Abstract
Polynomial homotopy continuation is at the heart of numerical algebraic geometry, an area whose primary goal is to solve systems of polynomial equations. Recently this field developed rapidly producing several software packages that solve some problems out of reach for purely symbolic techniques. However, the homotopy tracking procedures employ heuristics to follow the homotopy continuation paths. Jointly with Carlos Beltran we have devised a certified homotopy tracking algorithm, which was implemented in Macaulay2. In addition we conducted experiments shedding light on some developments in complexity analysis of polynomial systems solving.
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