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2019-07-28 18:36:06 +0200	asked a question	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.