Internals

Function fields, in Hecke, come in several different types:

• RationalFunctionField: a field of the form $k(x)$ for a field $k$.
• FunctionField: a finite extension of a rational function field given by a polynomial.

Function fields with the type FunctionField are referred to as simple fields in the rest of this document. They are also referred to as being absolute.

Absolute Simple Fields

Internally function fields of type FunctionField are essentially represented as a unvariate quotient with the arithmetic provided by the AbstractAlgebra and Nemo packages. As they are defined generically for all AbstractAlgebra, Nemo and Hecke fields $k$ the function field type is implemented in AbstractAlgebra.