Undecidability of Parametric Solutions of Polynomial Equations
K. H. Kim, F.W. Roush · Proceedings of the American Mathematical Society · 1993
We prove that, for any field ${\mathbf {F}}$ of characteristic $0$ satisfying a hypothesis related to not being algebraically closed, the problem of finding non-constant parametric solutions in ${\mathbf {F}}(t)$ to a polynomial system with coefficients in ${\mathbf {F}}$ is algorithmically unsolvable.