Number fields¶
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class
sage.categories.number_fields.
NumberFields
(s=None)¶ Bases:
sage.categories.category_singleton.Category_singleton
The category of number fields.
EXAMPLES:
We create the category of number fields:
sage: C = NumberFields() sage: C Category of number fields
Notice that the rational numbers \(\QQ\) are considered as an object in this category:
sage: RationalField() in C True
However, we can define a degree 1 extension of \(\QQ\), which is of course also in this category:
sage: x = PolynomialRing(RationalField(), 'x').gen() sage: K = NumberField(x - 1, 'a'); K Number Field in a with defining polynomial x - 1 sage: K in C True
Number fields all lie in this category, regardless of the name of the variable:
sage: K = NumberField(x^2 + 1, 'a') sage: K in C True
TESTS:
sage: TestSuite(NumberFields()).run()
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class
ElementMethods
¶
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class
NumberFields.
ParentMethods
¶
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NumberFields.
super_categories
()¶ EXAMPLES:
sage: NumberFields().super_categories() [Category of fields]
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class