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#include <CGAL/Polynomial.h>
#include <CGAL/Polynomial_traits_d.h>
#include <CGAL/Polynomial_type_generator.h>
int main(){
CGAL::set_pretty_mode(std::cout);
typedef CGAL::Polynomial_type_generator<int,2>::Type Poly_2;
typedef CGAL::Polynomial_traits_d<Poly_2> PT_2;
//construction using shift
Poly_2 x = PT_2::Shift()(Poly_2(1),1,0); // = x^1
Poly_2 y = PT_2::Shift()(Poly_2(1),1,1); // = y^1
Poly_2 F // = (11*x^2 + 5*x)*y^4 + (7*x^2)*y^3
= 11 * CGAL::ipower(y,4) * CGAL::ipower(x,2)
+ 5 * CGAL::ipower(y,4) * CGAL::ipower(x,1)
+ 7 * CGAL::ipower(y,3) * CGAL::ipower(x,2);
std::cout << "The bivariate polynomial F: " << F <<"\n"<< std::endl;
PT_2::Get_coefficient get_coefficient;
std::cout << "Coefficient of y^0: "<< get_coefficient(F,0) << std::endl;
std::cout << "Coefficient of y^1: "<< get_coefficient(F,1) << std::endl;
std::cout << "Coefficient of y^2: "<< get_coefficient(F,2) << std::endl;
std::cout << "Coefficient of y^3: "<< get_coefficient(F,3) << std::endl;
std::cout << "Coefficient of y^4: "<< get_coefficient(F,4) << std::endl;
std::cout << "Coefficient of y^5: "<< get_coefficient(F,5) << std::endl;
std::cout << std::endl;
PT_2::Leading_coefficient lcoeff;
std::cout << "Leading coefficient with respect to y: "
<< lcoeff(F) // = 11*x^2 + 5*x
<< std::endl;
PT_2::Get_innermost_coefficient get_icoeff;
std::cout << "Innermost coefficient of monomial x^1y^4: "
<< get_icoeff(F,CGAL::Exponent_vector(1,4)) // = 5
<< std::endl;
PT_2::Innermost_leading_coefficient ilcoeff;
std::cout << "Innermost leading coefficient with respect to y: "
<< ilcoeff(F) // = 11
<< std::endl;
}
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