On The Volume And Integral Points Of A polyhedron In

Computing the volume and integral points of a polyhedron in is a very important subject in different areas of mathematics. There are two representations for the polyhedron, namely the H-representation and the V-representation. For each representation we give a different method of finding the volume and number of integral points. Moreover, the Ehrhart polynomial of a bounded polyhedron is discussed with some methods for finding it. One of these methods is modified and we prove two theorems for computing the coefficients of the Ehrhart polynomial. Also, a modified method for counting the number of integral points of   a bounded polyhedron is given, and it makes matrix operations on the matrix that represents the bounded polyhedron, and studies the effect of these operations on these numbers.All of the used methods are demonstrated with different examples.