gh-35218: reduce exponents of AbelianGroup elements modulo the respective orders
    
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Fixes #35216

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URL: #35218
Reported by: Peter Bruin
Reviewer(s): Alex J Best

Author: Release Manager

src/sage/groups/abelian_gps/element_base.py

@@ -65,15 +65,25 @@ def __init__(self, parent, exponents):
             sage: A,B,C = Fd.gens()
             sage: A*B^-1 in Fd
             True
+
+        Check that :issue:`35216` is fixed::
+
+            sage: M = AbelianGroup([3])
+            sage: M([5]) == M([2])
+            True
+            sage: M([3]).is_trivial()
+            True
         """
         MultiplicativeGroupElement.__init__(self, parent)
         n = parent.ngens()
         if exponents == 1:
-            self._exponents = tuple( ZZ.zero() for i in range(n) )
+            self._exponents = tuple(ZZ.zero() for i in range(n))
         else:
-            self._exponents = tuple( ZZ(e) for e in exponents )
-            if len(self._exponents) != n:
-                raise IndexError('argument length (= %s) must be %s.'%(len(exponents), n))
+            if len(exponents) != n:
+                raise IndexError('argument length (= %s) must be %s'
+                                 % (len(exponents), n))
+            self._exponents = tuple(ZZ(e % o if o else e) for e, o in
+                                    zip(exponents, parent.gens_orders()))
 
     def __hash__(self):
         r"""
@@ -257,9 +267,8 @@ def _div_(left, right):
         """
         G = left.parent()
         assert G is right.parent()
-        exponents = [ (x-y)%order if order!=0 else x-y
-                      for x, y, order in
-                      zip(left._exponents, right._exponents, G.gens_orders()) ]
+        exponents = [x - y for x, y in
+                     zip(left._exponents, right._exponents)]
         return G.element_class(G, exponents)
 
     def _mul_(left, right):
@@ -276,9 +285,8 @@ def _mul_(left, right):
         """
         G = left.parent()
         assert G is right.parent()
-        exponents = [ (x+y)%order if order!=0 else x+y
-                      for x, y, order in
-                      zip(left._exponents, right._exponents, G.gens_orders()) ]
+        exponents = [x + y for x, y in
+                     zip(left._exponents, right._exponents)]
         return G.element_class(G, exponents)
 
     def __pow__(self, n):
@@ -295,8 +303,7 @@ def __pow__(self, n):
         if n != m:
             raise TypeError('argument n (= '+str(n)+') must be an integer.')
         G = self.parent()
-        exponents = [ (m*e) % order if order!=0 else m*e
-                      for e,order in zip(self._exponents, G.gens_orders()) ]
+        exponents = [m * e for e in self._exponents]
         return G.element_class(G, exponents)
 
     def __invert__(self):
@@ -320,8 +327,7 @@ def __invert__(self):
             (-1, 4)
         """
         G = self.parent()
-        exponents = [(-e) % order if order != 0 else -e
-                     for e, order in zip(self._exponents, G.gens_orders())]
+        exponents = [-e for e in self._exponents]
         return G.element_class(G, exponents)
 
     def is_trivial(self):