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()
sage: K
Category of finite fields

A finite field is a finite monoid with the structure of a field:

sage: K.super_categories()
[Category of fields, Category of finite commutative rings]

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

TESTS:

sage: TestSuite(FiniteFields()).run()
sage: FiniteFields().is_subcategory(FiniteEnumeratedSets())
True
class ElementMethods
class FiniteFields.ParentMethods

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