From 84b9f46f69d904eb7e9992227f5e9c801d21ee9c Mon Sep 17 00:00:00 2001
From: user202729 <25191436+user202729@users.noreply.github.com>
Date: Wed, 17 Dec 2025 16:19:37 +0700
Subject: [PATCH] Make conversion from integer-valued real number to rational
 exact

---
 src/sage/rings/rational.pyx | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/src/sage/rings/rational.pyx b/src/sage/rings/rational.pyx
index 02fe3b23af0..105a4c69207 100644
--- a/src/sage/rings/rational.pyx
+++ b/src/sage/rings/rational.pyx
@@ -495,6 +495,11 @@ cdef class Rational(sage.structure.element.FieldElement):
         1267650600228229401496703205376/515377520732011331036461129765621272702107522001
         sage: QQ((-2r^100r, -3r^100r))
         1267650600228229401496703205376/515377520732011331036461129765621272702107522001
+
+    Conversion from real number::
+
+        sage: QQ(RR(2^100))
+        1267650600228229401496703205376
     """
     def __cinit__(self):
         r"""
@@ -602,7 +607,10 @@ cdef class Rational(sage.structure.element.FieldElement):
                 mpq_set_si(self.value, 0, 1)
                 return
             if not base:
-                set_from_Rational(self, x.simplest_rational())
+                if x.is_integer():
+                    set_from_Rational(self, x.exact_rational())
+                else:
+                    set_from_Rational(self, x.simplest_rational())
             else:
                 # Truncate in base 10 to match repr(x).
                 # See https://github.com/sagemath/sage/issues/21124