From ac1d86163e41bd36d43011edcf92d73d2c20c520 Mon Sep 17 00:00:00 2001
From: user202729 <25191436+user202729@users.noreply.github.com>
Date: Wed, 18 Dec 2024 16:23:37 +0700
Subject: [PATCH 1/2] Mark test in qqbar.py as random to avoid test failure

---
 src/sage/rings/qqbar.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/rings/qqbar.py b/src/sage/rings/qqbar.py
index 3806663eaf0..4c7397ce7e4 100644
--- a/src/sage/rings/qqbar.py
+++ b/src/sage/rings/qqbar.py
@@ -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

From 8f584400693927a490775593e40922fba988650c Mon Sep 17 00:00:00 2001
From: user202729 <25191436+user202729@users.noreply.github.com>
Date: Wed, 18 Dec 2024 18:39:04 +0700
Subject: [PATCH 2/2] Make a few more tests deterministic

---
 src/sage/rings/number_field/number_field.py | 62 ++++++++++++---------
 1 file changed, 35 insertions(+), 27 deletions(-)

diff --git a/src/sage/rings/number_field/number_field.py b/src/sage/rings/number_field/number_field.py
index 2559771ae62..59653381572 100644
--- a/src/sage/rings/number_field/number_field.py
+++ b/src/sage/rings/number_field/number_field.py
@@ -8662,7 +8662,7 @@ 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
@@ -8774,32 +8774,40 @@ 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, 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
-              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 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, Ring morphism:
-              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: a3 |--> 2*a^3 + 5*a, None),
-            (Number Field in a4 with defining polynomial x^4 + 1, Ring morphism:
-              From: Number Field in a4 with defining polynomial x^4 + 1
-              To:   Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
-              Defn: a4 |--> a^3 + 1/2*a^2 + 5/2*a + 3/4, Ring morphism:
-              From: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
-              To:   Number Field in a4 with defining polynomial x^4 + 1
-              Defn: a |--> -1/2*a4^3 + a4^2 - 1/2*a4)
-            ]
+            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 a3 with defining polynomial x^2 + 2
+                To:   Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
+                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 a0 with defining polynomial x,
+              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
+                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:
+                From: Number Field in a4 with defining polynomial x^4 + 1
+                To:   Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
+                Defn: a4 |--> a^3 + 1/2*a^2 + 5/2*a + 3/4,
+              Ring morphism:
+                From: Number Field in a with defining polynomial 2*x^4 + 6*x^2 + 1/2
+                To:   Number Field in a4 with defining polynomial x^4 + 1
+                Defn: a |--> -1/2*a4^3 + a4^2 - 1/2*a4)]
         """
         return self._subfields_helper(degree=degree, name=name,
                                       both_maps=True, optimize=False)