Complexity results for triangular sets

  title={Complexity results for triangular sets},
  author={{\'E}ric Schost},
  journal={J. Symb. Comput.},
We study the representation of the solutions of a polynomial system by triangular sets, and concentrate on the positive-dimensional case. We reduce to dimension zero by placing the free variables in the base field, so the solutions can be represented by triangular sets with coefficients in a rational function field. We give intrinsic-type bounds on the degree of the coefficients in such a triangular set, and on the degree of an associated degeneracy hypersurface. Then we show how to apply… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 49 references

Lower bounds for Diophantine approximation

  • M. Giusti, K. Hägele, J. Heintz, J. E. Morais, J. L. Montaña, L. M. Pardo
  • Journal of Pure and Applied Algebra,
  • 1997
Highly Influential
10 Excerpts

Ensembles triangulaires de polynômes et résolution de systèmes algébriques

  • P. Aubry
  • Implantation en Axiom. PhD thesis, Universite…
  • 1999
Highly Influential
5 Excerpts

Efficient algorithms and bounds for Wu-Ritt characteristic sets

  • G. Gallo, B. Mishra
  • In Proceedings of MEGA’90,
  • 1990
Highly Influential
7 Excerpts

Commutative Algebra with a view toward Algebraic Geometry, volume 150 of Graduate Texts in Mathematics

  • D. Eisenbud
  • 1996
Highly Influential
2 Excerpts

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