An auxiliary function whose grid exceeds the zero count and whose non-zero derivatives give small integer polynomials, when only e^{x₁y₂} and e^{x₂y₂} are algebraic

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An auxiliary function whose grid exceeds the zero count and whose non-zero derivatives give small integer polynomials, when only e^{x₁y₂} and e^{x₂y₂} are algebraic · Prove2Me