|Title||Efficient algorithms for ideal operations|
|Author(s)|| Massimo Caboara, Carlo Traverso|
|Type||Article in Conference Proceedings|
|Abstract||In this paper we review the known algorithms for performing the basic algorithms for ideal and submodule operations: intersection, transporter and saturation.|
The algorithms known in the literature for these operations on polynomial rings fall largely into two classes: syzygy algorithms and elimination algorithms. We show that the two classes substantially coincide: they can be seen at most as variants of the same algorithm.
We show moreover that these algorithms can be generalized to another algorithm, a module elimination algorithm, that allows the use of a Hilbert function driven algorithm and that, with this feature, appears to be the most efficient algorithm in this class.
We give some examples that support this assertion.
Because of space constraints we skip all the proofs, that will appear in a full paper together with more exhaustive experiments.