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

CGAL 4.8 - Algebraic Kernel

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Algebraic_kernel_d/Sign_at_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::Coefficient Coefficient;
typedef AK::Bound Bound;
typedef AK::Multiplicity_type Multiplicity_type;
int main(){
AK ak;
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;
}
#else
int main(){
std::cout << "This example requires CGAL to be configured with library MPFI." << std::endl;
return 0;
}
#endif