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28 changes: 14 additions & 14 deletions src/sage/rings/number_field/number_field.py
Original file line number Diff line number Diff line change
Expand Up @@ -8656,7 +8656,7 @@ def optimized_subfields(self, degree=0, name=None, both_maps=True):
polynomials are supported (:issue:`252`)::

sage: K.<a> = NumberField(2*x^4 + 6*x^2 + 1/2)
sage: K.optimized_subfields()
sage: K.optimized_subfields() # random
[(Number Field in a0 with defining polynomial x,
Ring morphism:
From: Number Field in a0 with defining polynomial x
Expand Down Expand Up @@ -8780,30 +8780,30 @@ def subfields(self, degree=0, name=None):
polynomials are supported (:issue:`252`)::

sage: K.<a> = NumberField(2*x^4 + 6*x^2 + 1/2)
sage: K.subfields()
[(Number Field in a0 with defining polynomial x,
sage: sorted(K.subfields(), key=lambda x: x[0].discriminant())
[(Number Field in a3 with defining polynomial x^2 + 2,
Ring morphism:
From: Number Field in a0 with defining polynomial x
To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
Defn: 0 |--> 0,
None),
(Number Field in a1 with defining polynomial x^2 - 2,
Ring morphism:
From: Number Field in a1 with defining polynomial x^2 - 2
From: Number Field in a3 with defining polynomial x^2 + 2
To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
Defn: a1 |--> a^2 + 3/2,
Defn: a3 |--> 2*a^3 + 5*a,
None),
(Number Field in a2 with defining polynomial x^2 + 4,
Ring morphism:
From: Number Field in a2 with defining polynomial x^2 + 4
To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
Defn: a2 |--> 2*a^3 + 7*a,
None),
(Number Field in a3 with defining polynomial x^2 + 2,
(Number Field in a0 with defining polynomial x,
Ring morphism:
From: Number Field in a3 with defining polynomial x^2 + 2
From: Number Field in a0 with defining polynomial x
To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
Defn: a3 |--> 2*a^3 + 5*a,
Defn: 0 |--> 0,
None),
(Number Field in a1 with defining polynomial x^2 - 2,
Ring morphism:
From: Number Field in a1 with defining polynomial x^2 - 2
To: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
Defn: a1 |--> a^2 + 3/2,
None),
(Number Field in a4 with defining polynomial x^4 + 1,
Ring morphism:
Expand Down
2 changes: 1 addition & 1 deletion src/sage/rings/qqbar.py
Original file line number Diff line number Diff line change
Expand Up @@ -2711,7 +2711,7 @@ def number_field_elements_from_algebraics(numbers, minimal=False,
-1
sage: nfI^2
-1
sage: sum = nfrt2 + nfrt3 + nfI + nfz3; sum
sage: sum = nfrt2 + nfrt3 + nfI + nfz3; sum # random
a^5 + a^4 - a^3 + 2*a^2 - a - 1
sage: hom(sum)
2.646264369941973? + 1.866025403784439?*I
Expand Down