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
characteristic(R::MyParent)
Return the characteristic of the field. If the characteristic is not known, an exception is raised.
Basic functions
is_unit(f::MyElem)
Return true
if the given element is invertible, i.e. nonzero in the field.