static vector<long double> findAllRoots(const Polynomial & f)
{
vector<long double> ret;
Polynomial f_ = f.qiudiao();
long double minRoot = -200.0;
long double maxRoot = 200.0;
for (int iter = 0; iter <= 1000; ++iter)
{
//cout << iter << endl;
long double x0 = (long double) rand() / (long double) RAND_MAX;
x0 = minRoot + (maxRoot - minRoot) * x0;
long double root;
bool findRoot = newton_root(x0, f, f_, root);
if (findRoot)
{
bool newroot = true;
for (int i = 0; i < ret.size(); ++i)
if (fabs(ret[i] - root) < bigeps)
newroot = false;
if (newroot)
{
int multi = findRootMultiple(root, f);
vector<long double> newroots(multi, root);
ret.insert(ret.end(), newroots.begin(), newroots.end());
}
}
}
sort(ret.begin(), ret.end());
return ret;
}
// after we find a root of a polynomial, use this method to determine its multiple
static int findRootMultiple(long double x, const Polynomial & f)
{
int ret = 1;
Polynomial now = f;
double zeroeps = 1e-6;
while (true)
{
now = now.qiudiao();
if (now.coff.size() == 0) break;
long double nowf = now.func(x);
if (fabs(nowf) < zeroeps) ret++;
else break;
zeroeps *= 4;
}
return ret;
}