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

Zaubertrank
23 ●4 ●5 ●9

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?

Thanks

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answered 12 years ago

Francis Clarke
386 ●4 ●10

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 ( 12 years ago )

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Asked: 12 years ago

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Last updated: Oct 21 '12

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