int inc(zz_pE& x)
{
long d = deg(x.modulus()), i;
zz_pE tee = to_zz_pE(zz_pX(1,1)), tee_to_i = to_zz_pE(zz_pX(0,1));
i = 0;
do {
x += tee_to_i;
tee_to_i *= tee;
} while (coeff(x.LoopHole(),i) == 0 && ++i < d);
return (i >= d) ? 1 : 0;
}
void buildLinPolyMatrix(mat_zz_pE& M, long p)
{
long d = zz_pE::degree();
M.SetDims(d, d);
for (long j = 0; j < d; j++)
conv(M[0][j], zz_pX(j, 1));
for (long i = 1; i < d; i++)
for (long j = 0; j < d; j++)
M[i][j] = power(M[i-1][j], p);
}
void applyLinPoly(zz_pE& beta, const vec_zz_pE& C, const zz_pE& alpha, long p)
{
long d = zz_pE::degree();
assert(d == C.length());
zz_pE gamma, res;
gamma = to_zz_pE(zz_pX(1, 1));
res = C[0]*alpha;
for (long i = 1; i < d; i++) {
gamma = power(gamma, p);
res += C[i]*to_zz_pE(CompMod(rep(alpha), rep(gamma), zz_pE::modulus()));
}
beta = res;
}
int main(int argc, char *argv[])
{
argmap_t argmap;
argmap["p"] = "5";
argmap["m"] = "101";
argmap["r"] = "1";
if (!parseArgs(argc, argv, argmap)) usage(argv[0]);
long p = atoi(argmap["p"]);
long m = atoi(argmap["m"]);
long r = atoi(argmap["r"]);
cout << "p=" << p << ", m=" << m << ", r=" << r << "\n";
ZZX phimx = Cyclotomic(m);
zz_p::init(p);
zz_pX phimx_modp = to_zz_pX(phimx);
vec_zz_pX factors = SFCanZass(phimx_modp);
vec_ZZX FFactors;
MultiLift(FFactors, factors, phimx, r);
zz_p::init(power_long(p, r));
vec_zz_pX Factors;
Factors.SetLength(FFactors.length());
for (long i = 0; i < Factors.length(); i++)
conv(Factors[i], FFactors[i]);
zz_pX G = Factors[0];
long d = deg(G);
cout << "d=" << d << "\n";
zz_pE::init(G);
// L selects the even coefficients
vec_zz_pE L;
L.SetLength(d);
for (long j = 0; j < d; j++) {
if (j % 2 == 0)
L[j] = to_zz_pE(zz_pX(j, 1));
}
vec_zz_pE C;
buildLinPolyCoeffs(C, L, p, r);
zz_pE alpha, beta;
random(alpha);
applyLinPoly(beta, C, alpha, p);
cout << alpha << "\n";
cout << beta << "\n";
}
