Some applications of Gröbner bases
Eugenio Roanes-lozano, Eugenio Roanes-macías, Luis M. Laita · 2004
... this article, we give more details about Gröbner bases and describe their main application (algebraic system solving) along with some surprising derived ones: inclusion of varieties, automatic theorem-proving in geometry, expert systems, and railway interlocking systems. Reduced Gröbner Bases In the previous article, we introduced Gröbner bases of ideals—with an ideal being the set of algebraic linear combinations of a given set of polynomials—as a tool for algebraic system solving (that is, general polynomial system solving). We solved such systems using simple commands in a computer algebra system such as Maple. Let’s review an example from the previous article. Example 1. The solution set of the system ⎧ 2 2 ⎪x − y − z = 0 (hyperbolic paraboloid)