Re: Conversion (MATHEMATICA to PARI/GP)

[Predrag Terzic <pedja.terzic@hotmail.com>]

For more info see this post : https://mathoverflow.net/q/286304

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From: Predrag Terzic <pedja.terzic@hotmail.com>
Sent: Tuesday, May 14, 2019 8:27 PM
To: pari-users@pari.math.u-bordeaux.fr
Subject: Conversion (MATHEMATICA to PARI/GP)

 

Can anyone help me to convert this Mathematica code (see attachment) to PARI/GP code?

Mathematica code :

polmul[f_, g_, r_, n_] := Mod[f.NestList[RotateRight, g, r - 1], n]

matmul[a_, b_, r_, n_] :=

 Mod[{{polmul[a[[1, 1]], b[[1, 1]], r, n] +

     polmul[a[[1, 2]], b[[2, 1]], r, n],

    polmul[a[[1, 1]], b[[1, 2]], r, n] +

     polmul[a[[1, 2]], b[[2, 2]], r, n]}, {polmul[a[[2, 1]],

      b[[1, 1]], r, n] + polmul[a[[2, 2]], b[[2, 1]], r, n],

    polmul[a[[2, 1]], b[[1, 2]], r, n] +

     polmul[a[[2, 2]], b[[2, 2]], r, n]}}, n]

matsq[a_, r_, n_] := matmul[a, a, r, n]

matpow[a_, k_, r_, n_] :=

 If[k == 1, a,

  If[EvenQ[k], matpow[matsq[a, r, n], k/2, r, n],

   matmul[a, matpow[matsq[a, r, n], (k - 1)/2, r, n], r, n]]]

xmat[r_, n_] := {{PadRight[{0, 2}, r],

   PadRight[{n - 1}, r]}, {PadRight[{1}, r], ConstantArray[0, r]}}

smallestr[n_] := Module[{r}, If[n == 1 \[Or] EvenQ[n], Return[0]];

  For[r = 3, MemberQ[{0, 1, r - 1}, Mod[n, r]], r = NextPrime[r + 1],

   If[r < n \[And] Mod[n, r] == 0, Return[0]]];

  r]

isprime[n_] :=

 With[{r = smallestr[n]},

  If[r == 0, n == 2,

   With[{xp = matpow[xmat[r, n], n - 1, r, n]},

    Mod[RotateRight[xp[[1, 1]]] + xp[[1, 2]], n] ===

     PadRight[Append[ConstantArray[0, Mod[n, r]], 1], r]]]]