Quotient<NT>

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CGAL::Quotient<NT>

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 5.5) has been the basis for Quotient<NT>. A Quotient<NT> q is represented as a pair of NTs, representing numerator and denominator.

NT must be at least model of concept IntegralDomainWithoutDivision.
NT must be a model of concept RealEmbeddable.

#include <CGAL/Quotient.h>

Is Model for the Concepts

Field
RealEmbeddable
Fraction

Creation

Quotient<NT> q;

introduces an uninitialized variable q.

template <class T>

Quotient<NT> q ( T t);

introduces the quotient t/1. NT needs to have a constructor from T.

template <class T>

Quotient<NT> q ( Quotient<T> t);

introduces the quotient NT(t.numerator())/NT(t.denominator()). NT needs to have a constructor from T.

Quotient<NT> q ( NT n, NT d);

introduces the quotient n/d.

Precondition:

d ≠ 0.

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.

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

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

std::ostream&	std::ostream& out << q	writes q to ostream out in format ```n/d`'', where `n`==q.numerator() and `d`==q.denominator().

std::istream&	std::istream& in >> & q	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`.

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

double	to_double ( q)	returns some double approximation to q.
bool	is_valid ( q)	returns true, if numerator and denominator are valid.
bool	is_finite ( q)	returns true, if numerator and denominator are finite.
Quotient<NT>	sqrt ( q)	returns the square root of q. This is supported if and only if NT supports the square root as well.

Next: Number_type_checker<NT1,NT2,Comparator>

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CGAL Open Source Project. Release 4.0.1. 2 July 2012.