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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 [D2]
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 [Ha]
 R. Hartshorne, Algebraic geometry, SpringerVerlag, Berlin, 1977. MR 0463157 (57:3116)
 [KR]
 K. H. Kim and F. W. Roush, Diophantine undecidability of , J. Algebra (to appear).
 [P]
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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
