Undecidability of parametric solutions of polynomial equations
Authors:
K. H. Kim and F. W. Roush
Journal:
Proc. Amer. Math. Soc. 118 (1993), 345348
MSC:
Primary 03D35; Secondary 03D80, 11U05, 12L05
MathSciNet review:
1132414
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Abstract: We prove that, for any field of characteristic 0 satisfying a hypothesis related to not being algebraically closed, the problem of finding nonconstant parametric solutions in to a polynomial system with coefficients in is algorithmically unsolvable.
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 , The Diophantine problem for polynomial rings of positive characteristic, Logic Colloq., vol. 82, NorthHolland, Amsterdam, 1979. MR 567668 (81h:03090)
 [Ha]
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 K. H. Kim and F. W. Roush, Diophantine undecidability of , J. Algebra (to appear).
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 T. Pheidas, An undecidability result for power series rings of positive characteristic. II, Proc. Amer. Math. Soc. 100 (1987), 526530. MR 891158 (89c:03075)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199311324145
PII:
S 00029939(1993)11324145
Keywords:
Diophantine problem in polynomial equation,
parametric solution
Article copyright:
© Copyright 1993
American Mathematical Society
