5 Conclusions

This paper represents the actual realization of the ideas presented in Paper I. The performance of the new numerical code is a clear indication that analytical studies on the RTE, as the one presented in Paper I, are of great importance not only from the theoretical point of view, but also from the practical point of view, as they can provide

us with high-performance codes capable of solving more and more complicated model atmospheres in reasonable times.

Measurement of magnetic fields in the sun rely on inversion codes based nowadays on minimization techniques which make an intensive use of integrators. Any improvement in the performance of these integrators involves an immediate improvement on the results obtained with the inversors. The number of instruments providing polarimetric information is in permanent growing, as well as the quantity of information provided by each one of them. It is an imperious necessity therefore to accelerate and improve at the same time the available integration and inversion methods if we want to deal with all that fresh data.

Two main trends can be followed for that purpose, the first one is to rely on purely numerical techniques, the second one to deepen in the knowledge of the RTE to take advantage of its symmetries, characteristics and so on. DIAGONAL was conceived in this second spirit. It is worth noting that both trends may be combined and profit from a theoretical advantage by means of powerful numerical techniques. In this sense DIAGONAL will be a first prototype of new integrators grounded on deep theoretical basis. The code is available, upon request to the authors.