Rational Numbers ( rational )

Definition

An instance q of type rational is a rational number where the numerator and the denominator are both of type integer.

#include < LEDA/rational.h >

Creation

rational	q	creates an instance q of type rational.
rational	q(integer n)	creates an instance q of type rational and initializes it with the integer n.
rational	q(integer n, integer d)	creates an instance q of type rational and initializes it to the rational number n/d.
rational	q(double x)	creates an instance q of type rational and initializes it with the value of x.

Operations

The arithmetic operations +, -, *, /, + =, - =, * =, / =, -(unary), + +, - -, the comparison operations <, < =, >, > =, = =, ! = and the stream operations are all available.

void	q.negate()	negates q.
void	q.invert()	inverts q.
rational	q.inverse()	returns the inverse of q.
integer	q.numerator()	returns the numerator of q.
integer	q.denominator()	returns the denominator of q.
rational&	q.simplify(integer a)	simplifies q by a. Precondition a divides the numerator and the denominator of q.
rational&	q.normalize()	normalizes q.
double	to_float()	returns a double floating point approximation of q. If the q is approximable by a normalized, finite floating point number, the error is 3ulps, i.e., three units in the last place.
string	q.to_string()	returns a string representation of q.

Non-member functions

int	sign(rational q)	returns the sign of q.
rational	abs(rational q)	returns the absolute value of q.
rational	sqr(rational q)	returns the square of q.
integer	trunc(rational q)	returns the integer with the next smaller absolute value.
rational	pow(rational q, int n)	returns the n-th power of q.
rational	pow(rational q, integer a)
		returns the a-th power of q.
integer	floor(rational q)	returns the next smaller integer.
integer	ceil(rational q)	returns the next bigger integer.
integer	round(rational q)	rounds q to the nearest integer.
rational	small_rational_between(rational p, rational q)
		returns a rational number between p and q whose denominator is as small as possible.
rational	small_rational_near(rational p, rational eps)
		returns a rational number between p - eps and p + eps whose denominator is as small as possible.

Implementation

A rational is implemented by two integernumbers which represent the numerator and the denominator. The sign is represented by the sign of the numerator.