Sharp estimates for triangular sets

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. Categories and Subject Descriptors

• Type: Conference
• Year: 2004
• Where: ISSAC
• Authors: Xavier Dahan, Éric Schost
• Keywords: ISSAC 2004, Rational Function field, Triangular Representation, Triangular Sets