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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.

flag	asked Dec 14 at 0:51 Gwyn Whieldon 831●3●12

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It should not be difficult to code this in Mathematica, for example. – Mariano Suárez-Alvarez Dec 14 at 0:59

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You might try pinging Ezra Miller. I don't know about this particular case, but he is the sort of person who would write code to output the Tikz rather than do it by hand, and he's very friendly. (Bernd Sturmfels, who is also very friendly, is the sort of person who would get his co-author to output the code that output the Tikz :).) – David Speyer Dec 14 at 1:52

Software Reference Request: Three Dimensional Staircase Visualizers for Monomial Ideals

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