|Title||Yet Another Algorithm for Ideal Decomposition|
|Author(s)|| Massimo Caboara, Pasqualina Conti, Carlo Traverso|
|Type||Article in Conference Proceedings|
|Abstract||In this paper we describe algorithms to compute equidimensional decompositions of an ideal I of a polynomial ring.|
The decompositions that we can compute are either faithful , i.e. the intersection of the components is the ideal itself, reduced , i.e. the components coincide with their radical, and their intersection is the radical of I, or iso-radical.
The algorithms do not require change of coordinates, nor lexicographical Gröbner bases and GCD on algebraic extensions, and are based on projections in codimension 1 and flatness analysis.
In our algorithms there are several points where an arbitrary choices are required. In our experience, smart choice strategies offer a substantial performance improvement.
We report a series of experiments both with semi-automatic computations and with an experimental implementation in CoCoA. They seem to support the claim that the algorithm for reduced decomposition, with smart choice strategies, is much more efficient than the Eisenbud-Huneke-Vasconcelos algorithm for the radical implemented in Macaulay, since the range of problems that we are able to solve seems to be far larger.