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// $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.6-branch/Algebraic_kernel_d/examples/Algebraic_kernel_d/Isolate_1.cpp $
// $Id: Isolate_1.cpp 53480 2009-12-17 16:11:42Z penarand $
#include <CGAL/Algebraic_kernel_d_1_RS_Gmpz.h>
#include <vector>
typedef CGAL::Algebraic_kernel_d_1_RS_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; // an object of Algebraic_kernel_d_1_RS_Gmpz
AK::Construct_algebraic_real_1 construct_algreal_1 = ak.construct_algebraic_real_1_object();
AK::Isolate_1 isolate_1 = ak.isolate_1_object();
AK::Compute_polynomial_1 compute_polynomial_1 = ak.compute_polynomial_1_object();
// construct an algebraic number from an integer
Algebraic_real_1 frominteger=construct_algreal_1(int(2));
std::cout << "Construct from int: " << frominteger << "\n";
// the constructed algebraic number is root of a polynomial
Polynomial_1 pol=compute_polynomial_1(frominteger);
std::cout << "The constructed number is root of: " << pol << "\n";
// construct an algebraic number from a polynomial and an isolating interval
Polynomial_1 x = CGAL::shift(AK::Polynomial_1(1),1); // the monomial x
Algebraic_real_1 frominterval=construct_algreal_1(x*x-2,Bound(0),Bound(2));
std::cout << "Construct from isolating interval: " << frominterval << "\n";
// isolate the second algebraic number from the first: this is to say,
// isolating the second algebraic number with respect to the polynomial
// of which the first constructed number is root
std::pair<Bound,Bound> isolation1 = isolate_1(frominterval,pol);
std::cout << "Isolating the second algebraic number gives: ["
<< isolation1.first << "," << isolation1.second << "]\n";
// isolate again the same algebraic number, this time with respect to
// the polynomial 10*x-14 (which has root 1.4, close to this algebraic
// number)
std::pair<Bound,Bound> isolation2 = isolate_1(frominterval,10*x-14);
std::cout << "Isolating again the second algebraic number gives: ["
<< isolation2.first << "," << isolation2.second << "]\n";
return 0;
}
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