Undecidability of parametric solutions of polynomial equations

Kim, K. H.; Roush, F. W.

doi:10.1090/S0002-9939-1993-1132414-5

Undecidability of parametric solutions of polynomial equations
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by K. H. Kim and F. W. Roush PDF

Proc. Amer. Math. Soc. 118 (1993), 345-348 Request permission

Abstract:

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.

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