org.mathIT.numbers

Class Rational

java.lang.Object

org.mathIT.numbers.Rational

public class Rational
extends Object

This class enables the creation of a rational number n ∈ ℚ and the implementation of mathematical functions operating on them. A rational number n ∈ ℚ is uniquely determined by n = p/q where the numerator p and the denominator q are relatively prime integers. Internally, a rational number n is internally represented by two BigIntegers.

Version:

1.1

Author:

Andreas de Vries

Constructor Summary

Constructors

Constructor and Description
Rational(BigInteger p, BigInteger q) Creates a rational number p/q with the numerator p and the denominator q.
Rational(long p, long q) Creates a rational number p/q with the numerator p and the denominator q.

Method Summary

Modifier and Type	Method and Description
Rational	add(Rational n) Returns the rational number k = m + n where m is this rational number.
static BigInteger[]	cancel(BigInteger p, BigInteger q) Returns a two-element array representing the fraction p/q where all common factors of numerator and denominator are cancelled.
Rational	divide(BigInteger n) Returns the rational number k = m/n where m is this rational number.
Rational	divide(long n) Returns the rational number k = m/n where m is this rational number.
Rational	divide(Rational n) Returns the rational number k = m/n where m is this rational number.
Rational	minus(Rational n) Returns the rational number k = m - n where m is this rational number.
Rational	multiply(BigInteger n) Returns the rational number k = mn where m is this rational number.
Rational	multiply(Rational n) Returns the rational number k = mn where m is this rational number.
Rational	negate() Returns the negative of this rational number.
Rational	plus(Rational n) Returns the rational number k = m + n where m is this rational number.
Rational	reciprocal() Returns the reciprocal 1/n of this rational n.
Rational	subtract(Rational n) Returns the rational number k = m - n where m is this rational number.
String	toString() Returns a string representation of this rational number.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

Rational

public Rational(long p,
                long q)

Creates a rational number p/q with the numerator p and the denominator q. p and q need not be relatively prime, the contructor cancels common divisors automatically. Moreover, it is guaranteed q > 0. If q = 0, then it is set p = 0 and q = 1.

Parameters:

p - the numerator

q - the denominator

Rational

public Rational(BigInteger p,
                BigInteger q)

Creates a rational number p/q with the numerator p and the denominator q. p and q need not be relatively prime, the contructor cancels common divisors automatically. Moreover, it is guaranteed q > 0. If q = 0, then it is set p = 0 and q = 1.

Parameters:

p - the numerator

q - the denominator

Method Detail

add

public Rational add(Rational n)

Returns the rational number k = m + n where m is this rational number.

Parameters:

n - the summand

Returns:

the rational number representing this + n

See Also:

plus(Rational)

cancel

public static BigInteger[] cancel(BigInteger p,
                                  BigInteger q)

Returns a two-element array representing the fraction p/q where all common factors of numerator and denominator are cancelled. Here a fraction is represented by a two-element array whose first entry is the numerator and whose second entry is the denominator.

Parameters:

p - the numerator

q - the denominator

Returns:

the array {p', q'} where p' and q' emerge from p and q by cancelling all common factors

divide

public Rational divide(Rational n)

Returns the rational number k = m/n where m is this rational number.

Parameters:

n - the divisor

Returns:

the rational number representing this / n

See Also:

divide(BigInteger), divide(long)

divide

public Rational divide(BigInteger n)

Returns the rational number k = m/n where m is this rational number.

Parameters:

n - the divisor

Returns:

the rational number representing this / n

See Also:

divide(Rational), divide(long)

divide

public Rational divide(long n)

Returns the rational number k = m/n where m is this rational number.

Parameters:

n - the divisor

Returns:

the rational number representing this / n

See Also:

divide(Rational), divide(BigInteger)

minus

public Rational minus(Rational n)

Returns the rational number k = m - n where m is this rational number.

Parameters:

n - the subtrahend

Returns:

the rational number representing this - n

multiply

public Rational multiply(Rational n)

Returns the rational number k = mn where m is this rational number.

Parameters:

n - the factor

Returns:

the rational number representing this * n

multiply

public Rational multiply(BigInteger n)

Returns the rational number k = mn where m is this rational number.

Parameters:

n - the factor

Returns:

the rational number representing this * n

negate

public Rational negate()

Returns the negative of this rational number.

Returns:

-this

plus

public Rational plus(Rational n)

Returns the rational number k = m + n where m is this rational number.

Parameters:

n - the summand

Returns:

the rational number representing this + n

reciprocal

public Rational reciprocal()

Returns the reciprocal 1/n of this rational n.

Returns:

the reciprocal of this rational

subtract

public Rational subtract(Rational n)

Returns the rational number k = m - n where m is this rational number.

Parameters:

n - the subtrahend

Returns:

the rational number representing this - n

See Also:

minus(Rational)

toString

public String toString()

Returns a string representation of this rational number.

Overrides:

toString in class Object

Returns:

a string representation of this rational number