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# isNormal(Polyhedron) -- checks if a polytope is normal in the ambient lattice

- Function: isNormal
- Usage:
    `b = isNormal P`
- Inputs:
  - P, a convex polyhedron, which must be compact
- Outputs:
  - b, a Boolean value, true if P is normal in the ambient lattice

## Description

isNormal can only be applied to polytopes, i.e. compact polyhedra. It embeds the polytope on height 1 in a space of dimension plus 1 and takes the Cone over this polytope. Then it checks if all elements of the Hilbert basis lie in height 1.

    i1 : P = convexHull transpose matrix {{0,0,0},{1,0,0},{0,1,0},{1,1,3}}

    o1 = {ambient dimension => 3           }
          dimension of lineality space => 0
          dimension of polyhedron => 3
          number of facets => 4
          number of rays => 0
          number of vertices => 4

    o1 : Polyhedron

    i2 : isNormal P

    o2 = false

## Ways to use this method:

- isNormal(Polyhedron) -- checks if a polytope is normal in the ambient lattice

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/OldPolyhedra.m2:5696:0.