Evaluate sums of powers of polynomial roots
%By Chukwunomso Agunwamba
%Evaluates sums of powers of polynomial roots
##
##This mathematical code is provided as is, for the end user to be able to use it
##and to edit it for educational purposes. However, any modified version must
##include my name as the original producer of the code.
##The name of the mfile code is getsumofpws. It has two input arguments.
##The first input is the power to which to raise the roots.
##The second input is the polynomial. (Note that if one has the roots already,
## one can simply directly raise them to the power and sum. But this code is
## for when one only has the coefficients of the polynomial.)
##
##So, symbolically speaking (not usage syntax),
##getsumofpws(k,Q) = sum((-V).^k), with Q(V) = 0 for each V. The polynomial
##coefficient vector is given in increasing powers here (not in reducing powers).
##
##Usage syntax examples:
##C = getsumofpws(3,[3 2 1])
##C = -10
##
##C = getsumofpws(4,[4 3 2 1])
##C = 18
## compare this to the result from: sum((-roots([1 2 3 4])).^4)