CGAL 6.1 - Algebraic Foundations

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Algebraic_foundations/integralize.cpp
#include <CGAL/Fraction_traits.h>
#include <CGAL/IO/io.h>
#include <vector>
#include <CGAL/number_utils.h>
template <class Fraction>
std::vector<typename CGAL::Fraction_traits<Fraction>::Numerator_type >
integralize(
const std::vector<Fraction>& vec,
typename CGAL::Fraction_traits<Fraction>::Denominator_type& d
) {
typedef CGAL::Fraction_traits<Fraction> FT;
typedef typename FT::Numerator_type Numerator_type;
typedef typename FT::Denominator_type Denominator_type;
typename FT::Decompose decompose;
std::vector<Numerator_type> num(vec.size());
std::vector<Denominator_type> den(vec.size());
// decompose each coefficient into integral part and denominator
for (unsigned int i = 0; i < vec.size(); i++) {
decompose(vec[i], num[i], den[i]);
}
// compute 'least' common multiple of all denominator
// We would like to use gcd, so let's think of Common_factor as gcd.
typename FT::Common_factor gcd;
d = 1;
for (unsigned int i = 0; i < vec.size(); i++) {
d *= CGAL::integral_division(den[i], gcd(d, den[i]));
}
// expand each (numerator, denominator) pair to common denominator
for (unsigned int i = 0; i < vec.size(); i++) {
// For simplicity ImplicitInteroperability is expected in this example
num[i] *= CGAL::integral_division(d, den[i]);
}
return num;
}
#ifdef CGAL_USE_GMP
#include <CGAL/Gmpz.h>
#include <CGAL/Gmpq.h>
int main(){
std::vector<CGAL::Gmpq> vec(3);
vec[0]=CGAL::Gmpq(1,4);
vec[1]=CGAL::Gmpq(1,6);
vec[2]=CGAL::Gmpq(1,10);
std::cout<< "compute an integralized vector" << std::endl;
std::cout<<"input vector: ["
<< vec[0] << "," << vec[1] << "," << vec[2] << "]" << std::endl;
CGAL::Gmpz d;
std::vector<CGAL::Gmpz> integral_vec = integralize(vec,d);
std::cout<<"output vector: ["
<< integral_vec[0] << ","
<< integral_vec[1] << ","
<< integral_vec[2] << "]" << std::endl;
std::cout<<"denominator : "<< d <<std::endl;
}
#else
int main(){ std::cout << "This examples needs GMP" << std::endl; }
#endif
Gmpq.h
Gmpz.h
CGAL::Fraction_traits
An instance of Fraction_traits is a model of FractionTraits, where T is the associated type.
Definition: Fraction_traits.h:13
CGAL::Gmpq
CGAL::Gmpz
CGAL::integral_division
result_type integral_division(const NT1 &x, const NT2 &y)
The function integral_division() (a.k.a. exact division or division without remainder) maps ring elem...