  The quantitative assessment of the entanglement in multipartite quantum
states is, apart from its fundamental importance, a practical problem. Recently
there has been significant progress in developing new methods to determine
certain entanglement measures. In particular, there is a method---in principle,
analytical---to compute a certified lower bound for the three-tangle. The
purpose of this work is to provide a manual for the implementation of this
approach and to explicitly discuss several analytically solvable cases in order
to gauge the numerical tools. Moreover, we derive a simple analytical bound for
the mixed state three-tangle.
