(self)
return hash(tuple(arr))
Define the hash of a monomial
        by the underlying variables.

        If hashing is implemented in O(v*log(v))
        where v represents the number of
        variables in the monomial,
        then search queries for the
        purposes of simplification of a
        polynomial can be performed in
        O(v*log(v)) as well; much better than
        the length of the polynomial.
Define the hash of a monomial
        by the underlying variables.
Define the hash of a monomial by the underlying variables .
def __hash__(self) -> int:
        """
        Define the hash of a monomial
        by the underlying variables.

        If hashing is implemented in O(v*log(v))
        where v represents the number of
        variables in the monomial,
        then search queries for the
        purposes of simplification of a
        polynomial can be performed in
        O(v*log(v)) as well; much better than
        the length of the polynomial.
        """
        arr = []
        for i in sorted(self.variables):
            if self.variables[i] > 0:
                for _ in range(self.variables[i]):
                    arr.append(i)
        return hash(tuple(arr))
def __hash__ ( self ) -> int : arr = [ ] for i in sorted ( self . variables ) : if self . variables [ i ] > 0 : for _ in range ( self . variables [ i ] ) : arr . append ( i ) return hash ( tuple ( arr ) )