From dbb3cbecb469e0a1d538a38e17f57e03fc9bfa68 Mon Sep 17 00:00:00 2001
From: RuchitJagodara <ruchit.jagodara@iitgn.ac.in>
Date: Thu, 21 Dec 2023 16:43:55 +0530
Subject: [PATCH 1/3] Simplify the expression before converting it to algebraic
 number

This commit changes the _algebraic_ function of Expression class to
simplify the expression with simplify_full() function before converting
it to algebraic number.
---
 src/sage/symbolic/expression.pyx | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sage/symbolic/expression.pyx b/src/sage/symbolic/expression.pyx
index 9d86a81b24b..6be5c2d5457 100644
--- a/src/sage/symbolic/expression.pyx
+++ b/src/sage/symbolic/expression.pyx
@@ -2040,7 +2040,7 @@ cdef class Expression(Expression_abc):
             0
         """
         from sage.symbolic.expression_conversions import algebraic
-        return algebraic(self, field)
+        return algebraic(self.simplify_full(), field)
 
     def __hash__(self):
         r"""

From 30b120a310f67e7bdfd24a642f7fb08a51d02730 Mon Sep 17 00:00:00 2001
From: RuchitJagodara <ruchit.jagodara@iitgn.ac.in>
Date: Thu, 21 Dec 2023 16:48:05 +0530
Subject: [PATCH 2/3] Added a doctest

Added the doctest for _element_constructor_() function of AlgebraicField class.
---
 src/sage/rings/qqbar.py | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/src/sage/rings/qqbar.py b/src/sage/rings/qqbar.py
index 5fc675ffd83..9b5605e8d15 100644
--- a/src/sage/rings/qqbar.py
+++ b/src/sage/rings/qqbar.py
@@ -1646,6 +1646,16 @@ def _element_constructor_(self, x):
             True
             sage: pi in QQbar                                                           # needs sage.symbolic
             False
+
+        TESTS::
+
+        Check if :trac:`12745` is fixed::
+
+            sage: x = exp(2*I*pi/7) + exp(-2*I*pi/7)
+            sage: QQbar(x) in AA
+            True
+            sage: AA(x)
+            1.246979603717467?
         """
         if isinstance(x, AlgebraicNumber):
             return x

From 52a00ba9119789c8b4c5fbcdb079dcdd3ce8c9bb Mon Sep 17 00:00:00 2001
From: RuchitJagodara <ruchit.jagodara@iitgn.ac.in>
Date: Thu, 21 Dec 2023 17:04:35 +0530
Subject: [PATCH 3/3] Corrected a linting error

---
 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 9b5605e8d15..f9d30f99531 100644
--- a/src/sage/rings/qqbar.py
+++ b/src/sage/rings/qqbar.py
@@ -1647,7 +1647,7 @@ def _element_constructor_(self, x):
             sage: pi in QQbar                                                           # needs sage.symbolic
             False
 
-        TESTS::
+        TESTS:
 
         Check if :trac:`12745` is fixed::