@@ -8780,41 +8780,9 @@ def subfields(self, degree=0, name=None):
87808780 polynomials are supported (:issue:`252`)::
87818781
87828782 sage: K.<a> = NumberField(2*x^4 + 6*x^2 + 1/2)
8783- sage: l = K.subfields(); l # random (see :issue:`39153`)
8784- [(Number Field in a0 with defining polynomial x,
8785- Ring morphism:
8786- From: Number Field in a0 with defining polynomial x
8787- To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
8788- Defn: 0 |--> 0,
8789- None),
8790- (Number Field in a1 with defining polynomial x^2 - 2,
8791- Ring morphism:
8792- From: Number Field in a1 with defining polynomial x^2 - 2
8793- To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
8794- Defn: a1 |--> a^2 + 3/2,
8795- None),
8796- (Number Field in a2 with defining polynomial x^2 + 4,
8797- Ring morphism:
8798- From: Number Field in a2 with defining polynomial x^2 + 4
8799- To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
8800- Defn: a2 |--> 2*a^3 + 7*a,
8801- None),
8802- (Number Field in a3 with defining polynomial x^2 + 2,
8803- Ring morphism:
8804- From: Number Field in a3 with defining polynomial x^2 + 2
8805- To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
8806- Defn: a3 |--> 2*a^3 + 5*a,
8807- None),
8808- (Number Field in a4 with defining polynomial x^4 + 1,
8809- Ring morphism:
8810- From: Number Field in a4 with defining polynomial x^4 + 1
8811- To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
8812- Defn: a4 |--> a^3 + 1/2*a^2 + 5/2*a + 3/4,
8813- Ring morphism:
8814- From: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
8815- To: Number Field in a4 with defining polynomial x^4 + 1
8816- Defn: a |--> -1/2*a4^3 + a4^2 - 1/2*a4)]
8817- sage: sorted([F.discriminant() for F, _, _ in l])
8783+ sage: K
8784+ Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
8785+ sage: sorted([F.discriminant() for F, _, _ in K.subfields()])
88188786 [-8, -4, 1, 8, 256]
88198787 """
88208788 return self ._subfields_helper (degree = degree , name = name ,
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