While thin on details, I found the article A new efficient algorithm for computing GrÃ¶bner basis intriguing. While a naive implementation of GrÃ¶bner bases is easy to come by, as a practical algorithm it is highly sensitive to the order in which you add new polynomials to the basis. This has given rise to a whole literature on strategies to add new polynomials. In the paper, Faugere seems to suggest that the whole question can be bypassed, and that polynomials can be added to the basis in bulk by using sparse linear algebra techniques.