Factoring a cyclotomic polynomial mod p
How can I factor a cyclotomic polynomial into polynomials that are irreducible modulo p?
How can I factor a cyclotomic polynomial into polynomials that are irreducible modulo p?
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?
The complex zeros of cyclotomic_polynomial(n)
are all the n
th primitive roots of unity, the degree of the polynomial is φ(n).
Thank you! That solved my problem.
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Asked: 4 years ago
Seen: 344 times
Last updated: May 13 '21