In his theory of exterior differential systems E. Cartan often studied algebraic structures which contain such information as the characters. This note studies one of these structures which we call the Cartan function. Inequivalent systems may have isomorphic Cartan functions. But if two systems have the same Cartan function so do their total prolongations, and this may be obtained algebraically. A similar theory for partial prolongations appears to be impossible, for two systems with identical Cartan functions may partially prolong to systems with different Cartan functions. All manifolds, functions and forms are infinitely differentiable.