# HG changeset patch
# User Maarten Derickx <m.derickx.student@gmail.com>
# Date 1314384115 25200
# Node ID f38b25e3737526e62ee551ccbaf526767f8d8bb3
# Parent  42b3c11f78ea1672d750dbfe2418e308c9f70772
11750 fix CRT_list for non coprime moduli

diff --git a/sage/rings/arith.py b/sage/rings/arith.py
--- a/sage/rings/arith.py
+++ b/sage/rings/arith.py
@@ -2800,7 +2800,19 @@
         3
         sage: c.parent()
         Univariate Polynomial Ring in x over Rational Field
-
+        
+    It also works if the moduli are not coprime::
+         
+        sage: CRT_list([32,2,2],[60,90,150])
+        452
+    
+    But with non coprime moduli there is not always a solution::
+
+        sage: CRT_list([32,2,1],[60,90,150])
+        Traceback (most recent call last):
+        ...
+        ValueError: No solution to crt problem since gcd(180,150) does not divide 92-1
+    
     The arguments must be lists::
 
         sage: CRT_list([1,2,3],"not a list")
@@ -2825,6 +2837,10 @@
         ...
         ValueError: Arguments to CRT_list should be lists of the same length
 
+    TESTS::
+
+        sage: CRT([32r,2r,2r],[60r,90r,150r])
+        452
 
     """
     if not isinstance(v,list) or not isinstance(moduli,list):
@@ -2839,7 +2855,7 @@
     m = moduli[0]
     for i in range(1,len(v)):
         x = CRT(x,v[i],m,moduli[i])
-        m *= moduli[i]
+        m = lcm(m,moduli[i])
     return x%m
 
 def CRT_basis(moduli):