Ask Your Question
1

Factoring a cyclotomic polynomial mod p

asked 2021-05-13 10:18:22 +0200

dtoprakhisar gravatar image

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

edit retag flag offensive close merge delete

1 Answer

Sort by ยป oldest newest most voted
2

answered 2021-05-13 11:57:29 +0200

rburing gravatar image

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)
edit flag offensive delete link more

Comments

Here n is the order right?

dtoprakhisar gravatar imagedtoprakhisar ( 2021-05-13 12:05:37 +0200 )edit

The complex zeros of cyclotomic_polynomial(n) are all the nth primitive roots of unity, the degree of the polynomial is $\varphi(n)$.

rburing gravatar imagerburing ( 2021-05-13 12:21:07 +0200 )edit

Thank you! That solved my problem.

dtoprakhisar gravatar imagedtoprakhisar ( 2021-05-13 12:29:47 +0200 )edit

Your Answer

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

Add Answer

Question Tools

1 follower

Stats

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

Seen: 76 times

Last updated: May 13