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Borel-fixed ideals play a key role in the study of Hilbert schemes. Indeedeach component and each intersection of components of a Hilbert scheme containsat least one Borel-fixed point, i.e. a point corresponding to a subschemedefined by a Borel-fixed ideal. Moreover Borel-fixed ideals have goodcombinatorial properties, which make them very interesting in an algorithmicperspective. In this paper, we propose an implementation of the algorithmcomputing all the saturated Borel-fixed ideals with number of variables andHilbert polynomial assigned, introduced from a theoretical point of view in thepaper "Segment ideals and Hilbert schemes of points", Discrete Mathematics 311(2011).

An efficient implementation of the algorithm computing the Borel-fixed points of a Hilbert scheme