Regular Decompositions

Guillaume Moroz (1)

1 SALSA - Solvers for Algebraic Systems and Applications

We introduce the notion of regular decomposition of an ideal and present a first algorithm to compute it. Designed to avoid generic perturbations and eliminations of variables, our algorithm seems to have a good behaviour with respect to the sparsity of the input system. Beside, the properties of the regular decompositions allow us to deduce new algorithms for the computation of the radical and the weak equidimensional decomposition of an ideal. A first implementation shows promising results.

Domaines: Informatique [cs]

Guillaume Moroz. Regular Decompositions. Computer Mathematics: 8th Asian Symposium, ASCM 2007, Revised and Invited Papers, Dec 2007, Singapore, Singapore. pp.263-277, ⟨10.1007/978-3-540-87827-8_22⟩. ⟨hal-01301333⟩