Computing the Degrees of All Cofactors in Mixed Polynomial Matrices

A mixed polynomial matrix is a polynomial matrix which has two kinds of nonzero coefficients: fixed constants that account for conservation laws and independent parameters that represent physical characteristics. This paper presents an algorithm for computing the degrees of all cofactors simultaneously in a regular mixed polynomial matrix. The algorithm is based on the valuated matroid intersection and all pair shortest paths. The technique is also used for improving the running time of the algorithm for minimizing the index of the differential-algebraic equation in the hybrid analysis for circuit simulation.