74 citations · 304 across the 21 of their papers we have counts for
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math.NA2017★ 2 cited
Rigid continuation paths I. Quasilinear average complexity for solving polynomial systems
Pierre Lairez
How many operations do we need on the average to compute an approximate root of a random Gaussian polynomial system? Beyond Smale's 17th problem that asked whether a polynomial bou…
cs.CG2017★ 18 cited
Computing the homology of basic semialgebraic sets in weak exponential time
Peter Bürgisser, Felipe Cucker, Pierre Lairez
We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of basic semialgebraic sets which works in weak exponential time. That is,…