An algorithm for unimodular completion over Laurent polynomial rings Original Research Article

We present a new and simple algorithm for completion of unimodular vectors with entries in a multivariate Laurent polynomial ring image over an infinite field K. More precisely, given ngreater-or-equal, slanted3 and a unimodular vector image (that is, such that left angle bracketv1,…,vnright-pointing angle bracket=R), the algorithm computes a matrix M in Mn(R) whose determinant is a monomial such that image, and thus M-1 is a completion of image to an invertible matrix.