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# containsFlag -- establishes whether or not a list of facet labels contains a flag in a polytope or matroid

## Synopsis

• Usage:
containsFlag(fl, P)
containsFlag(fl, M)
containsFlag(fl, S)
containsFlag(fl, V)
• Inputs:
• fl, a list, a list of facet labels
• P, , a polytope
• M, , a matroid
• S, , (symbolic) slack matrix
• V, a list, a list of vertex coordinates, matroid vectors, facet labels, or cone generators
• Optional inputs:
• Object => ..., default value "polytope", specify combinatorial object
• Outputs:
• , whether or not a list of facet labels contains a flag in a polytope or matroid

## Description

Given a list of facet labels fl and a polytope, a matroid, a (symbolic) slack matrix or a list of vertex coordinates, matroid vectors, facet labels, establishes whether or not fl contains a flag in the given object.

 i1 : V = {{0, 0, 0}, {0, 0, 1}, {1, 0, 0}, {1, 0, 1}, {0, 1, 0}, {0, 1, 1}}; i2 : containsFlag({0, 1, 2, 4}, V) Order of vertices is {{0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1, 0, 1}, {0, 1, 1}} o2 = true i3 : containsFlag({0, 1, 2, 8}, V, Object => "matroid") o3 = true i4 : containsFlag({0, 1, 2, 3}, {{0, 2, 3, 5}, {0, 1, 3, 4}, {1, 2, 4, 5}, {0, 1, 2}, {3, 4, 5}}, Object => "abstractPolytope") o4 = true

• findFlag -- computes a list of facet labels that make up a flag in a polytope
• reducedSlackMatrix -- a reduced slack matrix of a polytope

## Ways to use containsFlag :

• containsFlag(List,List)
• containsFlag(List,Matrix)
• containsFlag(List,Matroid)
• containsFlag(List,Polyhedron)

## For the programmer

The object containsFlag is .