Update app.py

app.py

@@ -166,7 +166,7 @@ def reverse_text(text: str) -> str:
     return text[::-1]
 
 @tool
-def find_non_commutative(table: dict) -> str:
+def find_non_commutative(table: dict[tuple[str, str]: str]) -> str:
     """
     Given a dictionary representing a multiplication table (keys are tuples (row_elem, col_elem)),
     finds all elements involved in non-commutative pairs (where table[(x,y)] != table[(y,x)]).
@@ -445,7 +445,7 @@ SYSTEM_MESSAGE = """You are a concise AI assistant with access to the following
 - wiki_get_page(title: string) → string
 - youtube_transcript(video_id: string) → string
 - reverse_text(text: string) → string
-- find_non_commutative(table: dict) -> list : Returns sorted list of non-commutative elements or a list containing an error message. Example table format: {('a','a'):'a', ('a','b'):'c', ('b','a'):'d', ...}
+- find_non_commutative(table: dict[tuple[str, str]: str]) -> str : Returns sorted list of non-commutative elements or a list containing an error message. Example table format: {('a','a'):'a', ('a','b'):'c', ('b','a'):'d', ...}
 - libretext_extract(url: string, selector: string) → string
 - classify_vegetables(items: list[string]) → list[string]
 - execute_code(code: string) → string