/*
Generates arguments for the L3check program.  Call L3args with the
desired value of q, then use the returned string as the argument
list to L3check.  e.g., for q = 7:

    $ magma -b L3.m
    > L3args(7);
    7 1 4 1 3 4 6 3 0 3 2 3 19
    > quit;
    $ L3check 7 1 4 1 3 4 6 3 0 3 2 3 19
    q = 7:  FAIL for beta = w^57, gamma = w^2 + w
*/
L3args := function(q)
    F := GF(q);
    p := Characteristic(F);
    n := Degree(F);
    a := PrimitiveElement(F);
    pol1 := MinimalPolynomial(a);
    C1 := ChangeUniverse(Eltseq(pol1), Integers());
    K := ext<F | 3>;
    w := PrimitiveElement(K);
    pol2 := MinimalPolynomial(w, F);
    C2 := [ IsZero(c) select q-1 else Log(a, c) : c in Eltseq(pol2) ];
    primes := [ t[1] : t in Factorisation(q^3 - 1) ];
    args := [p,n] cat C1 cat [3] cat C2 cat [#primes] cat primes;
    return Prune(&cat [ IntegerToString(x) cat " " : x in args ]);
end function;