Supplemental material for HDCV

This page includes supplemental material for “Higher distance commuting varieties”, by Madeleine Elyze, Alexander Guterman, and Ralph Morrison.  The supplemental files are all input for, or output from, Macaulay2.

  • For the distance-2 commuting variety with 2×2 matrices from the start of Section 5, this code generates the 8×4 D matrix, and computes its 3×3 minors. This code finds an alternate set of defining polynomials by performing the saturation/elimination technique.
  • For the distance-2 commuting variety with 3×3 matrices, this code generates the 18×9 D matrix; the ideal of 8×8 minors would be computed using the command minors(8,D). This code finds an alternate set of defining polynomials by performing the saturation/elimination technique.  It outputs these generators.  The commands dim() and degree() can be used to compute the dimension and the degree of the ideal, respectively.