Question: How do I show/prove no zeros in quadrant 3?

f:= 2*x^5-x^3*y+2*x^2*y^2-x*y^3+2*y^5;

This is symetrical in x and y.  subs(x=1,f) and  subs(y=1,f) are identical in form.

for idx to 10 do
end do;

This shows a curve to (0,0) in quadrant 2, rabit ears in quadrant 1, and a curve from (0,0) in quadrant 4.

Plotting this with python matplotlib shows values in quadrant 3.  I assume that matplotlib plots only the real zeros of the polynomial.  Looks like it, the plotted values match the real zeros in maple.

use RealDomain in
    for idx from -1/100 to 1/100 by 1/1000 do
    end do;
end use;

This shows no values in quadrant 3.

How do I show/prove no zeros in quadrant 3?

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