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A sufficient condition of Euclidean rings given by polynomial optimization over a box

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  • A sufficient condition of Euclidean rings is given by polynomial optimization. Then, through computation, we give all norm-Euclidean square number fields, four examples of norm-Euclidean cubic number fields and two examples of norm-Euclidean cyclotomic fields, with the absolute of a norm less than 1 over the corresponding box, respectively.
    Mathematics Subject Classification: Primary: 13F07; Secondary: 90C26.


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