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

CGAL 4.8 - Polynomial

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Polynomial/construction.cpp
#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;
typedef PT_2::Coefficient_type Poly_1;
typedef PT_2::Innermost_coefficient_type Integer;
PT_2::Construct_polynomial construct_polynomial;
Poly_2 dc;
// constructing a constant polynomial from int
Poly_2 two(2); // = 2
std::cout << "A constant polynomial: " << two << std::endl;
// construction from an iterator range of univariate polynomials
std::list<Poly_1> univariate_coeffs;
univariate_coeffs.push_back(Poly_1(3));
univariate_coeffs.push_back(Poly_1(0));
univariate_coeffs.push_back(Poly_1(5));
Poly_2 F = // 5*y^2 + 3
construct_polynomial(univariate_coeffs.begin(),univariate_coeffs.end());
std::cout << "The bivariate polynomial F: " << F << std::endl;
// construction from an iterator range over monomials
std::list<std::pair<CGAL::Exponent_vector, Integer> > innermost_coeffs;
innermost_coeffs.push_back(std::make_pair(CGAL::Exponent_vector(0,0),-2));
innermost_coeffs.push_back(std::make_pair(CGAL::Exponent_vector(3,5),2));
Poly_2 G = // (2*x^3)*y^5 + (-2)
construct_polynomial(innermost_coeffs.begin(),innermost_coeffs.end());
std::cout << "The bivariate polynomial G: " << G << std::endl;
//construction using shift
PT_2::Shift shift;
Poly_2 x = shift(Poly_2(1),1,0); // 'multiply' 1 by x_0^1
Poly_2 y = shift(Poly_2(1),1,1); // 'multiply' 1 by x_1^1
Poly_2 H = 5 * x * y + 3 * y * y; // = 3*y^2 + (5*x)*y
std::cout << "The bivariate polynomial H: " << H << std::endl;
}