m~ray said:
I wanted to know if there is any way of classifying the set of all non-linear multivariable functions. I wish to analyse something over all possible non linear functions with 4 variables. In fact these variables are binary variables. for example f(x,y,u,v)= x.y - u\oplusv
If you are concerned with classification, it is important to explain exactly what structure we have here. Are ##x,y,u,v## elements of some vector spaces? Are the products maps to the same or a different vector space, or perhaps field?
There are some well-studied objects with a structure that might be relevant for your problem. A
bilinear map is a function
$$B: V \times W \rightarrow X,$$
where ##V, W, X## are vector spaces and ##v \mapsto B(v,w)##, ##w \mapsto B(v,w)## are linear maps.
In the case where ##W=V## and ##X = F## is actually a field, we have a
bilinear form:
$$ V : V\times V \rightarrow F.$$
Closely related to this is the notion of a
sesquilinear form.
If your function of interest fits one of these categories, it might be possible to find additional information that might be relevant to your question.
