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2023-04-14 13:58:31 +0200 marked best answer Find a root of bivariate polynomial

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.

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2023-04-09 21:19:43 +0200 asked a question Find a root of bivariate polynomial

Find a root of bivariate polynomial Given a bivariate and symmetric polynomial $P(x,y)$ with a high degree (probably lar