Field functionality

Abstract types for rings

All field types in AbstractAlgebra belong to the Field abstract type and field elements belong to the FieldElem abstract type.

As Julia types cannot belong to our FieldElem type hierarchy, we also provide the union type FieldElement which includes FieldElem in union with the Julia types Rational and AbstractFloat.

Note that

Field <: Ring
FieldElem <: RingElem
FieldElement <: RingElement

Of course all Ring functionality is available for AbstractAlgebra fields and their elements.

Functions for types and parents of fields


Return the characteristic of the field. If the characteristic is not known, an exception is raised.

Basic functions


Return true if the given element is invertible, i.e. nonzero in the field.