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 convex polyhedron, a polytope
  • M, a matroid, a matroid
  • S, a matrix, (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:
  • a Boolean value, whether or not a list of facet labels contains a flag in a polytope or matroid

Description

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

See also

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