A lifted square formulation for certifiable Schubert calculus

2016 Formulating a Schubert problem as the solutions to a system of equations in either Plcker 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 primaldual 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 -theory.

A lifted square formulation for certifiable Schubert calculus Academic Article