Fields are important algebraic domains. Mathematically a field is a
commutative ring F (see chapter Rings), such that every element
except 0 has a multiplicative inverse. Thus F has two operations +
and * called addition and multiplication. (F,+) must be an abelian
group, whose identity is called 0_F. (F-{0_F},*) must be an
abelian group, whose identity element is called 1_F.
GAP supports the field of rationals (see Rationals), subfields of cyclotomic fields (see Subfields of Cyclotomic Fields), and finite fields (see Finite Fields).
This chapter begins with sections that describe how to test whether a domain is a field (see IsField), how to find the smallest field and the default field in which a list of elements lies (see Field and Fields over Subfields).
The next sections describes the operation applicable to field elements Operations for Field Elements).
The next sections describe the functions that are applicable to fields (see GaloisGroup) and their elements (see Conjugates, Norm, Trace, CharPol, and MinPol).
Field Homomorphisms, IsFieldHomomorphism, KernelFieldHomomorphism, Mapping Functions for Field Homomorphisms).
The last section describes how fields are represented internally (see Field Records).
Fields are domains, so all functions that are applicable to all domains are also applicable to fields (see chapter Domains).
All functions for fields are in LIBNAME/"field.g".
GAP 3.4.4