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  • ing's Method (see Theorem 4, here), P is a polynomial in A, B, C, ... with the coefficients symmetric in roots.(10) So, we can determine the coefficients of P based on the elementary symmetric polynomials using the roots [see Theorem 1, here].(11) We can therefore assume that the coefficients are known since we are assuming that the roots are known.(12) Since P is a product of nonzero polynomials,
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