1-INVERSES FOR POLYNOMIAL-MATRICES OF NONCONSTANT RANK

Let p//1. . . . , p//t be polynomials in C**n with a variety V of common zeros contained in a suitable open set U. Explicit formulas are provided to construct rational functions lambda //1,. . . . , lambda //s such that SIGMA p//i lambda //i equals 1, for i equals 1 to 5, and such that the singularities of the lambda //i are contained in U. This result is applied to compute rational functions-valued l-inverses of matrices with polynomial coefficients, which do not have constant rank, while retaining control over the location of the singularities of the rational functions themselves.