\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5.2 - Number Types
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CGAL::Quotient< NT > Class Template Reference
CGAL Number Types

#include <CGAL/Quotient.h>

Definition

An object of the class Quotient<NT> is an element of the field of quotients of the integral domain type NT.

If NT behaves like an integer, Quotient<NT> behaves like a rational number. LEDA's class rational (see Section ledant) has been the basis for Quotient<NT>. A Quotient<NT> q is represented as a pair of NTs, representing numerator and denominator.

Template Parameters
NTmust be at least model of concept IntegralDomainWithoutDivision and a model of concept RealEmbeddable.
Is Model Of:

Field

RealEmbeddable

Fraction

Operations

There are two access functions, namely to the numerator and the denominator of a quotient. Note that these values are not uniquely defined. It is guaranteed that q.numerator() and q.denominator() return values nt_num and nt_den such that q = nt_num/nt_den, only if q.numerator() and q.denominator() are called consecutively wrt q, i.e. q is not involved in any other operation between these calls.

The stream operations are available as well. They assume that corresponding stream operators for type NT exist.

The following functions are added to fulfill the CGAL requirements on number types.

Related Functions

(Note that these are not member functions.)

std::ostream & operator<< (std::ostream &out, const Quotient< NT > &q)
 writes q to ostream out in format n/d, where n \( ==\)q.numerator() and d \( ==\)q.denominator().
 
std::istream & operator>> (std::istream &in, Quotient< NT > &q)
 reads q from istream in. More...
 
double to_double (const Quotient< NT > &q)
 returns some double approximation to q.
 
bool is_valid (const Quotient< NT > &q)
 returns true, if numerator and denominator are valid.
 
bool is_finite (const Quotient< NT > &q)
 returns true, if numerator and denominator are finite.
 
Quotient< NT > sqrt (const Quotient< NT > &q)
 returns the square root of q. More...
 

Creation

 Quotient ()
 introduces an uninitialized variable q.
 
template<class T >
 Quotient (const T &t)
 introduces the quotient t/1. More...
 
template<class T >
 Quotient (const Quotient< T > &t)
 introduces the quotient NT(t.numerator())/NT(t.denominator()). More...
 
 Quotient (const NT &n, const NT &d)
 introduces the quotient n/d. More...
 

Operations

NT numerator () const
 returns a numerator of q.
 
NT denominator () const
 returns a denominator of q.
 

Constructor & Destructor Documentation

template<typename NT >
template<class T >
CGAL::Quotient< NT >::Quotient ( const T &  t)

introduces the quotient t/1.

NT needs to have a constructor from T.

template<typename NT >
template<class T >
CGAL::Quotient< NT >::Quotient ( const Quotient< T > &  t)

introduces the quotient NT(t.numerator())/NT(t.denominator()).

NT needs to have a constructor from T.

template<typename NT >
CGAL::Quotient< NT >::Quotient ( const NT &  n,
const NT &  d 
)

introduces the quotient n/d.

Precondition
\( d \neq0\).

Friends And Related Function Documentation

template<typename NT >
std::istream & operator>> ( std::istream &  in,
Quotient< NT > &  q 
)
related

reads q from istream in.

Expected format is n/d, where n and d are of type NT. A single n which is not followed by a / is also accepted and interpreted as n/1.

template<typename NT >
Quotient< NT > sqrt ( const Quotient< NT > &  q)
related

returns the square root of q.

This is supported if and only if NT supports the square root as well.