Suppose there is a set of complex variables(adsbygoogle = window.adsbygoogle || []).push({});

[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]

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# Solution of polynomial equations

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