# Extremal Rays of a Cone

Can I use Sage to compute the subspace of a vector space that lies in non-negative real Euclidean space?

For example,

If I compute the nullspace of the matrix,

A =

[ [ 1 0 0 -1 0]

[-1 1 0 0 1]

[ 0 -1 1 0 0]

[ 0 0 -1 1 -1] ]

I get,

[1,1,1,1,0],[0,−1,−1,0,1]

as basis. Now I would like to restrict the solution space to only vectors with non-negative entries. I believe the two basis vectors I am looking for are,

[1,1,1,1,0],[1,0,0,1,1].

My program is written in Python, but I am not sure there is anything written for this sort of problem. Using the simplex method of linear programming (objective function set to zero) only spits out a single solution vector which seems to be the sum of the two I want. I ask here because I see some classes for cones and methods that gives the extremal rays, but it seems I already have to know the extremal rays to use that class.