Finite Fields¶
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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 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
TESTS:
sage: K is Fields().Finite() True sage: TestSuite(K).run()
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class
ElementMethods
¶
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class
FiniteFields.
ParentMethods
¶
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FiniteFields.
extra_super_categories
()¶ Any finite field is assumed to be endowed with an enumeration.
TESTS:
sage: Fields().Finite().extra_super_categories() [Category of finite enumerated sets] sage: FiniteFields().is_subcategory(FiniteEnumeratedSets()) True
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class