Using the algorithms in Logar-Sturmfels and Fabianska-Quadrat, this package computes a free basis of a projective module over a polynomial ring with coefficients in the rationals, integers, or a finite field. It also provides methods to solve related problems involving completing a unimodular matrix to a square invertible matrix over a polynomial ring with coefficients in the rationals, integers, or a finite field, or a Laurent polynomial ring with coefficients in the rationals or a finite field.
For mathematical background and applications, see
A. Fabianska. Algorithmic analysis of presentations of groups and modules. http://darwin.bth.rwth-aachen.de/opus/volltexte/2009/2950/, Jan 2009.
T. Y. Lam. Serre's problem on projective modules. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2006.
A. Logar and B. Sturmfels. Algorithms for the Quillen-Suslin theorem. J. Algebra, 145(1):231-239, 1992.
A. Fabianska and A. Quadrat. Applications of the Quillen-Suslin theorem to multidimensional systems theory. Grobner bases in control theory and signal processing. Radon Series Comp. Appl. Math (3):23-106, 2007.