Uniform gaussoidsUniform gaussoids are orientations of the empty gaussoid. Since the
supporting gaussoid is empty, all symbols DownloadsWe enumerated uniform gaussoids for Realizability of uniform 4-gaussoidsTo search realizing matrices for gaussoids, it suffices to look for positive-definite
matrices with all 1s on the diagonal. For the Our SCIP input files are available as an archive: u4-scip.tar.bz2.
The numbering of the files follows Table 2 in the paper. We proceed to explain the contents
of the pip files. The 6 unknowns can be supposed to be positive and, given a uniform
gaussoid, are endowed with the appropriate signs inside the unknown realizing matrix.
The signs of the The contents of Table 2 are also available as a text file: table2.txt. There is a sage program to verify it: check-table2.sage. Enumeration detailsWe can use one Boolean variable (a^b)->(b^c^d) These are the files ucnf* in the table below. Orientations of a given gaussoidMore generally, we have a procedure to print a cnf describing all orientations of a given gaussoid. It works by mutilating all edge trinomials according to the gaussoid and adding specific compatibility clauses depending on how the mutilated polynomial turns out. Since all symbols which remain after mutilation are in
It suffices to replace 0 with + and 1 with - in the output of minisat2binary.pl to obtain a human-readable listing of uniform gaussoids: $ minisat2binary.pl <ucnf3-list | tr '01' '+-' >ucnf3-list.txt |