polynomial operator -(const polynomial& p1, const polynomial& p2)
{
size_t j=p1.degree( );
size_t q= p2.degree( );
polynomial answer;
if(j>=q)
{
answer.reserve(j+1);
size_t i;
for (i=0; i<=j; i++)
{
answer.add_to_coef((p1.coefficient(i)-p2.coefficient(i)),(i));
}
}
else
{
answer.reserve(q+1);
size_t i;
for (i=0; i<=q; i++)
{
answer.add_to_coef((p1.coefficient(i)-p2.coefficient(i)),(i));
}
}
return answer;
}
polynomial operator *(const polynomial& p1, const polynomial& p2)
{
polynomial answer;
size_t k=p1.degree( );
size_t q=p2.degree( );
answer.reserve((k+q)+2);
size_t i;
size_t j;
for (i=0; i<=k; i++)
{
for (j=0; j<=q; j++)
{
answer.add_to_coef((p1.coefficient(i)*p2.coefficient(j)),(i+j));
}
}
return answer;
}
int descartes_rule(const polynomial<data__> &f, bool positive)
{
// catch special case
if (f.degree()==0)
return 0;
// get the coefficients from the polynomial
std::vector<data__> a(f.degree()+1);
for (size_t i=0; i<a.size(); ++i)
{
a[i]=f.coefficient(i);
// change the sign of odd powers if want the negative root count
if (!positive && i%2==1)
a[i]*=-1;
}
return eli::mutil::poly::root::sign_changes(a.begin(), a.end());
}