A numerical semigroup S is cyclotomic if its semigroup polynomial \(\mathrm {P}_S\) is a product of cyclotomic polynomials. The number of irreducible factors of \(\mathrm {P}_S\) (with multiplicity) is the polynomial length \(\ell (S)\) of S. We show that a cyclotomic numerical semigroup is complete intersection if \(\ell (S)\le 2\). This establishes a particular case of a conjecture of Ciolan et al. (SIAM J Discrete Math 30(2):650–668, 2016) claiming that every cyclotomic numerical semigroup is complete intersection. In addition, we investigate the relation between \(\ell (S)\) and the embedding dimension of S.

如果数值半群S的半群多项式\(\mathrm {P}_S\)是分圆多项式的乘积，则它是分圆的。的不可约因子的数目\（\ mathrm {P} _S \） （与多重度）是多项式长度\（\ ELL（S）\）的小号。我们证明如果\(\ell (S)\le 2\)，一个分圆数值半群是完全交集。这建立了 Ciolan 等人的猜想的特殊情况。(SIAM J Discrete Math 30(2):650–668, 2016) 声称每个分圆数值半群都是完全交集。此外，我们研究了\(\ell (S)\)和S的嵌入维度之间的关系。