Factoring a cyclotomic polynomial mod p

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

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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 ( 2021-05-13 12:05:37 +0100 )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 ( 2021-05-13 12:21:07 +0100 )edit

Thank you! That solved my problem.

dtoprakhisar ( 2021-05-13 12:29:47 +0100 )edit

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Asked: 2021-05-13 10:18:22 +0100

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Last updated: May 13 '21