  In this paper we give a new and simple algorithm to put any multivariate
polynomial into a normal determinant form in which each entry has the form ,
and in each column the same variable appears. We also apply the algorithm to
obtain a triangular determinant representation, a reduced determinant
representation, and a uniform determinant representation of any multivariable
polynomial. The algorithm could be useful for obtaining representations of
dimensions smaller than those available up to now to solve numerical problems.
