This package is joint with Brett Barwick. 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.
- A. Fabianska., Algorithmic analysis of presentations of groups and modules, Jan 2009.
- 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.
- Logar, Alessandro; Sturmfels, Bernd. Algorithms for the Quillen-Suslin theorem. J. Algebra 145 (1992), no. 1, 231--239. MR1144671 (92k:13006)
- T. Y. Lam, Serre's problem on projective modules. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2006.
For more information about the Macaulay2 system see https://github.com/Macaulay2/M2.