From f44e0811984664c9ec57bf70c11e2b93c55b0056 Mon Sep 17 00:00:00 2001
From: user202729 <25191436+user202729@users.noreply.github.com>
Date: Mon, 4 Aug 2025 06:23:49 +0700
Subject: [PATCH 1/2] Fix LazyImport

---
 src/sage/misc/lazy_import.pyx               | 17 +++++++++++++++++
 src/sage/schemes/curves/projective_curve.py |  2 +-
 2 files changed, 18 insertions(+), 1 deletion(-)

diff --git a/src/sage/misc/lazy_import.pyx b/src/sage/misc/lazy_import.pyx
index 58365b2b272..9bac24a371e 100644
--- a/src/sage/misc/lazy_import.pyx
+++ b/src/sage/misc/lazy_import.pyx
@@ -36,6 +36,23 @@ that (s)he can remove the flag::
     UserWarning: Option ``at_startup=True`` for lazy import ZZ not needed anymore
     Integer Ring
 
+.. WARNING::
+
+    After the first usage, the imported object is directly injected into the
+    namespace; however, before that, the :class:`LazyImport` object
+    is not exactly equivalent to the actual imported object. For example::
+
+        sage: from sage.misc.lazy_import import LazyImport
+        sage: my_qqbar = LazyImport('sage.rings.qqbar', 'QQbar')
+        sage: my_qqbar(5) == QQbar(5)  # good
+        True
+        sage: isinstance(QQbar, Parent)
+        True
+        sage: isinstance(my_qqbar, Parent)  # fails!
+        False
+
+    To avoid this issue, you may execute the import inside the function instead.
+
 .. SEEALSO:: :func:`lazy_import`, :class:`LazyImport`
 
 AUTHOR:
diff --git a/src/sage/schemes/curves/projective_curve.py b/src/sage/schemes/curves/projective_curve.py
index 09fb3ffd3db..cd4462112ff 100644
--- a/src/sage/schemes/curves/projective_curve.py
+++ b/src/sage/schemes/curves/projective_curve.py
@@ -159,7 +159,6 @@
 
 lazy_import('sage.interfaces.singular', 'singular')
 lazy_import('sage.rings.number_field.number_field', 'NumberField')
-lazy_import('sage.rings.qqbar', ['number_field_elements_from_algebraics', 'QQbar'])
 
 from .curve import Curve_generic
 
@@ -1452,6 +1451,7 @@ def ordinary_model(self):
         """
         # helper function for extending the base field
 
+        from sage.rings.qqbar import number_field_elements_from_algebraics, QQbar
         def extension(self):
             F = self.base_ring()
             pts = self.change_ring(F.embeddings(QQbar)[0]).rational_points()

From fc2661696d342d0f7cfe45309957f6478dc5283a Mon Sep 17 00:00:00 2001
From: user202729 <25191436+user202729@users.noreply.github.com>
Date: Mon, 4 Aug 2025 17:39:12 +0700
Subject: [PATCH 2/2] Fix lint

---
 src/sage/schemes/curves/projective_curve.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/sage/schemes/curves/projective_curve.py b/src/sage/schemes/curves/projective_curve.py
index cd4462112ff..f65da51e1e7 100644
--- a/src/sage/schemes/curves/projective_curve.py
+++ b/src/sage/schemes/curves/projective_curve.py
@@ -1449,10 +1449,10 @@ def ordinary_model(self):
                       + (1/16*a + 1/16)*x*y*z^2 + (3/16*a + 3/16)*y^2*z^2
                       + (-3/16*a - 1/4)*y*z^3 + (1/16*a + 3/32)*z^4)
         """
-        # helper function for extending the base field
-
         from sage.rings.qqbar import number_field_elements_from_algebraics, QQbar
+
         def extension(self):
+            # helper function for extending the base field
             F = self.base_ring()
             pts = self.change_ring(F.embeddings(QQbar)[0]).rational_points()
             L = [t for pt in pts for t in pt]