Update app.py

app.py

@@ -25,29 +25,34 @@ class BasicAgent:
             to be put in the list is a number or a string."""
         )
     
-        # Operation table for the set S = {a, b, c, d, e}
-        self.operation_table = {
-            'a': {'a': 'a', 'b': 'b', 'c': 'c', 'd': 'b', 'e': 'd'},
-            'b': {'a': 'b', 'b': 'c', 'c': 'a', 'd': 'e', 'e': 'c'},
-            'c': {'a': 'c', 'b': 'a', 'c': 'b', 'd': 'b', 'e': 'a'},
-            'd': {'a': 'b', 'b': 'e', 'c': 'b', 'd': 'e', 'e': 'd'},
-            'e': {'a': 'd', 'b': 'b', 'c': 'a', 'd': 'd', 'e': 'c'}
-            }  
         
     def check_commutativity(self):
         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)
+        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
+            ['c', 'a', 'b', 'b', 'a'],  # c * a, c * b, c * c, c * d, c * e
+            ['b', 'e', 'b', 'e', 'd'],  # d * a, d * b, d * c, d * d, d * e
+            ['d', 'b', 'a', 'd', 'c']   # e * a, e * b, e * c, e * d, e * e
+        ]
+        
         # Check for commutativity violations
         for x in S:
             for y in S:
-                if self.operation_table[x][y] != self.operation_table[y][x]:
+                if self.operation_table[index[x]][index[y]] != self.operation_table[index[y]][index[x]]:
                     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()