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Factoring a cyclotomic polynomial mod p

asked 4 years ago

dtoprakhisar gravatar image

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

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answered 4 years ago

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)
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Here n is the order right?

dtoprakhisar gravatar imagedtoprakhisar ( 4 years ago )

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

rburing gravatar imagerburing ( 4 years ago )

Thank you! That solved my problem.

dtoprakhisar gravatar imagedtoprakhisar ( 4 years ago )

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Asked: 4 years ago

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Last updated: May 13 '21