LATTICES OF COMPATIBLY EMBEDDED FINITE-FIELDS

The design of a computational facility for finite fields that allows c omplete freedom in the manner in which fields are constructed, is comp licated by the fact that a field of fixed isomorphism type K may be co nstructed in many different ways. It is desirable that the user be abl e to perform simultaneous computations in different versions of K in s uch a way that isomorphisms identifying elements in the different vers ions are applied automatically whenever necessary. This paper presents a coherent scheme for solving this problem based on an efficient meth od for compatibly embedding one field within another. This scheme form s a central component of the MAGMA module for finite fields. The paper also outlines the different representations of finite fields employed in the package and comments briefly on some of the major algorithms. (C) 1997 Academic Press Limited.