function a = r8poly_n2p ( n, a, xarray )
%*****************************************************************************80
%
%% r8poly_n2p() converts a real polynomial from Newton form to power sum form.
%
% Discussion:
%
% This is done by shifting all the Newton abscissas to zero.
%
% Actually, what happens is that the abscissas of the Newton form
% are all shifted to zero, which means that A is the power sum
% polynomial description and A, XARRAY is the Newton polynomial
% description. It is only because all the abscissas are shifted to
% zero that A can be used as both a power sum and Newton polynomial
% coefficient array.
%
% The Newton form of a polynomial is described by an array of N coefficients
% A and N abscissas X:
%
% p(x) = a(1)
% + a(2) * (x-x(1))
% + a(3) * (x-x(1)) * (x-x(2))
% ...
% + a(n) * (x-x(1)) * (x-x(2)) * ... * (x-x(n-1))
%
% X(N) does not occur explicitly in the formula for the evaluation of p(x),
% although it is used in deriving the coefficients A.
%
% The power sum form of a polynomial is:
%
% p(x) = a(1) + a(2)*x + ... + a(n-1)*x^(n-2) + a(n)*x^(n-1)
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 06 June 2015
%
% Author:
%
% John Burkardt
%
% Input:
%
% integer N, the dimension of A.
%
% real A(N), the coefficients of the polynomial in Newton
% form.
%
% real XARRAY(N), the abscissas of the Newton form of the
% polynomial.
%
% Output:
%
% real A(N), the coefficients in power sum form.
%
for i = 1 : n
[ a, xarray ] = r8poly_nx ( n, a, xarray, 0.0 );
end
return
end