Finite fields¶

class
sage.categories.finite_fields.
FiniteFields
(base_category)¶ Bases:
sage.categories.category_with_axiom.CategoryWithAxiom_singleton
The category of finite fields.
EXAMPLES:
sage: K = FiniteFields(); K Category of finite enumerated fields
A finite field is a finite monoid with the structure of a field; it is currently assumed to be enumerated:
sage: K.super_categories() [Category of fields, Category of finite commutative rings, Category of finite enumerated sets]
Some examples of membership testing and coercion:
sage: FiniteField(17) in K True sage: RationalField() in K False sage: K(RationalField()) Traceback (most recent call last): ... TypeError: unable to canonically associate a finite field to Rational Field

class
ElementMethods
¶

class
ParentMethods
¶

extra_super_categories
()¶ Any finite field is assumed to be endowed with an enumeration.

class