Is anyone familiar with software that already exists to visualize monomial ideals in three variables as their staircase diagrams, in the sense of Combinatorial Commutative Algebra? It looks like their graphics were done using TikZ, but after a reasonable search, I wasn't able to find any pre-written packages or software that would automatically produce a picture of the staircase diagram of a monomial ideal.
It was easy enough to write a few lines of code in Macaulay2 to produce the TikZ code for the two-dimensional case, but I wasn't looking forward to writing code to do the same thing in the three variable case if this already existed somewhere. If there was code to draw these things using ideals encoded in Macaulay2, Singular, or Sage format, I would love that -- but if there's any pre-done visualizer for three variable monomial ideals, I would happily compromise on format.
Alternately, if someone has software (or knows a good reference to software) which produces visualizations of the Buchberger graph for one of these monomial ideals, I'd be willing to settle for that too.