A matrix algorithm for the root distribution of a set of polynomials with respect to conic contours

An existent conformal transformation technique for finding the root distribution of real polynomials with respect to circular contours is put into a matrix context that allows for the simultaneous testing of an arbitrary number of polynomials of the same degree. It is then shown that the algorithm can be extended to more general contours, and as an illustration it is applied to the family of conics.