Finite fields¶
- class sage.categories.finite_fields.FiniteFields(base_category)[source]¶
- Bases: - CategoryWithAxiom_singleton- The category of finite fields. - EXAMPLES: - sage: K = FiniteFields(); K Category of finite enumerated fields - >>> from sage.all import * >>> 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] - >>> from sage.all import * >>> 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 - >>> from sage.all import * >>> FiniteField(Integer(17)) in K True >>> RationalField() in K False >>> K(RationalField()) Traceback (most recent call last): ... TypeError: unable to canonically associate a finite field to Rational Field