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This is unironically an extremely good question. What is the general method for a computer to compute ANALYTICALLY the solution to any kind of equation, aka the zeroes of a function in a field taking any number of inputs.
>Newton-Raphson for R^n
>Fermat little-Theorem for prime-characteristic fields
These are exemples of explicit solution methods for definite classes of equations. I am talking about an oracle than solves even in non-closed form expression.