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For instance $p(x,y):=(x^2+y^2) (y-x^2)^2 $$f(x,y):= (y-x^2)^2 $.

For instance $p(x,y):=(x^2+y^2) (y-x^2)^2 $.

For instance $f(x,y):= (y-x^2)^2 $.

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Pietro Majer
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For instance $p(x,y):=(x^2+y^2) (y-x^2)^2 $.