Algorithms for the Quillen-Suslin theorem (Q1183295)

Let \(R\) be the polynomial ring in \(n\) variables over \(\mathbb{C}\) and let \(A\) be a unimodular \(k\times m\)-matrix \((k\leq m)\) over \(R\). The authors present an algorithm (using Gröbner bases) for computing a unimodular \(m\times m\)-matrix \(U\) (over \(R\)) such that \(A.U=(I_ k\mid 0)\). This implies a constructive proof of the Quillen-Suslin theorem. Moreover, this algorithm is applied to solve the following problem: Decide if an \(R\)-submodule of \(R^ s\), given by a finite set of generators, is free and (if it is) construct a \(R\)-basis of it.