void FindFactors(vec_ZZ_pEX& factors, const ZZ_pEX& f, const ZZ_pEX& g,
const vec_ZZ_pE& roots)
{
long r = roots.length();
factors.SetMaxLength(r);
factors.SetLength(0);
RecFindFactors(factors, f, g, roots, 0, r-1);
}
static
void GenerateBabySteps(ZZ_pEX& h1, const ZZ_pEX& f, const ZZ_pEX& h, long k,
long verbose)
{
double t;
if (verbose) { cerr << "generating baby steps..."; t = GetTime(); }
ZZ_pEXModulus F;
build(F, f);
ZZ_pEXArgument H;
#if 0
double n2 = sqrt(double(F.n));
double n4 = sqrt(n2);
double n34 = n2*n4;
long sz = long(ceil(n34/sqrt(sqrt(2.0))));
#else
long sz = 2*SqrRoot(F.n);
#endif
build(H, h, F, sz);
h1 = h;
long i;
if (!use_files) {
BabyStepFile.kill();
BabyStepFile.SetLength(k-1);
}
for (i = 1; i <= k-1; i++) {
if (use_files) {
ofstream s;
OpenWrite(s, FileName(ZZ_pEX_stem, "baby", i));
s << h1 << "\n";
s.close();
}
else
BabyStepFile(i) = h1;
CompMod(h1, h1, H, F);
if (verbose) cerr << "+";
}
if (verbose)
cerr << (GetTime()-t) << "\n";
}
static
void FileCleanup(long k, long l)
{
if (use_files) {
long i;
for (i = 1; i <= k-1; i++)
remove(FileName(ZZ_pEX_stem, "baby", i));
for (i = 1; i <= l; i++)
remove(FileName(ZZ_pEX_stem, "giant", i));
}
else {
BabyStepFile.kill();
GiantStepFile.kill();
}
}
static
void MulByXPlusY(vec_ZZ_pEX& h, const ZZ_pEX& f, const ZZ_pEX& g)
// h represents the bivariate polynomial h[0] + h[1]*Y + ... + h[n-1]*Y^k,
// where the h[i]'s are polynomials in X, each of degree < deg(f),
// and k < deg(g).
// h is replaced by the bivariate polynomial h*(X+Y) (mod f(X), g(Y)).
{
long n = deg(g);
long k = h.length()-1;
if (k < 0) return;
if (k < n-1) {
h.SetLength(k+2);
h[k+1] = h[k];
for (long i = k; i >= 1; i--) {
MulByXMod(h[i], h[i], f);
add(h[i], h[i], h[i-1]);
}
MulByXMod(h[0], h[0], f);
}
else {
ZZ_pEX b, t;
b = h[n-1];
for (long i = n-1; i >= 1; i--) {
mul(t, b, g.rep[i]);
MulByXMod(h[i], h[i], f);
add(h[i], h[i], h[i-1]);
sub(h[i], h[i], t);
}
mul(t, b, g.rep[0]);
MulByXMod(h[0], h[0], f);
sub(h[0], h[0], t);
}
// normalize
k = h.length()-1;
while (k >= 0 && IsZero(h[k])) k--;
h.SetLength(k+1);
}
void EDF(vec_ZZ_pEX& factors, const ZZ_pEX& ff, const ZZ_pEX& bb,
long d, long verbose)
{
ZZ_pEX f = ff;
ZZ_pEX b = bb;
if (!IsOne(LeadCoeff(f)))
LogicError("EDF: bad args");
long n = deg(f);
long r = n/d;
if (r == 0) {
factors.SetLength(0);
return;
}
if (r == 1) {
factors.SetLength(1);
factors[0] = f;
return;
}
if (d == 1) {
RootEDF(factors, f, verbose);
return;
}
double t;
if (verbose) {
cerr << "computing EDF(" << d << "," << r << ")...";
t = GetTime();
}
factors.SetLength(0);
RecEDF(factors, f, b, d, verbose);
if (verbose) cerr << (GetTime()-t) << "\n";
}
void IterFindFactors(vec_ZZ_pEX& factors, const ZZ_pEX& f,
const ZZ_pEX& g, const vec_ZZ_pE& roots)
{
long r = roots.length();
long i;
ZZ_pEX h;
factors.SetLength(r);
for (i = 0; i < r; i++) {
sub(h, g, roots[i]);
GCD(factors[i], f, h);
}
}
void RootEDF(vec_ZZ_pEX& factors, const ZZ_pEX& f, long verbose)
{
vec_ZZ_pE roots;
double t;
if (verbose) { cerr << "finding roots..."; t = GetTime(); }
FindRoots(roots, f);
if (verbose) { cerr << (GetTime()-t) << "\n"; }
long r = roots.length();
factors.SetLength(r);
for (long j = 0; j < r; j++) {
SetX(factors[j]);
sub(factors[j], factors[j], roots[j]);
}
}
void SFCanZass(vec_ZZ_pEX& factors, const ZZ_pEX& ff, long verbose)
{
ZZ_pEX f = ff;
if (!IsOne(LeadCoeff(f)))
LogicError("SFCanZass: bad args");
if (deg(f) == 0) {
factors.SetLength(0);
return;
}
if (deg(f) == 1) {
factors.SetLength(1);
factors[0] = f;
return;
}
factors.SetLength(0);
double t;
ZZ_pEXModulus F;
build(F, f);
ZZ_pEX h;
if (verbose) { cerr << "computing X^p..."; t = GetTime(); }
FrobeniusMap(h, F);
if (verbose) { cerr << (GetTime()-t) << "\n"; }
vec_pair_ZZ_pEX_long u;
if (verbose) { cerr << "computing DDF..."; t = GetTime(); }
NewDDF(u, f, h, verbose);
if (verbose) {
t = GetTime()-t;
cerr << "DDF time: " << t << "\n";
}
ZZ_pEX hh;
vec_ZZ_pEX v;
long i;
for (i = 0; i < u.length(); i++) {
const ZZ_pEX& g = u[i].a;
long d = u[i].b;
long r = deg(g)/d;
if (r == 1) {
// g is already irreducible
append(factors, g);
}
else {
// must perform EDF
if (d == 1) {
// root finding
RootEDF(v, g, verbose);
append(factors, v);
}
else {
// general case
rem(hh, h, g);
EDF(v, g, hh, d, verbose);
append(factors, v);
}
}
}
}
