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Trying to display the roots of a polynomial over a finite field

asked 2012-10-20 17:20:48 -0500

Zaubertrank gravatar image

So I'm trying to use the .roots() command on a polynomial over the quotient ring F_2[x]/x^5 + x^2 + 1, which is a field isomorphic to F_32. But it keeps giving me the following error:

NotImplementedError: root finding with multiplicities for this polynomial not implemented (try the multiplicities=False option)

Is there a way to get this to work?


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answered 2012-10-20 23:05:02 -0500

Francis Clarke gravatar image

Sage allows you to construct finite fields with a root of any irreducible polynomial as a generator. Thus

sage: PF2.<x> = GF(2)[]
sage: f = x^5 + x^2 + 1
sage: F32.<a> = GF(32, modulus=f)
sage: a.minimal_polynomial()
x^5 + x^2 + 1
sage: PF32.<s> = F32[]
sage: PF32.random_element().roots()
[(a^2 + a + 1, 1), (a^4 + a^3 + a^2, 1)]
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Thank you!

Zaubertrank gravatar imageZaubertrank ( 2012-10-21 07:10:02 -0500 )edit

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Asked: 2012-10-20 17:20:48 -0500

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Last updated: Oct 20 '12