Basics for a polyhedron semiring

We explore the polyhedron semiring and show an approximation to solving matrix equalities over the polyhedron semiring, as well as show that some of the unbounded facets behave as a semiring and that the matrix equality can be reduced to individual inequalities. Finally, convex hull of vectors of polyhedra is introduced. This paper can be used to advance neural networks or to do calculations with intervals instead of average values.