Irreducible decomposition of algebraic varieties via characteristics sets and Gröbner bases

This paper presents a method for decomposing algebraic varieties into irreducible components by using characteristic sets and Gröbner bases. A set of 16 examples is provided to explain the geometric meaning of the irreducible decomposition and as a test bed for our experiments with the method. A function that implements the presented method has been included in the author's characteristic sets package in the Maple system and used to decompose a number of non-trivial algebraic varieties. A few strategies adopted in our implementation and the timing statistics for the 16 test examples are given.