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Using symmetric functions to describe the solution set of a zero dimensional ideal

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References

  1. M.-E. Alonso, E. Becker, M.-F. Roy and T. Wörmann: Zeros, Multiplicities and Idempotents for Zerodimensional Systems. To appear in the proceedings of MEGA-94 to be published by Birkhaüsei in the series Progress in Mathematics (1994).

    Google Scholar 

  2. W. Auzinger and H. J. Stetter: An Elimination Algorithm for the Computation of all Zeros of a System of Multivariate Polynomial Equations. Int. Series in Numerical Mathematics 86, 11–30, Birkhäuser (1988).

    Google Scholar 

  3. E. Becker, M. G. Marinari, T. Mora and C. Traverso: The shape of the Shape Lemma. Proceedings of ISSAC-94, 129–133, ACM Press (1993).

    Google Scholar 

  4. E. Becker and T. Wörmann: On the trace formula for quadratic forms and some applications. Recent Advances in Real Algebraic Geometry and Quadratic Forms. Contemporary Mathematics 155, 271–291, AMS Publications (1993).

    Google Scholar 

  5. J. F. Canny: The complexity of robot motion planning. ACM Doctoral Dissertation Series, MIT Press, Cambridge Mass. (1988).

    Google Scholar 

  6. E. Cattani, A. Dickenstein and B. Sturmfels: Computing Multidimensional Residues. To appear in the book Algorithms in Algebraic Geometry and Applications to be published by Birkhaüser in the series Progress in Mathematics (1994).

    Google Scholar 

  7. J. C. Faugère: Résolution de systèmes d'équations algébriques. Doctoral Thesis, Université Paris 6, February 1994.

    Google Scholar 

  8. P. Gianni and T. Mora: Algebraic solution of polynomial equations using Gröbner bases. Proceedings AAECC-5. Lectures Notes in Computer Science 359, 247–257, Springer-Verlag (1989).

    Google Scholar 

  9. M. Giusti and J. Heintz: La determination des points isoles et de la dimension d'une variete algebrique peut se faire en temps polynomial. To appear in the Proc. of the International Meeting on Computational Commutative Algebra, 1991.

    Google Scholar 

  10. T. Krick and L. M. Pardo: A Computational Method for Diophantine Approximation. To appear in the book Algorithms in Algebraic Geometry and Applications to be published by Birkhaüser in the series Progress in Mathematics (1994).

    Google Scholar 

  11. Y. N. Lakshman and D. Lazard: On the Complexity of Zero-dimensional Algebraic Systems. Effective Methods in Algebraic Geometry. Progress in Mathematics 94, 217–225, Birkhauser (1991).

    Google Scholar 

  12. I. G. Macdonald: Symmetric functions and Hall polynomials. Oxford University Press (1979).

    Google Scholar 

  13. P. Pedersen, M.-F. Roy and A. Szpirglas: Counting Real Zeros in the muitivariate case. Computational Algebraic Geometry, Progress in Mathematics 109, 61–76, Birkhaüser (1993).

    Google Scholar 

  14. F. Rouillier. Doctoral thesis in preparation (1995).

    Google Scholar 

  15. A. K. Tsikh: Multidimensional Residues and Their Applications. Translations of Mathematical Monographs 103, American Mathematical Society (1992).

    Google Scholar 

  16. K. Yokoyama, M. Noro and T. Takeshima: Solutions of Systems of Algebraic Equations and Linear Maps on Residue Class Rings. Journal of Symbolic Computation 14, 399–417 (1992).

    Google Scholar 

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Gérard Cohen Marc Giusti Teo Mora

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© 1995 Springer-Verlag Berlin Heidelberg

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González-Vega, L., Trujillo, G. (1995). Using symmetric functions to describe the solution set of a zero dimensional ideal. In: Cohen, G., Giusti, M., Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1995. Lecture Notes in Computer Science, vol 948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60114-7_17

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  • DOI: https://doi.org/10.1007/3-540-60114-7_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60114-2

  • Online ISBN: 978-3-540-49440-9

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