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 | References | Similar Articles | Additional Information

Abstract: We prove that, for any field of characteristic 0 satisfying a hypothesis related to not being algebraically closed, the problem of finding non-constant parametric solutions in to a polynomial system with coefficients in 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