Yet another ideal decomposition algorithm

  • Massimo Caboara
  • Pasqualina Conti
  • Carlo Traverse
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1255)


Open Subset Prime Ideal Commutative Algebra Geometric Point Hilbert Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    B. Amrhein, O. Gloor, W. Küchlin, Walking faster, DISCO 1996, LNCS (1996)Google Scholar
  2. 2.
    M.F. Atiyah, I.G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, (1969)Google Scholar
  3. 3.
    M. Alonso, T. Mora, M. Raimondo, Local decomposition algorithms, ISSAC 1990, LNCS (1990)Google Scholar
  4. 4.
    D. Bayer, A. Galligo, M. Stillman, Gröbner bases and extensions of scalars, in: D. Eisenbud, L. Robbiano, Computational methods in Algebraic Geometry and Commutative Algebra, Symposia Mathematica 24 (1993)Google Scholar
  5. 5.
    W. Boege, R. Gebauer, H. Kredel, Some examples for solving systems of algebraic equations by calculating Gröbner bases, J. Symb. Comp. 2, 83–89Google Scholar
  6. 6.
    A. Bigatti, P. Conti, L. Robbiano, C. Traverse, A “Divide and Conquer” approach to the computation of the Hilbert-Poincaré series. AAECC-10, (1993)Google Scholar
  7. 7.
    P. Conti, C. Traverso, A Case of Automatic Theorem Proving in Euclidean Geometry: the Maclane 83 Theorem, Proc. AAECC-11, 1995, LNCS 948, 183–193Google Scholar
  8. 8.
    D. Cox, J. Little, D. O'Shea, Ideals, Varieties, and Algorithms, Springer-Verlag, (1992)Google Scholar
  9. 9.
    J.H. Davenport, Polynomial factorization, MEGA-96, to appear on J. Pure Appl. AlgebraGoogle Scholar
  10. 10.
    D. Eisenbud, Commutative Algebra, with a view towards Algebraic Geometry, Springer Verlag, (1994)Google Scholar
  11. 11.
    D. Eisenbud, C. Huneke, W. Vasconcelos, Direct methods for primary decomposition, Inventones Math, 110, (1992), p. 207–235.Google Scholar
  12. 12.
    D. Eisenbud, B. Sturmfels, Binomial ideals, Duke Math. J. 84, 1–45 (1996).Google Scholar
  13. 13.
    J.C. Faugère, P. Gianni, D. Lazard, T. Mora, Efficient computation of zero-dimensional Gröbner bases by change of ordering, J. Symb. Comp. 16(4), 329–344 (1993)Google Scholar
  14. 14.
    P. Gianni, Properties of Gröbner bases under specialization, Eurocal 1987, LNCS (1988)Google Scholar
  15. 15.
    P. Gianni, B. Trager, G. Zacharias, Gröbner bases and primary decomposition of polynomial ideals, J. Symb. Comp. 6, 149–167 (1988)Google Scholar
  16. 16.
    M. Kalkbrener, Solving systems of algebraic equations by using Gröbner bases, Eurocal 1987, LNCS (1988)Google Scholar
  17. 17.
    M. Kalkbrener, A generalized euclidean algorithm for computing triangular representations of algebraic varieties, J. Symb. Comp., 15:143–167, 1993.Google Scholar
  18. 18.
    M. Kalkbrener, Prime decomposition of radicals in polynomial rings, J. Symb. Comp. 18, 365–372, (1994)Google Scholar
  19. 19.
    D. Lazard, A new method for solving algebraic systems of positive dimension, Discr. App. Math, 33:147–160, (1991)Google Scholar
  20. 20.
    D. Mumford, Lectures on Curves on an Algebraic Surface, Annals of Math. Studies, (1966)Google Scholar
  21. 21.
    T. Shimoyama, K. Yokoyama, Localization and primary decomposition of polynomial ideals, J. Symbolic Computation 22, 247–277 (1996).Google Scholar
  22. 22.
    C. Traverso, Hilbert functions and the Buchberger algorithm, J. Symb. Comp. (1996)Google Scholar
  23. 23.
    W.V. Vasconcelos, Jacobian matrices and constructions in Algebra, AAECC-9, LNCS 539, (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Massimo Caboara
    • 1
  • Pasqualina Conti
    • 2
  • Carlo Traverse
    • 1
  1. 1.Dipartimento di MatematicaPisa
  2. 2.Dipartimento di Matematica applicataPisa

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