There is a description of the appropriate Groebner basis algorithm in this book: Franz Pauer, Andreas Unterkircher. [Gröbner Bases for Ideals in Laurent Polynomial Rings and their Application to Systems of Difference Equations.][1] AAECC 9, 271-291 (1999) I've implemented it in the single-variable case (in the software Regina) and I've been meaning to implement it in the multi-variable case as well. But I usually get too sad to finish -- when I look at how inefficient the algorithm is. Some day I'll have it fully implemented in Regina. The book is quite well written. I find it easy to read. [1]: http://www.springerlink.com/content/qgbwymag351atn71/fulltext.pdf