Algorithms for Del Pezzo surfaces of degree 5 (construction, parametrization)

@article{GonzlezSnchez2012AlgorithmsFD,
  title={Algorithms for Del Pezzo surfaces of degree 5 (construction, parametrization)},
  author={Jon Gonz{\'a}lez-S{\'a}nchez and Michael Harrison and Irene Polo-Blanco and Josef Schicho},
  journal={J. Symb. Comput.},
  year={2012},
  volume={47},
  pages={342-353}
}
It is well known that every Del Pezzo surface of degree 5 defined over a field k is parametrizable over k. In this paper we give an algorithm for parametrizing, as well as algorithms for constructing examples in every isomorphism class and for deciding equivalence.