\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - Algebraic Kernel

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Algebraic_kernel_d/Solve_1.cpp
// $URL$
// $Id$
#include <CGAL/basic.h>
#ifdef CGAL_USE_MPFI
#include <CGAL/Algebraic_kernel_d_1.h>
#include <CGAL/Gmpz.h>
#include <vector>
typedef CGAL::Algebraic_kernel_d_1<CGAL::Gmpz> AK;
typedef AK::Polynomial_1 Polynomial_1;
typedef AK::Algebraic_real_1 Algebraic_real_1;
typedef AK::Bound Bound;
typedef AK::Multiplicity_type Multiplicity_type;
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;
}
#else
int main(){
std::cout << "This example requires CGAL to be configured with library MPFI." << std::endl;
return 0;
}
#endif