flowPolytope -- generate the polytope associated to a toric quiver

Synopsis

• Usage:

  flowPolytope Q

  flowPolytope(W, Q)

• Inputs:
  • Q, an instance of the type ToricQuiver,
  • W, a list, of integer values specifying a weight on the vertices
• Optional inputs:
  • Format (missing documentation) => a string, default value "SimplifiedBasis", specifying what basis to use. The default value SimplifiedBasis returns the polytope in a basis giving the minimal degree necessary for polytope dimension.
• Outputs:
  • a matrix, giving the coordinates of the vertices defining the flow polytope

Description

i1 : flowPolytope(bipartiteQuiver(2, 3))

o1 = {{-1, 1}, {-1, 0}, {1, -1}, {0, -1}, {1, 0}, {0, 1}}

o1 : List

i2 : flowPolytope({-3,-3,2,2,2}, bipartiteQuiver(2, 3))

o2 = {{-1, 1}, {-1, 0}, {1, -1}, {0, -1}, {1, 0}, {0, 1}}

o2 : List

See also

• basisForFlowPolytope -- compute the necessary basis vectors for the hyperplane of a flow polytope