  Traditional formulations of geometric problems from the Schubert calculus,
either in Plucker coordinates or in local coordinates provided by Schubert
cells, yield systems of polynomials that are typically far from complete
intersections and (in local coordinates) typically of degree exceeding two. We
present an alternative primal-dual formulation using parametrizations of
Schubert cells in the dual Grassmannians in which intersections of Schubert
varieties become complete intersections of bilinear equations. This formulation
enables the numerical certification of problems in the Schubert calculus.
