- #1
- 5,779
- 172
Suppose there is a set of complex variables
[tex]\{x_i,\,i=1 \ldots M;\;\;y_k,\,k=1 \ldots N\}[/tex]
and a polynomial equation
[tex]p(x_i, y_k) = 0[/tex]
Is there a way to prove or disprove for such an equation whether it can be reformulated as
[tex]f(x_i) = g(y_k) [/tex]
with two functions f and g with
[tex]\nabla_y f= 0[/tex]
[tex]\nabla_x g= 0[/tex]
[tex]\{x_i,\,i=1 \ldots M;\;\;y_k,\,k=1 \ldots N\}[/tex]
and a polynomial equation
[tex]p(x_i, y_k) = 0[/tex]
Is there a way to prove or disprove for such an equation whether it can be reformulated as
[tex]f(x_i) = g(y_k) [/tex]
with two functions f and g with
[tex]\nabla_y f= 0[/tex]
[tex]\nabla_x g= 0[/tex]