void CharPoly(ZZX& gg, const mat_ZZ& a, long deterministic)
{
long n = a.NumRows();
if (a.NumCols() != n)
LogicError("CharPoly: nonsquare matrix");
if (n == 0) {
set(gg);
return;
}
if (n == 1) {
ZZ t;
SetX(gg);
negate(t, a(1, 1));
SetCoeff(gg, 0, t);
return;
}
long bound = 2 + CharPolyBound(a);
zz_pBak bak;
bak.save();
ZZ_pBak bak1;
bak1.save();
ZZX g;
ZZ prod;
clear(g);
set(prod);
long i;
long instable = 1;
long gp_cnt = 0;
for (i = 0; ; i++) {
if (NumBits(prod) > bound)
break;
if (!deterministic &&
!instable && bound > 1000 && NumBits(prod) < 0.25*bound) {
long plen = 90 + NumBits(max(bound, MaxBits(g)));
ZZ P;
GenPrime(P, plen, 90 + 2*NumBits(gp_cnt++));
ZZ_p::init(P);
mat_ZZ_p A;
ZZ_pX G;
conv(A, a);
CharPoly(G, A);
if (CRT(g, prod, G))
instable = 1;
else
break;
}
zz_p::FFTInit(i);
mat_zz_p A;
zz_pX G;
conv(A, a);
CharPoly(G, A);
instable = CRT(g, prod, G);
}
gg = g;
bak.restore();
bak1.restore();
}
NTL_START_IMPL
void CharPolyMod(ZZX& gg, const ZZX& a, const ZZX& f, long deterministic)
{
if (!IsOne(LeadCoeff(f)) || deg(f) < 1 || deg(a) >= deg(f))
Error("CharPolyMod: bad args");
if (IsZero(a)) {
clear(gg);
SetCoeff(gg, deg(f));
return;
}
long bound = 2 + CharPolyBound(a, f);
long gp_cnt = 0;
zz_pBak bak;
bak.save();
ZZ_pBak bak1;
bak1.save();
ZZX g;
ZZ prod;
clear(g);
set(prod);
long i;
long instable = 1;
for (i = 0; ; i++) {
if (NumBits(prod) > bound)
break;
if (!deterministic &&
!instable && bound > 1000 && NumBits(prod) < 0.25*bound) {
long plen = 90 + NumBits(max(bound, MaxBits(g)));
ZZ P;
GenPrime(P, plen, 90 + 2*NumBits(gp_cnt++));
ZZ_p::init(P);
ZZ_pX G, A, F;
conv(A, a);
conv(F, f);
CharPolyMod(G, A, F);
if (CRT(g, prod, G))
instable = 1;
else
break;
}
zz_p::FFTInit(i);
zz_pX G, A, F;
conv(A, a);
conv(F, f);
CharPolyMod(G, A, F);
instable = CRT(g, prod, G);
}
gg = g;
bak.restore();
bak1.restore();
}
