% diff_arith.m
% Demonstrates how a simple differentiation arithmetic
% can be implemented in Matlab, and applies it to the
% computation of (x-3)^2/(2x-5).

function diff_arith
  format compact
  x = var(2)
  c3 = const(3)
  c2 = const(2)
  c5 = const(5)

  numer = pow( sub(x,c3), 2 )
  denom = sub( mul(c2,x), c5 )
  y = div( numer, denom )
end


function r = add(u,v)
   r = u + v;
end

function r = sub(u,v)
   r = u - v;
end

function r = mul(u,v)
   r(1) = u(1)*v(1);
   r(2) = u(1)*v(2) + u(2)*v(1);
end

function r = div(u,v)
   r(1) = u(1)/v(1);
   r(2) = ( u(2)*v(1) - u(1)*v(2) ) / v(1)^2;
end

function r = pow(u,n)
   r(1) = u(1)^n;
   r(2) = n*u(1)^(n-1)*u(2);
end

function r = const(u)
   r = [u,0];
end

function r = var(u)
   r = [u,1];
end