Triangular Systems and Factorized Gröbner Bases

In a preceding paper [9] we reported on some experience with a new version of the well known Grobner algorithm with factorization and constraint inequalities. Here we discuss, how this approach may be refined to produce triangular systems in the sense of [12] and [13]. Such a refinement guarantees, different to the usual Grobner factorizer, to produce a quasi prime decomposition, i.e. the resulting components are at least pure dimensional radical ideals. As in [9] our method weakens the usual restriction to lexicographic term orders.