In a series of papers, Dr. Le Ngoc Long (University of Passau and Hue University), Prof. Lorenzo Robbiano (Università di Genova) and Prof. Martin Kreuzer develop algorithms to check 0-dimenisonal schemes for certain algebraic and geometric properties. Furthermore, they derive algorithms to compute the locus of all schemes having a particular property inside the moduli space given by the border basis scheme.
-  M. Kreuzer, Le Ngoc Long and L. Robbiano, On the Cayley-Bacharach property, Comm. Algebra 47 (2019), 328-354, DOI:10.1080/00927872.2018.1476525
-  M. Kreuzer, L.N. Long and L. Robbiano, Algorithms for checking zero-dimensional complete intersections, J. Commut. Algebra (to appear), available at arXiv:1903.09563 [math.AC]
-  M. Kreuzer, Le N. Long and L. Robbiano, Computing subschemes of the border basis scheme, Preprint 2019, available at arXiv:1910.09426 [math.AC]
The following CoCoA code was implemented by Dr. Le Ngoc Long:
CoCoA-5 package: BBS_subschemes.cpkg
Source code for the examples in : BBS_examples.cocoa5
Details can be found on the projects website.
In this software project the computeralgebra framework ApCoCoA is developed.