inInterior -- checks if a point lies in the relative interior of a Cone/Polyhedron

Synopsis

• Usage:

  b = inInterior(p,C)

  b = inInterior(p,P)

• Inputs:
  • p, a matrix, over ZZ or QQ with only one column representing a point
  • C, a convex rational cone
  • P, a convex polyhedron
• Outputs:
  • b, a Boolean value, true if p lies in the relative interior of the Cone/Polyhedron, false otherwise

Description

inInterior checks if the smallest face of the Cone or the Polyhedron containing p is the Cone or the Polyhedron itself. For this the number of rows of p must equal the ambient dimension of the second argument.

i1 : P = cyclicPolytope(3,5)

o1 = P

o1 : Polyhedron

i2 : p = matrix{{2},{4},{8}}

o2 = | 2 |
     | 4 |
     | 8 |

              3        1
o2 : Matrix ZZ  <--- ZZ

i3 : q = matrix{{2},{6},{20}}

o3 = | 2  |
     | 6  |
     | 20 |

              3        1
o3 : Matrix ZZ  <--- ZZ

i4 : inInterior(p,P)

o4 = false

i5 : inInterior(q,P)

o5 = true