Summary: In some practical situations (e.g., in econometrics), it is important to check whether a given linear subspace of a space \(\mathbb R^m\) with component-wise order is a lattice -- and if it is not, whether it is at least a directed ordered space. Because of the practical importance, it is desirable to have feasible algorithms for solving these problems -- which in Computer Science is usually interpreted as algorithms whose computation time does not exceed a polynomial of the length of the input. No such algorithms were previously known. In this paper, we present feasible algorithms for solving both problems.