Package org.nevec.rjm

Class Rational

java.lang.Object

org.nevec.rjm.Rational

All Implemented Interfaces:

java.lang.Cloneable, java.lang.Comparable<Rational>

public class Rational
extends java.lang.Object
implements java.lang.Cloneable, java.lang.Comparable<Rational>

Fractions (rational numbers). They are divisions of two BigInteger numbers, reduced to coprime numerator and denominator.

Since:

2006-06-25

Author:

Richard J. Mathar

Field Summary

Fields

Modifier and Type	Field	Description
static Rational	HALF	The constant 1/2
static java.math.BigInteger	MAX_INT	The maximum and minimum value of a standard Java integer, 2^31.
static java.math.BigInteger	MIN_INT
static Rational	ZERO	The constant 0.

Constructor Summary

Constructors

Constructor	Description
Rational()	Default ctor, which represents the zero.
Rational(int n)	ctor from an integer.
Rational(int a, int b)	ctor from a numerator and denominator.
Rational(java.lang.String str)	ctor from a string representation.
Rational(java.lang.String str, int radix)	ctor from a string representation in a specified base.
Rational(java.math.BigInteger a)	ctor from a numerator.
Rational(java.math.BigInteger a, java.math.BigInteger b)	ctor from a numerator and denominator.

Method Summary

Modifier and Type	Method	Description
Rational	abs()	Absolute value.
Rational	add(int val)	Add another integer.
Rational	add(java.math.BigInteger val)	Add another integer.
Rational	add(Rational val)	Add another fraction.
java.math.BigDecimal	BigDecimalValue(java.math.MathContext mc)	Return a representation as BigDecimal.
static Rational	binomial(Rational n, int m)	binomial (n choose m).
static Rational	binomial(Rational n, java.math.BigInteger m)	binomial (n choose m).
java.math.BigInteger	ceil()	ceil(): the nearest integer not smaller than this.
Rational	clone()	Create a copy.
int	compareTo(java.math.BigInteger val)	Compares the value of this with another constant.
int	compareTo(Rational val)	Compares the value of this with another constant.
java.math.BigInteger	denom()	Get the denominator.
Rational	divide(int val)	Divide by an integer.
Rational	divide(java.math.BigInteger val)	Divide by an integer.
Rational	divide(Rational val)	Divide by another fraction.
double	doubleValue()	Return a double value representation.
float	floatValue()	Return a float value representation.
java.math.BigInteger	floor()	floor(): the nearest integer not greater than this.
static Rational	hankelSymb(Rational n, int k)	Hankel's symbol (n,k)
boolean	isBigInteger()	True if the value is integer.
boolean	isInteger()	True if the value is integer and in the range of the standard integer.
boolean	isIntegerFrac()	True if the value is a fraction of two integers in the range of the standard integer.
static java.math.BigInteger	lcmDenom(Rational[] vals)	Common lcm of the denominators of a set of rational values.
Rational	max(Rational val)	Compares the value of this with another constant.
Rational	min(Rational val)	Compares the value of this with another constant.
Rational	multiply(int val)	Multiply by an integer.
Rational	multiply(java.math.BigInteger val)	Multiply by a BigInteger.
Rational	multiply(Rational val)	Multiply by another fraction.
Rational	negate()	Compute the negative.
protected void	normalize()	Normalize to coprime numerator and denominator.
java.math.BigInteger	numer()	Get the numerator.
Rational	Pochhammer(int n)	Compute pochhammer's symbol (this)_n.
Rational	Pochhammer(java.math.BigInteger n)	Compute Pochhammer's symbol (this)_n.
Rational	pow(int exponent)	Power to an integer.
Rational	pow(java.math.BigInteger exponent)	Power to an integer.
Rational	pow(Rational exponent)	Raise to a rational power.
Rational	root(java.math.BigInteger r)	r-th root.
int	signum()	The sign: 1 if the number is >0, 0 if ==0, -1 if <0
Rational	subtract(int val)	Subtract an integer.
Rational	subtract(java.math.BigInteger val)	Subtract an integer.
Rational	subtract(Rational val)	Subtract another fraction.
java.lang.String	toFString(int digits)	Return a string in floating point format.
java.lang.String	toString()	Return a string in the format number/denom.
java.math.BigInteger	trunc()	Remove the fractional part.

Methods inherited from class java.lang.Object

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

Field Detail

MAX_INT

public static java.math.BigInteger MAX_INT

The maximum and minimum value of a standard Java integer, 2^31.

Since:

2009-05-18

MIN_INT

public static java.math.BigInteger MIN_INT

ZERO

public static Rational ZERO

The constant 0.

HALF

public static Rational HALF

The constant 1/2

Since:

2010-05-25

Constructor Detail

Rational

public Rational()

Default ctor, which represents the zero.

Since:

2007-11-17

Rational

public Rational(java.math.BigInteger a,
                java.math.BigInteger b)

ctor from a numerator and denominator.

Parameters:

a - the numerator.

b - the denominator.

Rational

public Rational(java.math.BigInteger a)

ctor from a numerator.

Parameters:

a - the BigInteger.

Rational

public Rational(int a,
                int b)

ctor from a numerator and denominator.

Parameters:

a - the numerator.

b - the denominator.

Rational

public Rational(int n)

ctor from an integer.

Parameters:

n - the integer to be represented by the new instance.

Since:

2010-07-18

Rational

public Rational(java.lang.String str)
         throws java.lang.NumberFormatException

ctor from a string representation.

Parameters:

str - the string. This either has a slash in it, separating two integers, or, if there is no slash, is representing the numerator with implicit denominator equal to 1. Warning: this does not yet test for a denominator equal to zero

Throws:

java.lang.NumberFormatException

Rational

public Rational(java.lang.String str,
                int radix)
         throws java.lang.NumberFormatException

ctor from a string representation in a specified base.

Parameters:

str - the string. This either has a slash in it, separating two integers, or, if there is no slash, is just representing the numerator.

radix - the number base for numerator and denominator Warning: this does not yet test for a denominator equal to zero

Throws:

java.lang.NumberFormatException

Method Detail

clone

public Rational clone()

Create a copy.

Overrides:

clone in class java.lang.Object

Since:

2008-11-07

multiply

public Rational multiply(Rational val)

Multiply by another fraction.

Parameters:

val - a second rational number.

Returns:

the product of this with the val.

multiply

public Rational multiply(java.math.BigInteger val)

Multiply by a BigInteger.

Parameters:

val - a second number.

Returns:

the product of this with the value.

multiply

public Rational multiply(int val)

Multiply by an integer.

Parameters:

val - a second number.

Returns:

the product of this with the value.

pow

public Rational pow(int exponent)

Power to an integer.

Parameters:

exponent - the exponent.

Returns:

this value raised to the power given by the exponent. If the exponent is 0, the value 1 is returned.

pow

public Rational pow(java.math.BigInteger exponent)
             throws java.lang.NumberFormatException

Power to an integer.

Parameters:

exponent - the exponent.

Returns:

this value raised to the power given by the exponent. If the exponent is 0, the value 1 is returned.

Throws:

java.lang.NumberFormatException

Since:

2009-05-18

root

public Rational root(java.math.BigInteger r)
              throws java.lang.NumberFormatException

r-th root.

Parameters:

r - the inverse of the exponent. 2 for the square root, 3 for the third root etc

Returns:

this value raised to the inverse power given by the root argument, this^(1/r).

Throws:

java.lang.NumberFormatException

Since:

2009-05-18

pow

public Rational pow(Rational exponent)
             throws java.lang.NumberFormatException

Raise to a rational power.

Parameters:

exponent - The exponent.

Returns:

This value raised to the power given by the exponent. If the exponent is 0, the value 1 is returned.

Throws:

java.lang.NumberFormatException

Since:

2009-05-18

divide

public Rational divide(Rational val)

Divide by another fraction.

Parameters:

val - A second rational number.

Returns:

The value of this/val

divide

public Rational divide(java.math.BigInteger val)

Divide by an integer.

Parameters:

val - a second number.

Returns:

the value of this/val

divide

public Rational divide(int val)

Divide by an integer.

Parameters:

val - A second number.

Returns:

The value of this/val

add

public Rational add(Rational val)

Add another fraction.

Parameters:

val - The number to be added

Returns:

this+val.

add

public Rational add(java.math.BigInteger val)

Add another integer.

Parameters:

val - The number to be added

Returns:

this+val.

add

public Rational add(int val)

Add another integer.

Parameters:

val - The number to be added

Returns:

this+val.

Since:

May 26 2010

negate

public Rational negate()

Compute the negative.

Returns:

-this.

subtract

public Rational subtract(Rational val)

Subtract another fraction.

Parameters:

val - the number to be subtracted from this

Returns:

this - val.

subtract

public Rational subtract(java.math.BigInteger val)

Subtract an integer.

Parameters:

val - the number to be subtracted from this

Returns:

this - val.

subtract

public Rational subtract(int val)

Subtract an integer.

Parameters:

val - the number to be subtracted from this

Returns:

this - val.

binomial

public static Rational binomial(Rational n,
                                java.math.BigInteger m)

binomial (n choose m).

Parameters:

n - the numerator. Equals the size of the set to choose from.

m - the denominator. Equals the number of elements to select.

Returns:

the binomial coefficient.

Since:

2006-06-27

binomial

public static Rational binomial(Rational n,
                                int m)

binomial (n choose m).

Parameters:

n - the numerator. Equals the size of the set to choose from.

m - the denominator. Equals the number of elements to select.

Returns:

the binomial coefficient.

Since:

2009-05-19

hankelSymb

public static Rational hankelSymb(Rational n,
                                  int k)

Hankel's symbol (n,k)

Parameters:

n - the first parameter.

k - the second parameter, greater or equal to 0.

Returns:

Gamma(n+k+1/2)/k!/GAMMA(n-k+1/2)

Since:

2010-07-18

numer

public java.math.BigInteger numer()

Get the numerator.

Returns:

The numerator of the reduced fraction.

denom

public java.math.BigInteger denom()

Get the denominator.

Returns:

The denominator of the reduced fraction.

abs

public Rational abs()

Absolute value.

Returns:

The absolute (non-negative) value of this.

floor

public java.math.BigInteger floor()

floor(): the nearest integer not greater than this.

Returns:

The integer rounded towards negative infinity.

ceil

public java.math.BigInteger ceil()

ceil(): the nearest integer not smaller than this.

Returns:

The integer rounded towards positive infinity.

Since:

2010-05-26

trunc

public java.math.BigInteger trunc()

Remove the fractional part.

Returns:

The integer rounded towards zero.

compareTo

public int compareTo(Rational val)

Compares the value of this with another constant.

Specified by:

compareTo in interface java.lang.Comparable<Rational>

Parameters:

val - the other constant to compare with

Returns:

-1, 0 or 1 if this number is numerically less than, equal to, or greater than val.

compareTo

public int compareTo(java.math.BigInteger val)

Compares the value of this with another constant.

Parameters:

val - the other constant to compare with

Returns:

-1, 0 or 1 if this number is numerically less than, equal to, or greater than val.

toString

public java.lang.String toString()

Return a string in the format number/denom. If the denominator equals 1, print just the numerator without a slash.

Overrides:

toString in class java.lang.Object

Returns:

the human-readable version in base 10

doubleValue

public double doubleValue()

Return a double value representation.

Returns:

The value with double precision.

Since:

2008-10-26

floatValue

public float floatValue()

Return a float value representation.

Returns:

The value with single precision.

Since:

2009-08-06

BigDecimalValue

public java.math.BigDecimal BigDecimalValue(java.math.MathContext mc)

Return a representation as BigDecimal.

Parameters:

mc - the mathematical context which determines precision, rounding mode etc

Returns:

A representation as a BigDecimal floating point number.

Since:

2008-10-26

toFString

public java.lang.String toFString(int digits)

Return a string in floating point format.

Parameters:

digits - The precision (number of digits)

Returns:

The human-readable version in base 10.

Since:

2008-10-25

max

public Rational max(Rational val)

Compares the value of this with another constant.

Parameters:

val - The other constant to compare with

Returns:

The arithmetic maximum of this and val.

Since:

2008-10-19

min

public Rational min(Rational val)

Compares the value of this with another constant.

Parameters:

val - The other constant to compare with

Returns:

The arithmetic minimum of this and val.

Since:

2008-10-19

Pochhammer

public Rational Pochhammer(java.math.BigInteger n)

Compute Pochhammer's symbol (this)_n.

Parameters:

n - The number of product terms in the evaluation.

Returns:

Gamma(this+n)/Gamma(this) = this*(this+1)*...*(this+n-1).

Since:

2008-10-25

Pochhammer

public Rational Pochhammer(int n)

Compute pochhammer's symbol (this)_n.

Parameters:

n - The number of product terms in the evaluation.

Returns:

Gamma(this+n)/GAMMA(this).

Since:

2008-11-13

isBigInteger

public boolean isBigInteger()

True if the value is integer. Equivalent to the indication whether a conversion to an integer can be exact.

Since:

2010-05-26

isInteger

public boolean isInteger()

True if the value is integer and in the range of the standard integer. Equivalent to the indication whether a conversion to an integer can be exact.

Since:

2010-05-26

isIntegerFrac

public boolean isIntegerFrac()

True if the value is a fraction of two integers in the range of the standard integer.

Since:

2010-05-26

signum

public int signum()

The sign: 1 if the number is >0, 0 if ==0, -1 if <0

Returns:

the signum of the value.

Since:

2010-05-26

lcmDenom

public static java.math.BigInteger lcmDenom(Rational[] vals)

Common lcm of the denominators of a set of rational values.

Parameters:

vals - The list/set of the rational values.

Returns:

LCM(denom of first, denom of second, ..,denom of last)

Since:

2012-03-02

normalize

protected void normalize()

Normalize to coprime numerator and denominator. Also copy a negative sign of the denominator to the numerator.

Since:

2008-10-19