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Apr 14 at 14:14 history edited Iosif Pinelis CC BY-SA 4.0
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Apr 14 at 2:10 comment added Iosif Pinelis @user526214 : Do you have a further response?
Apr 12 at 21:14 history edited Iosif Pinelis CC BY-SA 4.0
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Apr 12 at 21:12 comment added Iosif Pinelis @user526214 : I have addressed this concern.
Apr 12 at 21:07 history edited Iosif Pinelis CC BY-SA 4.0
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Apr 12 at 20:55 comment added user526214 In my question I assume that the conic $Q(x,y)$ defined in $\mathbb{R}^2$ is real and irreducible. Now, what if the zeros of $P(x,y)$ and $Q(x,y)$ coincide in $\mathbb{R}^2$ but not in $\mathbb{C}^2$ as stated to apply Hilbert's Nullstellensatz? So is there a counterexample to my question?
Apr 12 at 20:19 history edited Iosif Pinelis CC BY-SA 4.0
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Apr 12 at 20:09 history answered Iosif Pinelis CC BY-SA 4.0