Given a 0-dimensional affine -algebra , where is an ideal in a polynomial ring over a field , or, equivalently, given a 0-dimensional affine scheme, we construct effective algorithms for checking whether is a complete intersection at a maximal ideal, whether is locally a complete intersection, and whether is a strict complete intersection. These algorithms are based on Wiebe’s characterization of 0-dimensional local complete intersections via the 0-th Fitting ideal of the maximal ideal. They allow us to detect which generators of form a regular sequence resp. a strict regular sequence, and they work over an arbitrary base field . Using degree filtered border bases, we can detect strict complete intersections in certain families of 0-dimensional ideals.
"Algorithms for checking zero-dimensional complete intersections." J. Commut. Algebra 14 (1) 61 - 76, Spring 2022. https://doi.org/10.1216/jca.2022.14.61