function babydecouple
global m n
m=2;n=2;
while 1
  a = randinseg(0,1);
  b = randinseg(0,a);
  phi = randlip(2,2);
  [lhs, rhs] = babycheck(a,b,phi);
  v0 = rhs - lhs;
  v1 = abpoly(a,b,phi);
  good = abs(v0-v1)<1e-9
  if ~good
    keyboard
  end
end
return

function v = abpoly(a,b,x)
A1  = - x(c2i([0 0])) + x(c2i([1 0])) + 3*x(c2i([0 1])) + x(c2i([1 1]));
B1  =   x(c2i([0 0])) - x(c2i([1 0])) - 3*x(c2i([0 1])) - x(c2i([1 1]));
A2 =   x(c2i([0 0])) + x(c2i([1 0])) -   x(c2i([0 1])) - x(c2i([1 1]));
B2 = - x(c2i([0 0])) - x(c2i([1 0])) +   x(c2i([0 1])) + x(c2i([1 1]));
%v = a*A1 + b*B1 + a^2*A2 + b^2*B2;

mu = a-b;
nu = a+b;
v = A1*mu + A2*mu*nu;


%A1 = - x00 + x10 + 3*x01 + x11
%B1 =   x00 - x10 - 3*x01 - x11
%A2 =   x00 + x10 -   x01 - x11
%B2 = - x00 - x10 +   x01 + x11

%d = A1^2 - 4*A2*(B1*b+B2*b^2)

%                                                                         2
%Out[12]= ((-1 + 2 b) x00 + (3 - 2 b) x01 + x10 + 2 b x10 + x11 - 2 b x11)
%

%d = (-1 + 2 b) x00 + (3 - 2 b) x01 + x10 + 2 b x10 + x11 - 2 b x11

% a=b

% OR

%         -2 ((-1 + b) x00 - (-3 + b) x01 + x10 + b x10 + x11 - b x11)
%Out[15]= ------------------------------------------------------------
%                            x00 - x01 + x10 - x11




return

function [lhs, rhs] = babycheck(a,b,x)
lhs = 2 * ( a*x(c2i([0 0])) + (1-a)*x(c2i([0 1])) + b*x(c2i([1 0])) + (1-b)*x(c2i([1 1])) );
rhs = (1+(a-b)) * ((a+b)*(x(c2i([0 0]))+x(c2i([1 0]))) + (2-a-b)*(x(c2i([0 1]))+x(c2i([1 1]))));
return


function i=c2i(c)
global m n
dims = repmat(m,[1 n]);
i = coord2ind(c+1,dims);
return