When I have this function $$f(x_1,x_2,x_3,x_4)=x_1x_3+x_2x_4$$
I convert it to a function with two variables
As an example $x_1=x_2=x,x_3=x_4=y$ I get $f(x,y)=2xy$
But I have many cases
1- $x_1=x_3=x,x_2=x_4=y$ I get $f(x,y)=x^2+x^2$
2-$x_1=x_4=x,x_3=x_4=y$ I get $f(x,y)=2xy$
...
I need to calculate all functions resulting from the restriction
There will be a repetitive process of hypothesis for variables.
What is the process of converting the function of four variables into a function with two variables ?
Is there a mathematical basis for this process as a theory?
Thanks for the help