From 94b7d4a477223d5a7a461363044d2d3bc62cb50d Mon Sep 17 00:00:00 2001
From: user202729 <25191436+user202729@users.noreply.github.com>
Date: Sat, 31 Aug 2024 00:26:25 +0700
Subject: [PATCH 1/2] Add is_integral method to algebraic numbers

---
 src/sage/rings/qqbar.py | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)

diff --git a/src/sage/rings/qqbar.py b/src/sage/rings/qqbar.py
index 5d2f2ca2216..a02d921ecb1 100644
--- a/src/sage/rings/qqbar.py
+++ b/src/sage/rings/qqbar.py
@@ -4485,6 +4485,26 @@ def as_number_field_element(self, minimal=False, embedded=False, prec=53):
         """
         return number_field_elements_from_algebraics(self, minimal=minimal, embedded=embedded, prec=prec)
 
+    def is_integral(self):
+        r"""
+        Determine if a number is an algebraic integer.
+
+        EXAMPLES::
+
+            sage: QQbar(sqrt(-23)).is_integral()
+            True
+            sage: AA(sqrt(23/2)).is_integral()
+            False
+
+        TESTS:
+
+        Method should return the same value as :meth:`NumberFieldElement.is_integral`::
+
+             sage: for a in [QQbar(2^(1/3)), AA(2^(1/3)), QQbar(sqrt(1/2)), AA(1/2), AA(2), QQbar(1/2)]:
+             ....:    assert a.as_number_field_element()[1].is_integral() == a.is_integral()
+        """
+        return all(a in ZZ for a in self.minpoly())
+
     def exactify(self):
         """
         Compute an exact representation for this number.

From 480bd938770a58f7287880c34798a74c9e7d4765 Mon Sep 17 00:00:00 2001
From: user202729 <25191436+user202729@users.noreply.github.com>
Date: Sat, 31 Aug 2024 11:15:15 +0700
Subject: [PATCH 2/2] Apply suggested change

---
 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 a02d921ecb1..074cf983b27 100644
--- a/src/sage/rings/qqbar.py
+++ b/src/sage/rings/qqbar.py
@@ -4487,7 +4487,7 @@ def as_number_field_element(self, minimal=False, embedded=False, prec=53):
 
     def is_integral(self):
         r"""
-        Determine if a number is an algebraic integer.
+        Check if this number is an algebraic integer.
 
         EXAMPLES::