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

CGAL 4.8 - Polynomial

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Polynomial/swap_move.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,3>::Type Poly_3;
typedef CGAL::Polynomial_traits_d<Poly_3> PT_3;
//construction using shift
Poly_3 x = PT_3::Shift()(Poly_3(1),1,0); // x_0^1
Poly_3 y = PT_3::Shift()(Poly_3(1),1,1); // x_1^1
Poly_3 z = PT_3::Shift()(Poly_3(1),1,2); // x_2^1
Poly_3 F = x*y*y*z*z*z;
std::cout << "The trivariate polynomial F: " << F << std::endl;
std::cout << std::endl;
PT_3::Swap swap;
PT_3::Move move;
PT_3::Permute permute;
std::cout << "x and z swapped: "<< swap(F,0,2) // = x^3*y^2*z
<< std::endl;
std::cout << "x and y swapped: "<< swap(F,0,1) // = x^2*y*z^3
<< std::endl << std::endl;
std::cout << "x moved to outermost position : "
<< move(F,0,2) // = x^2*y^3*z
<< std::endl;
std::cout << "Same as swap(swap(F,0,1),1,2) : "
<< swap(swap(F,0,1),1,2) // = x^2*y^3*z
<< std::endl;
std::cout << "Same as the permutation (0,1,2)->(2,0,1): ";
std::vector<int> perm;
perm.push_back(2);perm.push_back(0);perm.push_back(1);
std::cout << permute(F,perm.begin(),perm.end())// = x^2*y^3*z
<< std::endl;
}