def reaction_signature(eq, direction=False, stoichiometry=False):
    """Return unique signature object for :class:`Reaction`.

    Signature objects are hashable, and compare equal only if the reactions
    are considered the same according to the specified rules.

    Args:
        direction: Include reaction directionality when considering equality.
        stoichiometry: Include stoichiometry when considering equality.
    """
    def compounds_sig(compounds):
        if stoichiometry:
            return tuple(sorted(compounds))
        else:
            return tuple(sorted(compound for compound, _ in compounds))

    left = compounds_sig(eq.left)
    right = compounds_sig(eq.right)

    if left < right:
        reaction_sig = left, right
        direction_sig = eq.direction
    else:
        reaction_sig = right, left
        direction_sig = eq.direction.flipped()

    if direction:
        return reaction_sig, direction_sig
    return reaction_sig