Polyhedron function for detecting if points are vertices

Hello i have to detect if a point is a vertex of my polyhedron. Here is what i have for now:

function [ ] = vertexdetect (A,b,x)

%detecting the dimensions of A,b and x

 if (size(x,1)~=size(A,2))
            error('The dimensions of A and x don't fit')
elseif (size(b,1)~=size(A,1)
            error('The dimensions of A and b don't fit')
end

 if(size(A,1)<size(A,2))
            disp('x is not a vertex, A has less rows than columns')

First I have to detect if x is element of my polyhedron P and secondly if x is a vertex of P. I just dont know how to detect this on P.

Can anyone help me?

Thank you in advance.

PS: the polyhedron is defined as an intersection of a finite set of closed halfspaces, P:={x in R^n | Ax<=b}

Answer 1

[CommunityGast]

Hey, is it possible to get some help for the second step? here is the first one

 if(A*x<=b)
   disp(x is in P)
 else
   disp(x is not in P)
end