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单词 Cyclotomic polynomial
释义

Cyclotomic polynomial

中文百科

分圆多项式

n次分圆多项式,是指多项式x-1分解因式结果中的一个特定多项式f(x),满足f(x)=0的解都不是低于n次的形如x-1=0的方程的解。 n次的分圆多项式的根是e 而(k,n)=1

英语百科

Cyclotomic polynomial 分圆多项式

In mathematics, more specifically in algebra, the nth cyclotomic polynomial, for any positive integer n, is the unique irreducible polynomial with integer coefficients, which is a divisor of x^n-1 and is not a divisor of x^k-1 for any k < n. Its roots are the nth primitive roots of unity 
e^{2i\pi\frac{k}{n}}
, where k runs over the integers lower than n and coprime to n. In other words, the nth cyclotomic polynomial is equal to

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更新时间:2025/6/20 18:02:37