Finite fields comprise an important algebraic domain. The elements in a field form an additive group and the nonzero elements form a multiplicative group. For every prime power q there exists a unique field of size q up to isomorphism. GAP supports finite fields of size at most 2^{16}.
The first section in this chapter describes how you can enter elements of finite fields and how GAP prints them (see Finite Field Elements).
The next sections describe the operations applicable to finite field Operations for Finite Field Elements).
The next section describes the function that tests whether an object is a finite field element (see IsFFE).
The next sections describe the functions that give basic information about finite field elements (see CharFFE, DegreeFFE, and OrderFFE).
The next sections describe the functions that compute various other representations of finite field elements (see IntFFE and LogFFE).
The next section describes the function that constructs a finite field (see GaloisField).
Finite fields are domains, thus all set theoretic functions are Set Functions for Finite Fields).
Finite fields are of course fields, thus all field functions are Field Functions for Finite Fields).
All functions are in LIBNAME/"finfield.g".
GAP 3.4.4