Cyclotomic Factors and LRS-Degeneracy
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910005082456064 |
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| author | Abbott, John Mexis, Nico |
| author_facet | Abbott, John Mexis, Nico |
| contents | We present three new, practical algorithms for polynomials in $\mathbb{Z}[x]$: one to test if a polynomial is cyclotomic, one to determine which cyclotomic polynomials are factors, and one to determine whether the given polynomial is LRS-degenerate. A polynomial is "LRS-degenerate" iff it has two distinct roots $α, β$ such that $β= ζα$ for some root of unity $ζ$. All three algorithms are based on "intelligent brute force". The first two produce the indexes of the cyclotomic polynomials; the third produces a list of degeneracy orders. The algorithms are implemented in CoCoALib. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08751 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cyclotomic Factors and LRS-Degeneracy Abbott, John Mexis, Nico Commutative Algebra Number Theory 11R18, 11B37, 11C08 We present three new, practical algorithms for polynomials in $\mathbb{Z}[x]$: one to test if a polynomial is cyclotomic, one to determine which cyclotomic polynomials are factors, and one to determine whether the given polynomial is LRS-degenerate. A polynomial is "LRS-degenerate" iff it has two distinct roots $α, β$ such that $β= ζα$ for some root of unity $ζ$. All three algorithms are based on "intelligent brute force". The first two produce the indexes of the cyclotomic polynomials; the third produces a list of degeneracy orders. The algorithms are implemented in CoCoALib. |
| title | Cyclotomic Factors and LRS-Degeneracy |
| topic | Commutative Algebra Number Theory 11R18, 11B37, 11C08 |
| url | https://arxiv.org/abs/2403.08751 |