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单词 quadratic field
释义

quadratic field

Any field of the form ℚ[√d] where d is a square-free integer and d ≠ 0,1. The elements of ℚ[√d] have the form q1 + q2√d, where q1,q2 are rational. ℚ[√d] is a degree 2 field extension over ℚ. Its ring of integers consists of those elements ζ∊ℚ[√d] that satisfy a quadratic equation ζ2 + aζ + b = 0, where a,b are integers. When d = −19, the ring of integers is ℤ[(1 + inline)/2], which is a principal ideal domain which is not a Euclidean domain.

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更新时间:2025/4/29 16:35:14