Sharp estimates for triangular sets

Authors:
Xavier Dahan;Éric Schost
Affiliations:
École Polytechnique, Palaiseau, France;École Polytechnique, Palaiseau, France
Venue:
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Year:
2004

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Abstract

We study the triangular representation of zero-dimensional varieties defined over the rational field (resp. a rational function field). We prove polynomial bounds in terms of intrinsic quantities for the height (resp. degree) of the coefficients of such triangular sets, whereas previous bounds were exponential. We also introduce a rational form of triangular representation, for which our estimates become linear. Experiments show the practical interest of this new representation.