abstract: in this talk, i shall introduce the notion of polynomials with lorentzian signature. this class is a generalization to the remarkable class of lorentzian polynomials. the hyperbolic polynomials and conic polynomials are shown to be polynomials with lorentzian signature. using the notion of polynomials with lorentzian signature i shall describe how to compute the permanents of a special class of nonsingular matrices via hyperbolic programming. the nonsingular $k$ locally singular matrices are contained in the  special class of nonsingular matrices for which computing the permanents can be done via hyperbolic programming.