function [q,p,A] = ChebyshevRat(a,m,n)
%
% Chebyshev Rational Approximation f(x) = p(x)/q(x)
% where p(x), q(x) are polynomials of degree n and m,
% respectively, and N = m + n is the degree of the 
% approximation function.
%
% written by Ming Gu for Math128B, Spring 2009
%
N = m + n;
A = zeros(N+1,N+2);
a = a(:);
A(2:end,1)      = a(2:N+1);
a(2:end)        = a(2:end)/2;
A(1,1:m+1)      = a(1:m+1)';
%
% toepplitz and hankel are built-in matlab functions.
% toepplitz matrix has constant entries on each diagonal;
% whereas hankel matrix has constant entries on each anti-diagonal.
%
A(2:end,2:m+1)  = toeplitz(a(1:N),a(1:m))+hankel(a(3:N+2),a(N+2:N+m+1));
A(1:n+1,m+2:N+2)= -eye(n+1);
x = -A(:,2:end)\A(:,1);
q =[1;x(1:m)];
p =x(m+1:m+n+1);