Now, consider the case where we have clustered by support. The U(v)'s which appear all appear as a sum in an exponential when the representation 
is made. This yields the product representation 
for 
. By extension to power series other than that for Exp, we may write any average of any function 
as 
, where 
means take the sum of the functions arguments over arguments that are unique ordered subsets of 
. Thus, 
, etc. When we have a hierarchy of functions 
, or when we generate such a hierarchy from a single function's series expansion, we can solve this system for the 
.