard
    • Computer Science, Mathematics
    • J. Symb. Comput.
    • 1992
    • 203
    • PDF
    Equations for the projective closure and effective Nullstellensatz
    • 32
    Systems of Algebraic Equations Solved by Means of Endomorphisms
    • 38
    Gröbner-Bases, Gaussian elimination and resolution of systems of algebraic equations
    • D. Lazard
    • Mathematics, Computer Science
    • 1983
    • 425
    Solving Systems of Algebraic Equations
    • 19
    Algebraic Solution of Systems of Polynomial Equations Using Groebner Bases
    • 114