quasi
Posts:
10,411
Registered:
7/15/05


Re: Twovariable polynomials with a finite number of zeros
Posted:
May 4, 2014 5:42 PM


José Carlos Santos wrote: >José Carlos Santos wrote: >> >>I suppose that if P(x,y) is a polynomial in two variables with >>real coefficients which has only _n_ zeros, then the degree of >>P(x,y) is greater than or equal to 2n. Am I right? > >No, I am wrong! > > (x^3  x)^2 + (y^3  y)^2 > >has degree 6 and 9 zeros.
Which suggests ...
Conjecture:
If f in R[x,y] has exactly n zeros in R^2, then
(deg_x(f))*(deg_y(f)) >= 4n
where deg_x(f) denotes the degree of f in x, and deg_y(f) denotes the degree of f in y.
quasi

