
322 Algebraic Operads: An Algorithmic Companion
to our surprise that these computations illustrate the remarkable effectiveness
of the plex order in certain cases. We computed Gröbner bases for both the
ideal and its radical, and the zero sets in both cases, for all ranks r ≤ 9, using
a Lenovo ThinkCentre. The sets of original generators of the determinantal
ideals, namely the r × r minors, had the following sizes, after removing zero
polynomials and making remaining polynomials monic:
minors: 18, 123, 560, 1821, 4069, 5951, 5297, 2473, 420.
Using the plex order, the Gröbner bases of ideal and radical have these sizes:
order ideal radical
a ≺ b 3, 5,