next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
SlackIdeals :: findFlag

findFlag -- computes a list of facet labels that make up a flag in a polytope

Synopsis

Description

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

See also

Ways to use findFlag :