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Given an ideal $I$ over $\mathbb{C}$ and P, a polynomial, is it decidable whether $P\in I$?

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    $\begingroup$ How is the ideal given? ​ ​ $\endgroup$
    – user6973
    Oct 8, 2017 at 5:15

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Yes, that's the Ideal Membership Problem and it is solved using Gröbner bases.

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  • $\begingroup$ Thank you, you always give me perfect answer. and I wonder if it may be extended to other closed fields. $\endgroup$ Oct 8, 2017 at 5:23

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