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src/sage/rings/number_field/number_field.py

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@@ -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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