The standard formalism of differential geometry (and general relativity) consists simply of using the coordinate tetrad in the tetrad formalism. The coordinate tetrad is the canonical set of vectors associated with the coordinate chart. The coordinate tetrad is commonly denoted { ∂ ∂ μ μ } whereas the dual cotetrad is denoted { d x μ μ } . These tangent vectors are usually defined as directional derivative operators: given a chart φ φ = ( φ φ 1 , … … , φ φ n ) which maps a subset of the manifold into coordinate space R n , and any scalar field f , the coordinate vectors are such that: