Irreducible decomposition of algebraic varieties via characteristic sets and Gröbner bases (Q1195755)

The author investigates algorithms for decomposing affine algebraic varieties of low degree, defined over a field of characteristic 0, into irreducible components using Gröbner bases and characteristic sets. He describes his method and the algorithms he used as a function in his characteristic sets package in the Maple system. A list of examples is given with the timing statistics. More information on the author's factorization method are given in the author's previous papers [``An implementation of the characteristic set method in Maple'', Proc. DISCO'92, Bath, April 13-15 (1992), and ``A method for factorizing multivariate polynomials over successive algebraic extension fields'' (preprint, Res. Inst. Symb. Comput., Univ. Linz)].