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

CGAL 4.3 - Polynomial

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
Polynomial/gcd_up_to_constant_factor.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,1>::Type Poly_1;
typedef CGAL::Polynomial_traits_d<Poly_1> PT_1;
PT_1::Shift shift;
PT_1::Gcd gcd;
PT_1::Gcd_up_to_constant_factor gcd_utcf;
PT_1::Multivariate_content mcontent;
PT_1::Canonicalize canonicalize;
//construction using shift
Poly_1 x = shift(Poly_1(1),1,0); // x^1
// common factor 7 * (x^2-2)
Poly_1 F = 21*(x-5)*(x*x-2); // = 21*x^3 + (-105)*x^2 + (-42)*x + 210
Poly_1 G = 14*(x-3)*(x*x-2); // = 14*x^3 + (-42)*x^2 + (-28)*x + 84
std::cout << "The univariate polynomial F: " << F << std::endl;
std::cout << "The univariate polynomial G: " << G << std::endl;
std::cout << "Common multivariate content: "
<< CGAL::gcd(mcontent(F),mcontent(G)) // = 7
<< std::endl;
std::cout << "The gcd of F and G: "
<< gcd(F,G) // = 7*x^2 + (-14)
<< std::endl;
std::cout << "The gcd up to constant factor of F and G: "
<< gcd_utcf(F,G) // = x^2 + (-2)
<< std::endl;
std::cout << "Same as canonicalized gcd of F and G: "
<< canonicalize(gcd_utcf(F,G)) // = x^2 + (-2)
<< std::endl;
}