@@ -8780,41 +8780,9 @@ def subfields(self, degree=0, name=None):
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polynomials are supported (:issue:`252`)::
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sage: K.<a> = NumberField(2*x^4 + 6*x^2 + 1/2)
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- sage: l = K.subfields(); l # random (see :issue:`39153`)
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- [(Number Field in a0 with defining polynomial x,
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- Ring morphism:
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- From: Number Field in a0 with defining polynomial x
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- To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
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- Defn: 0 |--> 0,
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- None),
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- (Number Field in a1 with defining polynomial x^2 - 2,
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- Ring morphism:
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- From: Number Field in a1 with defining polynomial x^2 - 2
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- To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
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- Defn: a1 |--> a^2 + 3/2,
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- None),
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- (Number Field in a2 with defining polynomial x^2 + 4,
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- Ring morphism:
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- From: Number Field in a2 with defining polynomial x^2 + 4
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- To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
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- Defn: a2 |--> 2*a^3 + 7*a,
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- None),
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- (Number Field in a3 with defining polynomial x^2 + 2,
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- Ring morphism:
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- From: Number Field in a3 with defining polynomial x^2 + 2
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- To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
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- Defn: a3 |--> 2*a^3 + 5*a,
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- None),
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- (Number Field in a4 with defining polynomial x^4 + 1,
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- Ring morphism:
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- From: Number Field in a4 with defining polynomial x^4 + 1
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- To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
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- Defn: a4 |--> a^3 + 1/2*a^2 + 5/2*a + 3/4,
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- Ring morphism:
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- From: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
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- To: Number Field in a4 with defining polynomial x^4 + 1
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- Defn: a |--> -1/2*a4^3 + a4^2 - 1/2*a4)]
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- sage: sorted([F.discriminant() for F, _, _ in l])
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+ sage: K
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+ Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
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+ sage: sorted([F.discriminant() for F, _, _ in K.subfields()])
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[-8, -4, 1, 8, 256]
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"""
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return self ._subfields_helper (degree = degree , name = name ,
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