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Solving system of power sum symmetric polynomials

Thanks to Calvin in the comments. Following wikipedia, we can write the monic polynomial with roots $x_1, ..., x_n$ as $$\prod_{i=1}^n (x-x_i) = \sum_{k=0}^n (-1)^k e_k x^{n-k}$$ where the $e_k$ is ...
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