Bases: sage.categories.category.Category
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 are considered as an object in this category:
sage: RationalField() in C
True
However, we can define a degree 1 extension of , 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()
EXAMPLES:
sage: NumberFields().super_categories()
[Category of fields]