Is this Polynomial an SOS Polynomial?

[karate]

F = -0.2662*x^6 + 48.19*x^5 - 3424.2*x^4 + 121708*x^3 - 2*e^6*x^2 + 2*e^7*x - 6*e^7;

 

[gopher_p]

As mentioned in your other thread, $\lim_{x\rightarrow\pm\infty}F(x)=-\infty$. So $F$ is sometimes (you could even say way more often than not) negative. Since a sum of squares is always nonnegative, your polynomial is not a sum of squares.

 

[karate]

thank you sir, so what do you think is this type of equation?

 

[gopher_p]

thank you sir, so what do you think is this type of equation?

Well, first off the thing that (I think) you're asking me about is a function, not an equation. Secondly, I would characterize it as a polynomial of degree six.

Edit: I would also characterize this polynomial as apparently not being particularly well-suited for examination by analytic means.

 

[CellCoree]

Based on the given polynomial, it is not an SOS (Sum of Squares) polynomial. SOS polynomials have only non-negative coefficients, whereas this polynomial has negative coefficients. Additionally, SOS polynomials have a specific structure that is not present in this polynomial. Therefore, this is not an SOS polynomial.