quasi
Posts:
11,308
Registered:
7/15/05


Re: Twovariable polynomials with a finite number of zeros
Posted:
May 4, 2014 6:17 PM


Pubkeybreaker wrote: >On Saturday, May 3, 2014 10:10:28 AM UTC4, 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?
quasi

