NTL_CLIENT
int main()
{
ZZ_p::init(conv<ZZ>(17)); // define GF(17)
ZZ_pX P;
BuildIrred(P, 10); // generate an irreducible polynomial P
// of degree 10 over GF(17)
ZZ_pE::init(P); // define GF(17^10)
ZZ_pEX f, g, h; // declare polynomials over GF(17^10)
random(f, 20); // f is a random, monic polynomial of degree 20
SetCoeff(f, 20);
random(h, 20); // h is a random polynomial of degree less than 20
g = MinPolyMod(h, f); // compute the minimum polynomial of h modulo f
if (g == 0) Error("oops (1)"); // check that g != 0
if (CompMod(g, h, f) != 0) // check that g(h) = 0 mod f
Error("oops (2)");
}
NTL_CLIENT
int main()
{
zz_p::init(17);
zz_pX P;
BuildIrred(P, 10);
zz_pE::init(P);
zz_pEX f, g, h;
random(f, 20);
SetCoeff(f, 20);
random(h, 20);
g = MinPolyMod(h, f);
if (deg(g) < 0) Error("bad zz_pEXTest (1)");
if (CompMod(g, h, f) != 0)
Error("bad zz_pEXTest (2)");
vec_pair_zz_pEX_long v;
long i;
for (i = 0; i < 5; i++) {
long n = RandomBnd(20)+1;
cerr << n << " ";
random(f, n);
SetCoeff(f, n);
v = CanZass(f);
g = mul(v);
if (f != g) cerr << "oops1\n";
long i;
for (i = 0; i < v.length(); i++)
if (!DetIrredTest(v[i].a))
Error("bad zz_pEXTest (3)");
}
cerr << "\n";
cerr << "zz_pEXTest OK\n";
}
void EDFSplit(vec_ZZ_pEX& v, const ZZ_pEX& f, const ZZ_pEX& b, long d)
{
ZZ_pEX a, g, h;
ZZ_pEXModulus F;
vec_ZZ_pE roots;
build(F, f);
long n = F.n;
long r = n/d;
random(a, n);
TraceMap(g, a, d, F, b);
MinPolyMod(h, g, F, r);
FindRoots(roots, h);
FindFactors(v, f, g, roots);
}
void CharPolyMod(zz_pX& g, const zz_pX& a, const zz_pX& ff)
{
zz_pX f = ff;
MakeMonic(f);
long n = deg(f);
if (n <= 0 || deg(a) >= n)
Error("CharPoly: bad args");
if (IsZero(a)) {
clear(g);
SetCoeff(g, n);
return;
}
if (n > 90 || (zz_p::PrimeCnt() <= 1 && n > 45)) {
zz_pX h;
MinPolyMod(h, a, f);
if (deg(h) == n) {
g = h;
return;
}
}
if (zz_p::modulus() < n+1) {
HessCharPoly(g, a, f);
return;
}
vec_zz_p u(INIT_SIZE, n+1), v(INIT_SIZE, n+1);
zz_pX h, h1;
negate(h, a);
long i;
for (i = 0; i <= n; i++) {
u[i] = i;
add(h1, h, u[i]);
resultant(v[i], f, h1);
}
interpolate(g, u, v);
}
static CYTHON_INLINE struct ZZX* ZZX_minpoly_mod(struct ZZX* x, struct ZZX* y)
{
ZZX* f = new ZZX();
MinPolyMod(*f, *x, *y);
return f;
}
NTL_CLOSE_NNS
NTL_CLIENT
int main()
{
GF2X p;
BuildIrred(p, 200);
GF2E::init(p);
GF2EX f;
SetCoeff(f, 41);
SetCoeff(f, 1);
SetCoeff(f, 0);
GF2X a;
SetCoeff(a, 117);
SetCoeff(a, 10);
SetCoeff(a, 0);
GF2EX g, h;
SetX(g);
SetCoeff(g, 0, to_GF2E(a));
MinPolyMod(h, g, f);
f = h;
vec_pair_GF2EX_long u;
CanZass(u, f, 1);
cerr << "factorization pattern:";
long i;
for (i = 0; i < u.length(); i++) {
cerr << " ";
long k = u[i].b;
if (k > 1)
cerr << k << "*";
cerr << deg(u[i].a);
}
cerr << "\n\n\n";
GF2EX ff;
mul(ff, u);
if (f != ff || u.length() != 11) {
cerr << "GF2EXTest NOT OK\n";
return 1;
}
{
cerr << "multiplication test...\n";
BuildIrred(p, 512);
GF2E::init(p);
GF2EX A, B, C, C1;
random(A, 512);
random(B, 512);
double t;
long i;
t = GetTime();
for (i = 0; i < 10; i++) PlainMul(C, A, B);
t = GetTime() - t;
cerr << "time for plain mul of degree 511 over GF(2^512): " << (t/10) << "s\n";
t = GetTime();
for (i = 0; i < 10; i++) mul(C1, A, B);
t = GetTime() - t;
cerr << "time for karatsuba mul of degree 511 over GF(2^512): " << (t/10) << "s\n";
if (C != C1) {
cerr << "GF2EXTest NOT OK\n";
return 1;
}
}
{
cerr << "multiplication test...\n";
BuildIrred(p, 16);
GF2E::init(p);
GF2EX A, B, C, C1;
random(A, 512);
random(B, 512);
double t;
t = GetTime();
for (i = 0; i < 10; i++) PlainMul(C, A, B);
t = GetTime() - t;
cerr << "time for plain mul of degree 511 over GF(2^16): " << (t/10) << "s\n";
t = GetTime();
for (i = 0; i < 10; i++) mul(C1, A, B);
t = GetTime() - t;
cerr << "time for karatsuba mul of degree 511 over GF(2^16): " << (t/10) << "s\n";
if (C != C1) {
cerr << "GF2EXTest NOT OK\n";
return 1;
}
}
cerr << "GF2EXTest OK\n";
return 0;
}
void SFBerlekamp(vec_ZZ_pX& factors, const ZZ_pX& ff, long verbose)
{
ZZ_pX f = ff;
if (!IsOne(LeadCoeff(f)))
Error("SFBerlekamp: bad args");
if (deg(f) == 0) {
factors.SetLength(0);
return;
}
if (deg(f) == 1) {
factors.SetLength(1);
factors[0] = f;
return;
}
double t;
const ZZ& p = ZZ_p::modulus();
long n = deg(f);
ZZ_pXModulus F;
build(F, f);
ZZ_pX g, h;
if (verbose) { cerr << "computing X^p..."; t = GetTime(); }
PowerXMod(g, p, F);
if (verbose) { cerr << (GetTime()-t) << "\n"; }
vec_long D;
long r;
vec_ZZVec M;
if (verbose) { cerr << "building matrix..."; t = GetTime(); }
BuildMatrix(M, n, g, F, verbose);
if (verbose) { cerr << (GetTime()-t) << "\n"; }
if (verbose) { cerr << "diagonalizing..."; t = GetTime(); }
NullSpace(r, D, M, verbose);
if (verbose) { cerr << (GetTime()-t) << "\n"; }
if (verbose) cerr << "number of factors = " << r << "\n";
if (r == 1) {
factors.SetLength(1);
factors[0] = f;
return;
}
if (verbose) { cerr << "factor extraction..."; t = GetTime(); }
vec_ZZ_p roots;
RandomBasisElt(g, D, M);
MinPolyMod(h, g, F, r);
if (deg(h) == r) M.kill();
FindRoots(roots, h);
FindFactors(factors, f, g, roots);
ZZ_pX g1;
vec_ZZ_pX S, S1;
long i;
while (factors.length() < r) {
if (verbose) cerr << "+";
RandomBasisElt(g, D, M);
S.kill();
for (i = 0; i < factors.length(); i++) {
const ZZ_pX& f = factors[i];
if (deg(f) == 1) {
append(S, f);
continue;
}
build(F, f);
rem(g1, g, F);
if (deg(g1) <= 0) {
append(S, f);
continue;
}
MinPolyMod(h, g1, F, min(deg(f), r-factors.length()+1));
FindRoots(roots, h);
S1.kill();
FindFactors(S1, f, g1, roots);
append(S, S1);
}
swap(factors, S);
}
if (verbose) { cerr << (GetTime()-t) << "\n"; }
if (verbose) {
cerr << "degrees:";
long i;
for (i = 0; i < factors.length(); i++)
cerr << " " << deg(factors[i]);
cerr << "\n";
}
}