trees and plants said:
Perhaps the thread should be closed, i do not know the answer yet.
I think that you try to reinvent the wheel. When I was a kid I tried to figure out whether there could be a binary operation ##\circ## such that ##\log(a+b)=\log(a)\circ \log (b)##. I was fascinated by the fact that we can turn powers into multiplications ##\log(a^b)=b\log(a)## and multiplications into additions ##\log(a\cdot b)=\log(a)+\log(b)##. So why not turn additions into something even
smaller? I started to think about the fact that we have a fixed point: ##2^2=2\cdot 2 = 2+2=4,## so my only requirement was ##2\circ 2 = 4.##
Now, many years later, I know that there cannot be such an operation. Why? Because of the Leibniz rule of differentiation, or even more general: because of the definition of derivations. Differentiation of products yield sums, but differentiation of linear functions are themselves linear functions. There is no
smaller binary operation than addition. However, this insight took me a complete study of mathematics and time to gain an overview of the underlying principles. As tempting as it might be to
revolutionize a method, as it is in vain. To see this may take a while, and I have found other interesting unknown concepts. There are no shortcuts in science. You will have to do it like everybody else: study, learn, talk a lot about it, read even more, and maybe then, but surely not before then, you may find new concepts and views.