 A "k"-form on "T" is a linear operator acting on "k"-dimensional subcomplexes of "T"; e.g., a 0-form assigns values to points, and extends linearly to linear combinations of points; a 1-form assigns values to line segments in a similarly linear way.If "ω" is a "k"-form on "T", then the discrete exterior derivative d"ω" of "ω" is the unique ("k" + 1)-form defined so that Stokes' theorem holds