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# 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, , over ZZ or QQ with only one column representing a point
• Outputs:
• b, , 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 = {ambient dimension => 3 } dimension of lineality space => 0 dimension of polyhedron => 3 number of facets => 6 number of rays => 0 number of vertices => 5 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 .