Problem 60996. Dickson Polynomials

Dyuman Joshi

8 solvers

0 likes

Solve

Solve Later

Return the coefficients of nth (n>=0) Dickson polynomial of the 1st kind as follows - 
1st row of the output will be the coefficients of x, and, 2nd row of the output will be the coefficients of alpha.
When formulating the coefficitients of a variables, for terms where the other variable is present - consider the value of the other variable as 1. See examples below for a better understanding. 
%Examplesa
n=2;
D2(x, alpha) = x^2 - 2*alpha
Output =  [1 0 -2; 0 -2 1]
n=3;
D3(x, alpha) = x^3 - 3*x*alpha
Output = [1 0 -3 0; 0 0 -1 1]
n=5;
D5(x, alpha) = x^5 - 5*x^3*alpha + 5*x*alpha^2
% x (alpha=1) = 1*x^5 - 5*x^3*1 + 5*x*1^2 = [1 0 -5 0 5 0].*[x^5 x^4 x^3 x^2 x^1 x^0]
% alpha (x=1) = alpha^0*1^5 - 5*1^3*alpha^1 + 5*1*alpha^2
%             = [0 0 0 5 -5 1].*[alpha^5 alpha^4 alpha^3 alpha^2 alpha^1 alpha^0]
Output = [1 0 -5 0 5 0; 0 0 0 5 -5 1]
Only vectorized solutions will be accepted. Check the test suite for banned functions.