Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2109.07544 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909378355920896 |
|---|---|
| author | Cafure, Antonio Cesaratto, Eda |
| author_facet | Cafure, Antonio Cesaratto, Eda |
| contents | Cyclotomic polynomials are basic objects in Number Theory. Their properties depend on the number of distinct primes that intervene in the factorization of their order, and the binary case is thus the first nontrivial case. This paper sees the vector of coefficients of the polynomial as a word on a ternary alphabet $\{-1,0 ,+1\}$. It designs an efficient algorithm that computes a compact representation of this word. This algorithm is of linear time with respect to the size of the output, and, thus, optimal. This approach allows to recover known properties of coefficients of binary cyclotomic polynomials, and extends to the case of polynomials associated with numerical semi-groups of dimension 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_07544 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Binary Cyclotomic Polynomials: Representation via Words and Algorithms Cafure, Antonio Cesaratto, Eda Number Theory Combinatorics 11C08, 11Y16, 05A05 Cyclotomic polynomials are basic objects in Number Theory. Their properties depend on the number of distinct primes that intervene in the factorization of their order, and the binary case is thus the first nontrivial case. This paper sees the vector of coefficients of the polynomial as a word on a ternary alphabet $\{-1,0 ,+1\}$. It designs an efficient algorithm that computes a compact representation of this word. This algorithm is of linear time with respect to the size of the output, and, thus, optimal. This approach allows to recover known properties of coefficients of binary cyclotomic polynomials, and extends to the case of polynomials associated with numerical semi-groups of dimension 2. |
| title | Binary Cyclotomic Polynomials: Representation via Words and Algorithms |
| topic | Number Theory Combinatorics 11C08, 11Y16, 05A05 |
| url | https://arxiv.org/abs/2109.07544 |