# Factoring a cyclotomic polynomial mod p

How can I factor a cyclotomic polynomial into polynomials that are irreducible modulo p?

Factoring a cyclotomic polynomial mod p

How can I factor a cyclotomic polynomial into polynomials that are irreducible modulo p?

add a comment

2

It is quite easy:

```
sage: n = 11
sage: p = 3
sage: cyclotomic_polynomial(n).change_ring(GF(p)).factor()
(x^5 + 2*x^3 + x^2 + 2*x + 2) * (x^5 + x^4 + 2*x^3 + x^2 + 2)
```

Please start posting anonymously - your entry will be published after you log in or create a new account.

Asked: ** 2021-05-13 10:18:22 +0200 **

Seen: **76 times**

Last updated: **May 13**

is the class field a kind of field(group,ring,feild)? [closed]

how to run CyclotomicField([zeta7+zeta7^-1]?

Taking gcd with respect to one variable

Evaluating discriminant of a polynomial in Z_n[x]/<x^r-1>

how to find minimal polynomial

Problem with UniversalCyclotomicField?

How to Compute $\operatorname{Pic}(\mathbb{Z}[\zeta_p,1/p])$

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.