most citedStrong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry

9 citations · 14 across the 3 of their papers we have counts for

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cs.SC2009★ 3 cited

Computing rational points in convex semi-algebraic sets and SOS decompositions

Mohab Safey El Din, Lihong Zhi

Let , for , bounding the bit length of the coefficients of the 's, and be a quantif…

cs.SC2009★ 2 cited

A baby steps/giant steps Monte Carlo algorithm for computing roadmaps in smooth compact real hypersurfaces

Mohab Safey El Din, Éric Schost

We consider the problem of constructing roadmaps of real algebraic sets. The problem was introduced by Canny to answer connectivity questions and solve motion planning problems. Gi…

cs.SC2006★ 9 cited

Strong bi-homogeneous Bézout theorem and its use in effective real algebraic geometry

Mohab Safey El Din, Philippe Trebuchet

Let f1, ..., fs be a polynomial family in Q[X1,..., Xn] (with s less than n) of degree bounded by D. Suppose that f1, ..., fs generates a radical ideal, and defines a smooth algebr…