# Implementation Notes

The algorithms for recognizing Frobenius elements in Galois groups are described in [[Dokchitser and Dokchitser, 2013](../../references.md#cite-ddfrob13)]. They rely on the cycle type identification, Serre’s trick for alternating groups and the general machinery from [[Dokchitser and Dokchitser, 2013](../../references.md#cite-ddfrob13)]. Magma is usually able to handle Galois groups of size $<10000$ acting on a small number of points easily, and much larger special groups such as $A_n$ and $S_n$.