%0 Journal Article
%T A lifted square formulation for certifiable Schubert calculus
%A Nickolas Hein
%A Frank Sottile
%J Mathematics
%D 2015
%I arXiv
%X Formulating a Schubert problem as the solutions to a system of equations in either Pl\"ucker space or in the local coordinates of a Schubert cell usually involves more equations than variables. Using reduction to the diagonal, we previously gave a primal-dual formulation for Schubert problems that involved the same number of variables as equations (a square formulation). Here, we give a different square formulation by lifting incidence conditions which typically involves fewer equations and variables. Our motivation is certification of numerical computation using Smale's \alpha-theory.
%U http://arxiv.org/abs/1504.00979v2