Update tools.py

tools.py

@@ -86,12 +86,11 @@ def detect_non_commutative_subset(table_text: str) -> str:
         if len(lines) < 3:
             return "Error: Table format invalid or incomplete."
 
-        # Parse headers (elements)
+        # Parse headers (set elements)
         headers = [h.strip() for h in lines[0].split('|') if h.strip()]
 
-        # Parse operation table into a dict
         operation = {}
-        for line in lines[2:]:  # skip header + separator
+        for line in lines[2:]:  # skip header and separator
             cells = [c.strip() for c in line.split('|') if c.strip()]
             if len(cells) != len(headers) + 1:
                 continue  # skip malformed rows
@@ -100,7 +99,7 @@ def detect_non_commutative_subset(table_text: str) -> str:
                 col_label = headers[col_idx]
                 operation[(row_label, col_label)] = result
 
-        # Detect non-commutative cases
+        # Find mismatches: x*y ≠ y*x
         involved = set()
         for a in headers:
             for b in headers:
@@ -108,6 +107,7 @@ def detect_non_commutative_subset(table_text: str) -> str:
                     involved.update([a, b])
 
         return ", ".join(sorted(involved)) if involved else "The operation is commutative."
+
     except Exception as e:
         return f"Error analyzing table: {str(e)}"