Code:
\[ P(t):=\prod\big( t-a_{1}^{1/k}-\omega_{2}a_{2}^{1/k}-\cdots-\omega_{n}a_{n}^{1/k}\big)\in\mathbb{Q}[ a_{1}^{1/k},\ldots, a_{n}^{1/k}][t], \]
Code:
\[ P(t):=\prod\big( t-a_{1}^{1/k}-\omega_{2}a_{2}^{1/k}-\cdots-\omega_{n}a_{n}^{1/k}\big)\in\mathbb{Q}[ a_{1}^{1/k},\ldots, a_{n}^{1/k}][t], \]
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