  It is well known that the classification of pure multiparticle entangled
states according to stochastic local operations leads to a natural
classification of mixed states in terms of convex sets. We present a simple
algorithmic procedure to prove that a quantum state lies within a given convex
set. Our algorithm generalizes a recent algorithm for proving separability of
quantum states [J. Barreiro et al., Nature Phys. 6, 943 (2010)]. We give
several examples which show the wide applicability of our approach. We also
propose a procedure to determine a vicinity of a given quantum state which
still belongs to the considered convex set.
