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

CGAL 4.8 - Algebraic Kernel

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Algebraic_kernel_d/Compare_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::Coefficient Coefficient;
typedef AK::Polynomial_1 Polynomial_1;
typedef AK::Algebraic_real_1 Algebraic_real_1;
typedef AK::Bound Bound;
typedef std::pair<Bound,Bound> Interval;
int main(){
AK ak;
AK::Construct_algebraic_real_1 construct_algebraic_real_1 = ak.construct_algebraic_real_1_object();
Polynomial_1 x = CGAL::shift(AK::Polynomial_1(1),1); // the monomial x
Algebraic_real_1 a = construct_algebraic_real_1(x*x-2,1); // sqrt(2)
Algebraic_real_1 b = construct_algebraic_real_1(x*x-3,1); // sqrt(3)
// Algebraic_real_1 is RealEmbeddable (just some functions:)
std::cout << "sign of a is : " << CGAL::sign(a) << "\n";
std::cout << "double approximation of a is : " << CGAL::to_double(a) << "\n";
std::cout << "double approximation of b is : " << CGAL::to_double(b) << "\n";
std::cout << "double lower bound of a : " << CGAL::to_interval(a).first << "\n";
std::cout << "double upper bound of a : " << CGAL::to_interval(a).second << "\n";
std::cout << "LessThanComparable (a<b) : " << (a<b) << "\n\n";
// use compare_1 with int, Bound, Coefficient, Algebraic_real_1
AK::Compare_1 compare_1 = ak.compare_1_object();
std::cout << " compare with an int : " << compare_1(a ,int(2)) << "\n";
std::cout << " compare with an Coefficient : " << compare_1(a ,Coefficient(2)) << "\n";
std::cout << " compare with an Bound : " << compare_1(a ,Bound(2)) << "\n";
std::cout << " compare with another Algebraic_real_1: " << compare_1(a ,b) << "\n\n";
// get a value between two roots
AK::Bound_between_1 bound_between_1 = ak.bound_between_1_object();
std::cout << " value between sqrt(2) and sqrt(3) " << bound_between_1(a,b) << "\n";
std::cout << " is larger than sqrt(2) " << compare_1(bound_between_1(a,b),a) << "\n";
std::cout << " is less than sqrt(3) " << compare_1(bound_between_1(a,b),b) << "\n\n";
// approximate with relative precision
AK::Approximate_relative_1 approx_r = ak.approximate_relative_1_object();
std::cout << " lower bound of a with at least 100 bits: "<< approx_r(a,100).first << "\n";
std::cout << " upper bound of a with at least 100 bits: "<< approx_r(a,100).second << "\n\n";
// approximate with absolute error
AK::Approximate_absolute_1 approx_a = ak.approximate_absolute_1_object();
std::cout << " lower bound of b with error less than 2^-100: "<< approx_a(b,100).first << "\n";
std::cout << " upper bound of b with error less than 2^-100: "<< approx_a(b,100).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