Given a bivariate and symmetric polynomial $P(x,y)$ with a high degree (probably larger than 8). Is there any algorithm that helps me know if $P(x,y)$ has a root over $\mathbb{R}^+$ or not? I may not need a specific root, I just want to check if there is a root, or not.
*P/S: I'm new to SageMath. Currently, I know some basic operation with multivariate polynomial like factorizing, adding, substracting, ... two polynomials. It would be great if you can explain your answer a little bit. Thank you.
