Factoring a cyclotomic polynomial mod p

Processing math: 100%

First time here? Check out the FAQ!

dtoprakhisar
13 ●4

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

1 Answer

Sort by » oldest newest most voted

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)

Here n is the order right?

dtoprakhisar ( 4 years ago )

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

rburing ( 4 years ago )

Thank you! That solved my problem.

dtoprakhisar ( 4 years ago )

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

1 follower

Asked: 4 years ago

Seen: 344 times

Last updated: May 13 '21