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4 papers · 2 filters
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…
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…
Fast algorithms for differential equations in positive characteristic
Alin Bostan, Éric Schost
We address complexity issues for linear differential equations in characteristic : resolution and computation of the -curvature. For these tasks, our main focus is on algor…
On finding multiplicities of characteristic polynomial factors of black-box matrices
Jean-Guillaume Dumas, Clément Pernet, B. David Saunders
We present algorithms and heuristics to compute the characteristic polynomial of a matrix given its minimal polynomial. The matrix is represented as a black-box, i.e., by a functio…