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276 views

Finite Field matrix rank calculation

How does one define a matrix over $\mathrm{GF}(p^r)$ in Mathematica in order to compute rank? I am working with $\mathrm{GF}(2)$?
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Sum of zeros in finite Galois field

In the following code: << FiniteFields` GF[2][{0}] + GF[2][{0}] == GF[2][{0}] GF[2][{0}] + GF[2][{0}] + GF[2][{0}] == GF[2][{0}] Why does the second line ...
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73 views

Package FiniteFields

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 ...
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406 views

Elliptic curve cryptography in Mathematica

I can find no resources for doing elliptic curve cryptography. I have used the finite field package, but I find it cumbersome and it does not seem to have any builtin methods for ECC. How can I get ...
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377 views

Polynomial factorization over finite fields with non-prime order

One can easily factor a polynomial over finite fields of prime order, using Factor command: ...
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PolynomialExtendedGCD in 2 variables

Consider a field $R$ and the ring $A=R[y]$. Consider two polynomials $g,h\in A[x]$. I want to obtain $d=\gcd(g,h)\in A[x]$ and two polynomials $s,t\in A[x]$ satisfying the B├ęzout relation: $sg+th=d$. ...
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54 views

How can I express Sqrt[2] as an element in the field Q(2^(1/4))?

If I input: ToNumberField[Sqrt[2], 2^(1/4)] Mathematica returns: AlgebraicNumber[Root[-2 + #1^4 &, 2], {0, 0, 1, 0}] How ...
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39 views

Equality of Galois Fields (GF[5][{4}]^4 = GF[5][{3}]^4)?

under FiniteFields, how can i test if, for example, if GF[5][{3}]^4 == GF[5][{2}]^4 Using regular == won't work.