Questions tagged [finite-fields]

In a Mathematica session, I evaluate: Needs["FiniteFields`"]; fld = GF[2]; Now, for example, I'd like to compute $a^3+a^5$ for $a \in{Z_2}$. The result I'd like to have is $0$, because in $Z_2$, $a^n=a$ and $a+a=0$. I tried: fld[{a^3}] +…

I'm trying to use the Finite Fields package to show that $x$ is not a primitive element of $\mathbb{Z}_3[x]/\langle x^3 + 2x + 2 \rangle \cong GF(3^3)$. The idea is to take the following piece of code: i = 1; While[ReduceElement[GF[3, {2, 2, 0,…

If I input: ToNumberField[Sqrt[2], 2^(1/4)] Mathematica returns: AlgebraicNumber[Root[-2 + #1^4 &, 2], {0, 0, 1, 0}] How would I know which root of x^4 - 2 Mathematica is referring to here? In this simple example it must mean either of the two real…