# Is the relation decidable?

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

• How is the ideal given? ​ ​ – user6973 Oct 8 '17 at 5:15

## 1 Answer

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

• Thank you, you always give me perfect answer. and I wonder if it may be extended to other closed fields. – XL _At_Here_There Oct 8 '17 at 5:23