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Topic: Two-variable polynomials with a finite number of zeros
Replies: 9   Last Post: May 5, 2014 5:09 PM

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Posts: 12,067
Registered: 7/15/05
Re: Two-variable polynomials with a finite number of zeros
Posted: May 4, 2014 6:17 PM
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Pubkeybreaker wrote:
>On Saturday, May 3, 2014 10:10:28 AM UTC-4, José Carlos Santos wrote:
>> On 03/05/2014 15:02, Pubkeybreaker wrote: >> Hi all, If (a_1,b_1), (a_2,b_2), ..., (a_n,b_n) are _n_ distinct points of R^2, then these points are the zeros of the polynomial prod_k ((x - a_k)^2 + (y - b_k)^2), whose degree is 2n. I suppose that if P(x,y) is a polynomial in two variables with real coefficients which has only _n_
zeros, > > ??? Only n zeros??? Impossible. Fix y = y0. The result is a polynomial > in one variable, x. It has n zeros. This is true for ALL y0. I don't understand your remark. Are you saying that there are no polynomials in two variables and real coefficients with only a finite number of zeros in R^2?
>Nowhere do I see a stated condition that the zeros must be in R^2.
>I see a statement about "real coefficients".

To Pubkeybreaker:

Why do all your recent post badly mangle the formatting of the
quoted message?


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