Fall 2014

Bertini_real: Software for Real Algebraic Sets

Tuesday, October 14th, 2014 4:00 pm4:25 pm

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Calvin Lab Auditorium

Bertini_real is software for decomposing real algebraic sets in any number of variables. Using Bertini's homotopy continuation tracker as its main engine, Bertini_real uses random real linear projections to implicitly parametrize the targeted algebraic set. By finding the critical sets — the places where the set is singular with respect to the projections — and then connecting the computed points on them, we produce a decomposition in terms of cells, where the interior is a singularity-free region, and the boundaries are critical, singular, or an artificially imposed boundary capturing infinite behavior. Bertini_real currently will decompose sets of dimension 1 or 2; i.e. curves and surfaces. Bertini_real is a numerical method for performing decompositions, and offers improvements over existing algorithms in terms of the number of variables defining the variety, as well as allowing tracking on and decomposition of singular components. The cellular decomposition is readily refined, visualized, and 3D printed.