A FAMILY OF EXPLICIT WARING DECOMPOSITIONS OF A POLYNOMIAL

In this paper we settle some polynomial identity which provides a family of ex-plicit Waring decompositions of any monomial Xa0 0 Xa1 1 & BULL; & BULL; & BULL; Xan n over a field k. This gives an upper bound for the Waring rank of a given monomial and naturally leads to an explicit Waring decomposition of any homogeneous form and, eventually, of any polynomial via (de)homogenization. Note that such decomposition is very useful in many applications dealing with polynomial com-putations, symmetric tensor problems and so on. We discuss some computational aspect of our result as comparing with other known methods and also present a computer implementation for potential use in the end.