  A classical technique to construct polynomial preserving extensions of scalar
functions defined on the boundary of an $n$ simplex to the interior is to use
so-called rational blending functions. The purpose of this paper is to
generalize the construction by blending to the de Rham complex. More precisely,
we define polynomial preserving extensions which map traces of $k$ forms
defined on the boundary of the simplex to $k$ forms defined in the interior.
Furthermore, the extensions are cochain maps, i.e., they commute with the
exterior derivative.
