friend polynomial derivative(polynomial const& p) {
int s = p.size();
if(s == 0) return {};
polynomial res;
res.coeffs.resize(s-1);
for(int n = 0; n < s-1; ++n)
res.coeffs(n) = p.coeffs(n+1) * CoeffType(n+1);
return res;
}
friend polynomial antiderivative(polynomial const& p) {
int s = p.size();
if(s == 0) return {};
polynomial res;
res.coeffs.resize(s+1);
res.coeffs(0) = CoeffType{};
for(int n = 1; n < s+1; ++n)
res.coeffs(n) = p.coeffs(n-1) / CoeffType(n);
return res;
}