int main(){
AK ak;
AK::Construct_algebraic_real_1 construct_algreal_1 = ak.construct_algebraic_real_1_object();
AK::Solve_1 solve_1 = ak.solve_1_object();
AK::Sign_at_1 sign_at_1 = ak.sign_at_1_object();
AK::Is_zero_at_1 is_zero_at_1 = ak.is_zero_at_1_object();
// construct the polynomials p=x^2-5 and q=x-2
Polynomial_1 x = CGAL::shift(AK::Polynomial_1(1),1); // the monomial x
Polynomial_1 p = x*x-5;
std::cout << "Polynomial p: " << p << "\n";
Polynomial_1 q = x-2;
std::cout << "Polynomial q: " << q << "\n";
// find the roots of p (it has two roots) and q (one root)
std::vector<Algebraic_real_1> roots_p,roots_q;
solve_1(p,true, std::back_inserter(roots_p));
solve_1(q,true, std::back_inserter(roots_q));
// evaluate the second root of p in q
std::cout << "Sign of the evaluation of root 2 of p in q: "
<< sign_at_1(q,roots_p[1]) << "\n";
// evaluate the root of q in p
std::cout << "Sign of the evaluation of root 1 of q in p: "
<< sign_at_1(p,roots_q[0]) << "\n";
// check whether the evaluation of the first root of p in p is zero
std::cout << "Is zero the evaluation of root 1 of p in p? "
<< is_zero_at_1(p,roots_p[0]) << "\n";
return 0;
}
int main(){
AK ak; // an object of
AK::Solve_1 solve_1 = ak.solve_1_object();
Polynomial_1 x = CGAL::shift(AK::Polynomial_1(1),1); // the monomial x
// variant using a bool indicating a square free polynomial
// multiplicities are not computed
std::vector<Algebraic_real_1> roots;
solve_1(x*x-2,true, std::back_inserter(roots));
std::cout << "Number of roots is : " << roots.size() << "\n";
std::cout << "First root should be -sqrt(2): " << CGAL::to_double(roots[0]) << "\n";
std::cout << "Second root should be sqrt(2): " << CGAL::to_double(roots[1]) << "\n\n";
roots.clear();
// variant for roots in a given range of a square free polynomial
solve_1((x*x-2)*(x*x-3),true, Bound(0),Bound(10),std::back_inserter(roots));
std::cout << "Number of roots is : " << roots.size() << "\n";
std::cout << "First root should be sqrt(2): " << CGAL::to_double(roots[0]) << "\n";
std::cout << "Second root should be sqrt(3): " << CGAL::to_double(roots[1]) << "\n\n";
roots.clear();
// variant computing all roots with multiplicities
std::vector<std::pair<Algebraic_real_1,Multiplicity_type> > mroots;
solve_1((x*x-2), std::back_inserter(mroots));
std::cout << "Number of roots is : " << mroots.size() << "\n";
std::cout << "First root should be -sqrt(2): " << CGAL::to_double(mroots[0].first) << ""
<< " with multiplicity " << mroots[0].second << "\n";
std::cout << "Second root should be sqrt(2): " << CGAL::to_double(mroots[1].first) << ""
<< " with multiplicity " << mroots[1].second << "\n\n";
mroots.clear();
// variant computing roots with multiplicities for a range
solve_1((x*x-2)*(x*x-3),Bound(0),Bound(10),std::back_inserter(mroots));
std::cout << "Number of roots is : " << mroots.size() << "\n";
std::cout << "First root should be sqrt(2): " << CGAL::to_double(mroots[0].first) << ""
<< " with multiplicity " << mroots[0].second << "\n";
std::cout << "Second root should be sqrt(3): " << CGAL::to_double(mroots[1].first) << ""
<< " with multiplicity " << mroots[1].second << "\n\n";
return 0;
}
