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# Number fields

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()

  class `ElementMethods`
  class `NumberFields.``ParentMethods`
  `NumberFields.``super_categories`()

    EXAMPLES:

        sage: NumberFields().super_categories()
        [Category of fields]

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