This is more of a general question, I don't necessarily have a specific question I've been given.

Part of one of my modules includes finding Hilbert Basis of cones; a question I'm given might look something like:

Given $A= \pmatrix{2&3\\0&1}$ and $b=(9/2 , 3/2)^T$, use Chvatal-Gomory algorithm to find the integer hull $P_I$

Part of the working out of this question requires me to find the Hilbert basis, in this example I'm trying to find the Hilbert basis of the cone $A_F$ which is generated by $(2,3)^T$ and $(0,1)^T$ (obtained from $A$).

What I want to know is if there is a way to find these Hilbert basis without needing to draw the cone, in examples I have available to me the method used is to draw the cone and find the hilbert basis using the diagram, however, I really dislike this method, mainly because the diagram drawn must be extremely accurate otherwise I might miss out one of the Hilbert basis or some other error might occur.

If anyone knows another method that would work then I'd love to see it, or if the method of drawing the cone is the best method I have available to me then I guess I'll just have to accept it.

Any help would be greatly appreciated

Thanks in advance

  • $\begingroup$ I would just like to add that I am able to use the diagram method to obtain my hilbert basis, I'm just curious to know if there is another method available. $\endgroup$
    – Charlie P
    Jan 14 at 18:17

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