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);
}
void NormMod(zz_p& x, const zz_pX& a, const zz_pX& f)
{
if (deg(f) <= 0 || deg(a) >= deg(f))
Error("norm: bad args");
if (IsZero(a)) {
clear(x);
return;
}
zz_p t;
resultant(t, f, a);
if (!IsOne(LeadCoeff(f))) {
zz_p t1;
power(t1, LeadCoeff(f), deg(a));
inv(t1, t1);
mul(t, t, t1);
}
x = t;
}
static CYTHON_INLINE struct ZZ* ZZX_resultant(struct ZZX* x, struct ZZX* y, int proof)
{
ZZ* res = new ZZ();
resultant(*res, *x, *y, proof);
return res;
}
double TwoVector::angle(void) const {
double r = resultant();
if(r <= 0.) return 0.;
return std::acos(m_x/r); // angle in radians
}
