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

- 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

## Ways to use inInterior:

- `inInterior(Matrix,Cone)`
- `inInterior(Matrix,Polyhedron)`

## For the programmer

The object inInterior is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Polyhedra/documentation/old_documentation.m2:1721:0.