Given a polytope, a matroid, a cone, it finds a flag of facets or hyperplanes or cone generators that can be given as input to obtain a reduced slack matrix.
i1 : V = {{0, 0, 0}, {0, 0, 1}, {1, 0, 0}, {1, 0, 1}, {0, 1, 0}, {0, 1, 1}}; |
i2 : findFlag V Order of vertices is {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1, 0, 1}, {0, 1, 1}} Order of facets is {{0, 2, 3, 5}, {0, 1, 3, 4}, {1, 2, 4, 5}, {0, 1, 2}, {3, 4, 5}} o2 = {0, 1, 2, 4} o2 : List |
i3 : findFlag(V, Object => "matroid") Order of hyperplanes is {{2, 3, 4, 5}, {0, 1, 4, 5}, {1, 3, 5}, {0, 3, 5}, {1, 2, 5}, {0, 2, 5}, {1, 3, 4}, {0, 3, 4}, {1, 2, 4}, {0, 2, 4}, {0, 1, 2, 3}} o3 = {0, 1, 5, 7} o3 : List |
i4 : findFlag({{0, 2, 3, 5}, {0, 1, 3, 4}, {1, 2, 4, 5}, {0, 1, 2}, {3, 4, 5}}, Object => "abstractPolytope") Order of facets is {{0, 2, 3, 5}, {0, 1, 3, 4}, {1, 2, 4, 5}, {0, 1, 2}, {3, 4, 5}} o4 = {0, 1, 2, 4} o4 : List |
The object findFlag is a method function with options.