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

CGAL 4.3 - Algebraic Foundations

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Algebraic_foundations/algebraic_structure_dispatch.cpp
#include <CGAL/basic.h>
#include <CGAL/IO/io.h>
#include <CGAL/Algebraic_structure_traits.h>
template< typename NT > NT unit_part(const NT& x);
template< typename NT >
NT unit_part_(const NT& x, CGAL::Field_tag);
template< typename NT >
NT unit_part_(const NT& x, CGAL::Integral_domain_without_division_tag);
template< typename NT >
NT unit_part(const NT& x){
// the unit part of 0 is defined as 1.
if (x == 0 ) return NT(1);
typedef CGAL::Algebraic_structure_traits<NT> AST;
typedef typename AST::Algebraic_category Algebraic_category;
return unit_part_(x,Algebraic_category());
}
template< typename NT >
NT unit_part_(const NT& x, CGAL::Integral_domain_without_division_tag){
// For many other types the only units are just -1 and +1.
return NT(int(CGAL::sign(x)));
}
template< typename NT >
NT unit_part_(const NT& x, CGAL::Field_tag){
// For Fields every x != 0 is a unit.
// Therefore, every x != 0 is its own unit part.
return x;
}
int main(){
// Function call for a model of EuclideanRing, i.e. int.
std::cout<< "int: unit_part(-3 ): " << unit_part(-3 ) << std::endl;
// Function call for a model of FieldWithSqrt, i.e. double
std::cout<< "double: unit_part(-3.0): " << unit_part(-3.0) << std::endl;
return 0;
}
// Note that this is just an example
// This implementation for unit part won't work for some types, e.g.,
// types that are not RealEmbeddable or types representing structures that have
// more units than just -1 and +1. (e.g. MP_Float representing Z[1/2])
// From there Algebraic_structure_traits provides the functor Unit_part.