# Boltzmann generator for binary trees with the specification T = E + ZT^2
# and generator for the pointed class.  This improves the performance

BoltzmannTree := proc(x)
	      # set up	
	      u := evalf(rand()/10^12);	
	      	   # maple rand() gives a 12 digit nonneg int	

	      # handle union		
	      if u < 1/((1-sqrt(1-4*x))/(2*x)) then
	      	 return E;
	      end if;		      

	      # handle product
	      return [Z, BoltzmannTree(x), BoltzmannTree(x)];
end proc;
	      

BoltzmannPointedTree := proc(x)
		     # set up
		     T := (1-sqrt(1-4*z))/(2*z);
		     pointedT := diff(T, z);
		     T := subs(z=x, T);
		     pointedT := subs(z=x, pointedT);
		     u := evalf(rand()/10^12);	
	      	       	  # maple rand() gives a 12 digit nonneg int	

		     # handle union
		     if u < x*T/pointedT then
		     	return [Z, BoltzmannTree(x), BoltzmannTree(x)];
		     end if;
		     if u < x*T/pointedT + x*pointedT*T/pointedT then
		     	return [Z, BoltzmannPointedTree(x), BoltzmannTree(x)];
		     end if;
		     return [Z, BoltzmannTree(x), BoltzmannPointedTree(x)];
end proc;