Update app.py

app.py

@@ -27,13 +27,14 @@ class BasicAgent:
     
         
     def check_commutativity(self):
+        # Define the set S
         S = ['a', 'b', 'c', 'd', 'e']
         counter_example_elements = set()
     
         # Define a map for converting letters to table indices
         index = {'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4}
     
-        # Operation table (example)
+        # Operation table as provided
         self.operation_table = [
             ['a', 'b', 'c', 'b', 'd'],  # a * a, a * b, a * c, a * d, a * e
             ['b', 'c', 'a', 'e', 'c'],  # b * a, b * b, b * c, b * d, b * e
@@ -42,17 +43,22 @@ class BasicAgent:
             ['d', 'b', 'a', 'd', 'c']   # e * a, e * b, e * c, e * d, e * e
         ]
         
-        # Check for commutativity violations
+        # Check for commutativity violations (x * y != y * x)
         for x in S:
             for y in S:
-                if self.operation_table[index[x]][index[y]] != self.operation_table[index[y]][index[x]]:
+                # Convert x and y to their corresponding table indices
+                x_idx = index[x]
+                y_idx = index[y]
+    
+                # Check if the operation does not commute
+                if self.operation_table[x_idx][y_idx] != self.operation_table[y_idx][x_idx]:
+                    # If not commutative, add both elements to the set
                     counter_example_elements.add(x)
                     counter_example_elements.add(y)
     
         # Return the sorted list of elements involved in violations
         return sorted(counter_example_elements)
 
-
         
     def maybe_reversed(self, text: str) -> bool:
         words = text.split()