## Class Fraction

• All Implemented Interfaces:
Serializable, Comparable<Fraction>, FieldElement<Fraction>

public class Fraction
extends Number
implements FieldElement<Fraction>, Comparable<Fraction>, Serializable
Representation of a rational number.
Serialized Form
• ### Nested Class Summary

Nested Classes
Modifier and Type Class Description
static interface  Fraction.ConvergenceTest
A test to determine if a series of fractions has converged.
• ### Field Summary

Fields
Modifier and Type Field Description
static Fraction FOUR_FIFTHS
A fraction representing "4/5".
static Fraction MINUS_ONE
A fraction representing "-1 / 1".
static Fraction ONE
A fraction representing "1".
static Fraction ONE_FIFTH
A fraction representing "1/5".
static Fraction ONE_HALF
A fraction representing "1/2".
static Fraction ONE_QUARTER
A fraction representing "1/4".
static Fraction ONE_THIRD
A fraction representing "1/3".
static Fraction THREE_FIFTHS
A fraction representing "3/5".
static Fraction THREE_QUARTERS
A fraction representing "3/4".
static Fraction TWO
A fraction representing "2 / 1".
static Fraction TWO_FIFTHS
A fraction representing "2/5".
static Fraction TWO_QUARTERS
A fraction representing "2/4".
static Fraction TWO_THIRDS
A fraction representing "2/3".
static Fraction ZERO
A fraction representing "0".
• ### Constructor Summary

Constructors
Constructor Description
Fraction​(double value)
Create a fraction given the double value.
Fraction​(double value, double epsilon, int maxIterations)
Create a fraction given the double value and maximum error allowed.
Fraction​(double value, int maxDenominator)
Create a fraction given the double value and maximum denominator.
Fraction​(int num)
Create a fraction from an int.
Fraction​(int num, int den)
Create a fraction given the numerator and denominator.
• ### Method Summary

All Methods
Modifier and Type Method Description
Fraction abs()
Returns the absolute value of this fraction.
Fraction add​(int i)
Add an integer to the fraction.
Fraction add​(Fraction fraction)
Adds the value of this fraction to another, returning the result in reduced form.
int compareTo​(Fraction object)
Compares this object to another based on size.
static Pair<Fraction,​Boolean> convergent​(double value, int maxConvergents, Fraction.ConvergenceTest convergenceTest)
Returns the last element of the series of convergent-steps to approximate the given value.
static Stream<Fraction> convergents​(double value, int maxConvergents)
Generate a stream of convergents from a real number.
Fraction divide​(int i)
Divide the fraction by an integer.
Fraction divide​(Fraction fraction)
Divide the value of this fraction by another.
double doubleValue()
Gets the fraction as a double.
boolean equals​(Object other)
Test for the equality of two fractions.
float floatValue()
Gets the fraction as a float.
int getDenominator()
Access the denominator.
FractionField getField()
Get the Field to which the instance belongs.
int getNumerator()
Access the numerator.
double getReal()
Get the real value of the number.
static Fraction getReducedFraction​(int numerator, int denominator)
Creates a Fraction instance with the 2 parts of a fraction Y/Z.
int hashCode()
Gets a hashCode for the fraction.
int intValue()
Gets the fraction as an int.
boolean isInteger()
Check if a fraction is an integer.
long longValue()
Gets the fraction as a long.
Fraction multiply​(int i)
Multiply the fraction by an integer.
Fraction multiply​(Fraction fraction)
Multiplies the value of this fraction by another, returning the result in reduced form.
Fraction negate()
Return the additive inverse of this fraction.
double percentageValue()
Gets the fraction percentage as a double.
Fraction reciprocal()
Return the multiplicative inverse of this fraction.
int signum()
Returns the signum function of this fraction.
Fraction subtract​(int i)
Subtract an integer from the fraction.
Fraction subtract​(Fraction fraction)
Subtracts the value of another fraction from the value of this one, returning the result in reduced form.
String toString()
Returns the String representing this fraction, ie "num / dem" or just "num" if the denominator is one.
• ### Methods inherited from class java.lang.Number

byteValue, shortValue
• ### Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait
• ### Methods inherited from interface org.hipparchus.FieldElement

isZero
• ### Field Detail

• #### TWO

public static final Fraction TWO
A fraction representing "2 / 1".
• #### ONE

public static final Fraction ONE
A fraction representing "1".
• #### ZERO

public static final Fraction ZERO
A fraction representing "0".
• #### FOUR_FIFTHS

public static final Fraction FOUR_FIFTHS
A fraction representing "4/5".
• #### ONE_FIFTH

public static final Fraction ONE_FIFTH
A fraction representing "1/5".
• #### ONE_HALF

public static final Fraction ONE_HALF
A fraction representing "1/2".
• #### ONE_QUARTER

public static final Fraction ONE_QUARTER
A fraction representing "1/4".
• #### ONE_THIRD

public static final Fraction ONE_THIRD
A fraction representing "1/3".
• #### THREE_FIFTHS

public static final Fraction THREE_FIFTHS
A fraction representing "3/5".
• #### THREE_QUARTERS

public static final Fraction THREE_QUARTERS
A fraction representing "3/4".
• #### TWO_FIFTHS

public static final Fraction TWO_FIFTHS
A fraction representing "2/5".
• #### TWO_QUARTERS

public static final Fraction TWO_QUARTERS
A fraction representing "2/4".
• #### TWO_THIRDS

public static final Fraction TWO_THIRDS
A fraction representing "2/3".
• #### MINUS_ONE

public static final Fraction MINUS_ONE
A fraction representing "-1 / 1".
• ### Constructor Detail

• #### Fraction

public Fraction​(double value)
throws MathIllegalStateException
Create a fraction given the double value.
Parameters:
value - the double value to convert to a fraction.
Throws:
MathIllegalStateException - if the continued fraction failed to converge.
• #### Fraction

public Fraction​(double value,
double epsilon,
int maxIterations)
throws MathIllegalStateException
Create a fraction given the double value and maximum error allowed.

References:

Parameters:
value - the double value to convert to a fraction.
epsilon - maximum error allowed. The resulting fraction is within epsilon of value, in absolute terms.
maxIterations - maximum number of convergents
Throws:
MathIllegalStateException - if the continued fraction failed to converge.
• #### Fraction

public Fraction​(double value,
int maxDenominator)
throws MathIllegalStateException
Create a fraction given the double value and maximum denominator.

References:

Parameters:
value - the double value to convert to a fraction.
maxDenominator - The maximum allowed value for denominator
Throws:
MathIllegalStateException - if the continued fraction failed to converge
• #### Fraction

public Fraction​(int num)
Create a fraction from an int. The fraction is num / 1.
Parameters:
num - the numerator.
• #### Fraction

public Fraction​(int num,
int den)
Create a fraction given the numerator and denominator. The fraction is reduced to lowest terms.
Parameters:
num - the numerator.
den - the denominator.
Throws:
MathRuntimeException - if the denominator is zero
• ### Method Detail

• #### convergents

public static Stream<Fraction> convergents​(double value,
int maxConvergents)
Generate a stream of convergents from a real number.
Parameters:
value - value to approximate
maxConvergents - maximum number of convergents.
Returns:
stream of Fraction convergents approximating value
Since:
2.1
• #### convergent

public static Pair<Fraction,​Boolean> convergent​(double value,
int maxConvergents,
Fraction.ConvergenceTest convergenceTest)
Returns the last element of the series of convergent-steps to approximate the given value.

The series terminates either at the first step that satisfies the given convergenceTest or after at most maxConvergents elements. The returned Pair consists of that terminal Fraction and a Boolean that indicates if it satisfies the given convergence tests. If the returned pair's value is false the element at position maxConvergents was examined but failed to satisfy the convergenceTest. A caller can then decide to accept the result nevertheless or to discard it. This method is usually faster than convergents(double, int) if only the terminal element is of interest.

Parameters:
value - value to approximate
maxConvergents - maximum number of convergents to examine
convergenceTest - the test if the series has converged at a step
Returns:
the pair of last element of the series of convergents and a boolean indicating if that element satisfies the specified convergent test
• #### getReal

public double getReal()
Get the real value of the number.
Specified by:
getReal in interface FieldElement<Fraction>
Returns:
real value
• #### isInteger

public boolean isInteger()
Check if a fraction is an integer.
Returns:
true of fraction is an integer
• #### signum

public int signum()
Returns the signum function of this fraction.

The return value is -1 if the specified value is negative; 0 if the specified value is zero; and 1 if the specified value is positive.

Returns:
the signum function of this fraction
Since:
1.7
• #### abs

public Fraction abs()
Returns the absolute value of this fraction.
Returns:
the absolute value.
• #### compareTo

public int compareTo​(Fraction object)
Compares this object to another based on size.
Specified by:
compareTo in interface Comparable<Fraction>
Parameters:
object - the object to compare to
Returns:
-1 if this is less than object, +1 if this is greater than object, 0 if they are equal.
• #### doubleValue

public double doubleValue()
Gets the fraction as a double. This calculates the fraction as the numerator divided by denominator.
Specified by:
doubleValue in class Number
Returns:
the fraction as a double
• #### equals

public boolean equals​(Object other)
Test for the equality of two fractions. If the lowest term numerator and denominators are the same for both fractions, the two fractions are considered to be equal.
Overrides:
equals in class Object
Parameters:
other - fraction to test for equality to this fraction
Returns:
true if two fractions are equal, false if object is null, not an instance of Fraction, or not equal to this fraction instance.
• #### floatValue

public float floatValue()
Gets the fraction as a float. This calculates the fraction as the numerator divided by denominator.
Specified by:
floatValue in class Number
Returns:
the fraction as a float
• #### getDenominator

public int getDenominator()
Access the denominator.
Returns:
the denominator.
• #### getNumerator

public int getNumerator()
Access the numerator.
Returns:
the numerator.
• #### hashCode

public int hashCode()
Gets a hashCode for the fraction.
Overrides:
hashCode in class Object
Returns:
a hash code value for this object
• #### intValue

public int intValue()
Gets the fraction as an int. This returns the whole number part of the fraction.
Specified by:
intValue in class Number
Returns:
the whole number fraction part
• #### longValue

public long longValue()
Gets the fraction as a long. This returns the whole number part of the fraction.
Specified by:
longValue in class Number
Returns:
the whole number fraction part
• #### negate

public Fraction negate()
Return the additive inverse of this fraction.
Specified by:
negate in interface FieldElement<Fraction>
Returns:
the negation of this fraction.
• #### reciprocal

public Fraction reciprocal()
Return the multiplicative inverse of this fraction.
Specified by:
reciprocal in interface FieldElement<Fraction>
Returns:
the reciprocal fraction

public Fraction add​(Fraction fraction)
Adds the value of this fraction to another, returning the result in reduced form. The algorithm follows Knuth, 4.5.1.
Specified by:
add in interface FieldElement<Fraction>
Parameters:
fraction - the fraction to add, must not be null
Returns:
a Fraction instance with the resulting values
Throws:
NullArgumentException - if the fraction is null
MathRuntimeException - if the resulting numerator or denominator exceeds Integer.MAX_VALUE

public Fraction add​(int i)
Add an integer to the fraction.
Parameters:
i - the integer to add.
Returns:
this + i
• #### subtract

public Fraction subtract​(Fraction fraction)
Subtracts the value of another fraction from the value of this one, returning the result in reduced form.
Specified by:
subtract in interface FieldElement<Fraction>
Parameters:
fraction - the fraction to subtract, must not be null
Returns:
a Fraction instance with the resulting values
Throws:
NullArgumentException - if the fraction is null
MathRuntimeException - if the resulting numerator or denominator cannot be represented in an int.
• #### subtract

public Fraction subtract​(int i)
Subtract an integer from the fraction.
Parameters:
i - the integer to subtract.
Returns:
this - i
• #### multiply

public Fraction multiply​(Fraction fraction)
Multiplies the value of this fraction by another, returning the result in reduced form.
Specified by:
multiply in interface FieldElement<Fraction>
Parameters:
fraction - the fraction to multiply by, must not be null
Returns:
a Fraction instance with the resulting values
Throws:
NullArgumentException - if the fraction is null
MathRuntimeException - if the resulting numerator or denominator exceeds Integer.MAX_VALUE
• #### multiply

public Fraction multiply​(int i)
Multiply the fraction by an integer.
Specified by:
multiply in interface FieldElement<Fraction>
Parameters:
i - the integer to multiply by.
Returns:
this * i
• #### divide

public Fraction divide​(Fraction fraction)
Divide the value of this fraction by another.
Specified by:
divide in interface FieldElement<Fraction>
Parameters:
fraction - the fraction to divide by, must not be null
Returns:
a Fraction instance with the resulting values
Throws:
IllegalArgumentException - if the fraction is null
MathRuntimeException - if the fraction to divide by is zero
MathRuntimeException - if the resulting numerator or denominator exceeds Integer.MAX_VALUE
• #### divide

public Fraction divide​(int i)
Divide the fraction by an integer.
Parameters:
i - the integer to divide by.
Returns:
this * i
• #### percentageValue

public double percentageValue()
Gets the fraction percentage as a double. This calculates the fraction as the numerator divided by denominator multiplied by 100.
Returns:
the fraction percentage as a double.
• #### getReducedFraction

public static Fraction getReducedFraction​(int numerator,
int denominator)
Creates a Fraction instance with the 2 parts of a fraction Y/Z.

Any negative signs are resolved to be on the numerator.

Parameters:
numerator - the numerator, for example the three in 'three sevenths'
denominator - the denominator, for example the seven in 'three sevenths'
Returns:
a new fraction instance, with the numerator and denominator reduced
Throws:
MathRuntimeException - if the denominator is zero
• #### toString

public String toString()
Returns the String representing this fraction, ie "num / dem" or just "num" if the denominator is one.
Overrides:
toString in class Object
Returns:
a string representation of the fraction.
Object.toString()
public FractionField getField()
Get the Field to which the instance belongs.
getField in interface FieldElement<Fraction>
Field to which the instance belongs