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Undecidability of parametric solutions of polynomial equations


Authors: K. H. Kim and F. W. Roush
Journal: Proc. Amer. Math. Soc. 118 (1993), 345-348
MSC: Primary 03D35; Secondary 03D80, 11U05, 12L05
DOI: https://doi.org/10.1090/S0002-9939-1993-1132414-5
MathSciNet review: 1132414
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1132414-5
Keywords: Diophantine problem in polynomial equation, parametric solution
Article copyright: © Copyright 1993 American Mathematical Society

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