From 9a4a464ce889e636c005c9dfc231655979c794e9 Mon Sep 17 00:00:00 2001
From: Lorenz Panny <lorenz@yx7.cc>
Date: Thu, 12 Oct 2023 12:03:38 +0200
Subject: [PATCH] check coprimality of moduli in CRT_basis()

---
 src/sage/arith/misc.py | 13 ++++++++-----
 1 file changed, 8 insertions(+), 5 deletions(-)

diff --git a/src/sage/arith/misc.py b/src/sage/arith/misc.py
index aa0174580a1..5d3ef49f7c5 100644
--- a/src/sage/arith/misc.py
+++ b/src/sage/arith/misc.py
@@ -3584,10 +3584,6 @@ def CRT_basis(moduli):
       `a_i` is congruent to 1 modulo `m_i` and to 0 modulo `m_j` for
       `j\not=i`.
 
-    .. note::
-
-       The pairwise coprimality of the input is not checked.
-
     EXAMPLES::
 
         sage: a1 = ZZ(mod(42,5))
@@ -3610,7 +3606,14 @@ def CRT_basis(moduli):
     if n == 0:
         return []
     M = prod(moduli)
-    return [((xgcd(m,M//m)[2])*(M//m)) % M for m in moduli]
+    cs = []
+    for m in moduli:
+        Mm = M // m
+        d, _, v = xgcd(m, Mm)
+        if not d.is_one():
+            raise ValueError('moduli must be coprime')
+        cs.append((v * Mm) % M)
+    return cs
 
 
 def CRT_vectors(X, moduli):