Rational

java.lang.Object
- java.lang.Number
- - com.ekarp.math.Rational

All Implemented Interfaces:

java.io.Serializable, java.lang.Comparable<Rational>
```
public class Rational
extends java.lang.Number
implements java.lang.Comparable<Rational>
```
Arbitrary precision rational number. The sign of the number is always associated with the numerator.

See Also:
Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`static Rational`	`ONE` Representation of the number one, in rational format.
`static Rational`	`ONE_HALF` Representation of the number 1/2, in rational format.
`static Rational`	`ZERO` Representation of the number zero, in rational format.

Constructor Summary

Constructors
Constructor and Description
`Rational(java.math.BigDecimal bd)` Create a rational from a big decimal.
`Rational(java.math.BigInteger value)` Create a rational representing the big integer.
`Rational(java.math.BigInteger numerator, java.math.BigInteger denominator)` Create a rational from two big integers.
`Rational(long value)` Create a rational representing the long value.
`Rational(long numerator, long denominator)` Create a rational from two longs.
`Rational(java.lang.String rational)` Create a rational from a string representing a decimal number or "x/y" where x and y are base10 numbers.

Method Summary

Methods
Modifier and Type	Method and Description
`Rational`	`abs()` Returns the absolute value of this rational.
`Rational`	`add(java.math.BigDecimal other)` Adds the rational to the big decimal, returning a new rational.
`Rational`	`add(java.math.BigInteger other)` Adds the rational to the big integer, returning a new rational.
`Rational`	`add(long other)` Adds the rational to the long value, returning a new rational.
`Rational`	`add(Rational other)` Adds the rational to this one, returning a new rational.
`java.math.BigDecimal`	`bigDecimalValue()` Converts this rational to a big decimal, throwing an exception if the division results in a non-terminating decimal expansion.
`java.math.BigDecimal`	`bigDecimalValue(java.math.MathContext mc)` Converts this rational to a big decimal, using the math context for rounding.
`byte`	`byteValue()` Returns the rational as a byte (rounding down).
`java.math.BigInteger`	`ceiling()` Returns the ceiling of the rational (smallest integer greater than or equal to it).
`int`	`compareTo(Rational other)` Compares this rational with the other one.
`java.math.BigInteger`	`denominator()` Returns the denominator associated with the rational.
`Rational`	`divide(java.math.BigDecimal other)` Divides the rational by the big decimal, returning a new rational.
`Rational`	`divide(java.math.BigInteger other)` Divides the rational by the big integer, returning a new rational.
`Rational`	`divide(long other)` Divides the rational by the long, returning a new rational.
`Rational`	`divide(Rational other)` Divides the two rationals, returning a new rational.
`double`	`doubleValue()` Returns the rational as a double.
`boolean`	`equals(java.lang.Object obj)` Performs an equality check with the other object.
`float`	`floatValue()` Returns the rational as a float.
`java.math.BigInteger`	`floor()` Returns the floor of the rational (largest integer less than or equal to it).
`Rational`	`floorMod(java.math.BigDecimal moduloValue)` Returns this value modded by the given big decimal.
`Rational`	`floorMod(java.math.BigInteger moduloValue)` Returns this value modded by the given big integer.
`Rational`	`floorMod(long moduloValue)` Returns this value modded by the given long.
`Rational`	`floorMod(Rational moduloValue)` Returns this value modded by the given rational.
`int`	`hashCode()` Computes the hash code of the rational.
`int`	`intValue()` Returns the rational as an integer (rounding down).
`Rational`	`invert()` Returns the reciprocal of the rational.
`long`	`longValue()` Returns the rational as a long (rounding down).
`static Rational`	`max(java.lang.Iterable<Rational> rationals)` Takes the maximum of the rationals.
`static Rational`	`max(Rational... rationals)` Takes the maximum of the rationals.
`static Rational`	`min(java.lang.Iterable<Rational> rationals)` Takes the minimum of the rationals.
`static Rational`	`min(Rational... rationals)` Takes the minimum of the rationals.
`Rational`	`mod(java.math.BigDecimal moduloValue)` Returns this value modded by the given big decimal.
`Rational`	`mod(java.math.BigInteger moduloValue)` Returns this value modded by the given big integer.
`Rational`	`mod(long moduloValue)` Returns this value modded by the given long.
`Rational`	`mod(Rational m)` Returns this value modded by the given rational.
`Rational`	`multiply(java.math.BigDecimal other)` Multiplies the rational with the big decimal, returning a new rational.
`Rational`	`multiply(java.math.BigInteger other)` Multiplies the rational with the big integer, returning a new rational.
`Rational`	`multiply(long other)` Multiplies the rational with the long, returning a new rational.
`Rational`	`multiply(Rational other)` Multiplies the two rationals together, returning a new rational.
`Rational`	`negate()` Returns a rational that is the negated version of this one.
`java.math.BigInteger`	`numerator()` Returns the numerator associated with the rational.
`Rational`	`pow(int n)` Raise this rational to the N-th power.
`static Rational`	`product(java.lang.Iterable<Rational> rationals)` Convenience method to multiply an arbitrary number of rationals.
`static Rational`	`product(Rational... rationals)` Convenience method to multiply an arbitrary number of rationals.
`java.math.BigInteger`	`round()` Round the rational to the nearest integer (using the HALF_EVEN rounding mode).
`java.math.BigInteger`	`round(java.math.RoundingMode roundingMode)` Round the rational to the nearest integer (using the specified rounding mode).
`short`	`shortValue()` Returns the rational as a short (rounding down).
`int`	`sign()` Returns the sign of this rational.
`Rational`	`subtract(java.math.BigDecimal other)` Subtracts the big decimal from the rational, returning a new rational.
`Rational`	`subtract(java.math.BigInteger other)` Subtracts the big integer from the rational, returning a new rational.
`Rational`	`subtract(long other)` Subtracts the long from the rational, returning a new rational.
`Rational`	`subtract(Rational other)` Subtracts the rational from this one, returning a new rational.
`static Rational`	`sum(java.lang.Iterable<Rational> rationals)` Convenience method to sum an iterable of rationals.
`static Rational`	`sum(Rational... rationals)` Convenience method to sum an arbitrary number of rationals.
`java.lang.String`	`toString()` Convert this rational into a string.

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - ZERO
```
public static Rational ZERO
```
    Representation of the number zero, in rational format.
  - ONE
```
public static Rational ONE
```
    Representation of the number one, in rational format.
  - ONE_HALF
```
public static Rational ONE_HALF
```
    Representation of the number 1/2, in rational format.
- Constructor Detail
  - Rational
```
public Rational(java.math.BigInteger numerator,
        java.math.BigInteger denominator)
```
    Create a rational from two big integers.
    
    Parameters:
    numerator - the numerator
    denominator - the denominator
    
    Throws:
    
    java.lang.ArithmeticException - if the denominator is zero
  - Rational
```
public Rational(java.math.BigInteger value)
```
    Create a rational representing the big integer.
    
    Parameters:
    value - the value
  - Rational
```
public Rational(java.math.BigDecimal bd)
```
    Create a rational from a big decimal.
    
    Parameters:
    bd - the big decimal
  - Rational
```
public Rational(java.lang.String rational)
```
    Create a rational from a string representing a decimal number or "x/y" where x and y are base10 numbers.
    
    Parameters:
    rational - the number in string format; it can be in any format that is accepted by the BigDecimal constructor, or in the "x/y" format
    
    Throws:
    
    java.lang.NumberFormatException - if the string is not a valid representation of a decimal number or a rational number
    
    java.lang.ArithmeticException - if the denominator is zero
  - Rational
```
public Rational(long numerator,
        long denominator)
```
    Create a rational from two longs.
    
    Parameters:
    numerator - the numerator
    denominator - the denominator
    
    Throws:
    
    java.lang.ArithmeticException - if the denominator is zero
  - Rational
```
public Rational(long value)
```
    Create a rational representing the long value.
    
    Parameters:
    value - the value
- Method Detail
  - numerator
```
public java.math.BigInteger numerator()
```
    Returns the numerator associated with the rational. The numerator always carries the sign of the number.
    
    Returns:
    the numerator
  - denominator
```
public java.math.BigInteger denominator()
```
    Returns the denominator associated with the rational. Guaranteed to be a positive integer.
    
    Returns:
    the denominator
  - add
```
public Rational add(Rational other)
```
    Adds the rational to this one, returning a new rational.
    
    Parameters:
    other - the other rational number
    
    Returns:
    the result from the addition
  - add
```
public Rational add(java.math.BigInteger other)
```
    Adds the rational to the big integer, returning a new rational.
    
    Parameters:
    other - the other number
    
    Returns:
    the result from the addition
  - add
```
public Rational add(java.math.BigDecimal other)
```
    Adds the rational to the big decimal, returning a new rational.
    
    Parameters:
    other - the other number
    
    Returns:
    the result from the addition
  - add
```
public Rational add(long other)
```
    Adds the rational to the long value, returning a new rational.
    
    Parameters:
    other - the other number
    
    Returns:
    the result from the addition
  - subtract
```
public Rational subtract(Rational other)
```
    Subtracts the rational from this one, returning a new rational.
    
    Parameters:
    other - the other rational number
    
    Returns:
    the result from the subtraction
  - subtract
```
public Rational subtract(java.math.BigInteger other)
```
    Subtracts the big integer from the rational, returning a new rational.
    
    Parameters:
    other - the other number
    
    Returns:
    the result from the subtraction
  - subtract
```
public Rational subtract(java.math.BigDecimal other)
```
    Subtracts the big decimal from the rational, returning a new rational.
    
    Parameters:
    other - the other number
    
    Returns:
    the result from the subtraction
  - subtract
```
public Rational subtract(long other)
```
    Subtracts the long from the rational, returning a new rational.
    
    Parameters:
    other - the other number
    
    Returns:
    the result from the subtraction
  - multiply
```
public Rational multiply(Rational other)
```
    Multiplies the two rationals together, returning a new rational.
    
    Parameters:
    other - the other rational number
    
    Returns:
    the result from the multiplication
  - multiply
```
public Rational multiply(java.math.BigInteger other)
```
    Multiplies the rational with the big integer, returning a new rational.
    
    Parameters:
    other - the other number
    
    Returns:
    the result from the multiplication
  - multiply
```
public Rational multiply(java.math.BigDecimal other)
```
    Multiplies the rational with the big decimal, returning a new rational.
    
    Parameters:
    other - the other number
    
    Returns:
    the result from the multiplication
  - multiply
```
public Rational multiply(long other)
```
    Multiplies the rational with the long, returning a new rational.
    
    Parameters:
    other - the other number
    
    Returns:
    the result from the multiplication
  - divide
```
public Rational divide(Rational other)
```
    Divides the two rationals, returning a new rational.
    
    Parameters:
    other - the other rational number
    
    Returns:
    the result from the division
    
    Throws:
    
    java.lang.ArithmeticException - if other is zero
  - divide
```
public Rational divide(java.math.BigInteger other)
```
    Divides the rational by the big integer, returning a new rational.
    
    Parameters:
    other - the other number
    
    Returns:
    the result from the division
    
    Throws:
    
    java.lang.ArithmeticException - if other is zero
  - divide
```
public Rational divide(java.math.BigDecimal other)
```
    Divides the rational by the big decimal, returning a new rational.
    
    Parameters:
    other - the other number
    
    Returns:
    the result from the division
    
    Throws:
    
    java.lang.ArithmeticException - if other is zero
  - divide
```
public Rational divide(long other)
```
    Divides the rational by the long, returning a new rational.
    
    Parameters:
    other - the other number
    
    Returns:
    the result from the division
    
    Throws:
    
    java.lang.ArithmeticException - if other is zero
  - abs
```
public Rational abs()
```
    Returns the absolute value of this rational.
    
    Returns:
    the absolute value of the rational
  - negate
```
public Rational negate()
```
    Returns a rational that is the negated version of this one.
    
    Returns:
    a negated rational of the same absolute value
  - invert
```
public Rational invert()
```
    Returns the reciprocal of the rational.
    
    Returns:
    the rational representing (denominator / numerator)
    
    Throws:
    
    java.lang.ArithmeticException - if this rational is zero
  - floor
```
public java.math.BigInteger floor()
```
    Returns the floor of the rational (largest integer less than or equal to it).
    
    Returns:
    the big integer representing the floor of the rational
  - ceiling
```
public java.math.BigInteger ceiling()
```
    Returns the ceiling of the rational (smallest integer greater than or equal to it).
    
    Returns:
    the big integer representing the ceiling of the rational
  - round
```
public java.math.BigInteger round()
```
    Round the rational to the nearest integer (using the HALF_EVEN rounding mode).
    
    Returns:
    the big integer representing the rounded rational
    See Also:
    RoundingMode.HALF_EVEN
  - round
```
public java.math.BigInteger round(java.math.RoundingMode roundingMode)
```
    Round the rational to the nearest integer (using the specified rounding mode).
    
    Parameters:
    roundingMode - the rounding mode to use
    
    Returns:
    the big integer representing the rounded rational
    
    Throws:
    
    java.lang.ArithmeticException - if the rounding mode is UNNECESSARY but conversion to a big integer requires rounding
    
    java.lang.IllegalArgumentException - if roundingMode is not one of CEILING, DOWN, FLOOR, HALF_DOWN, HALF_EVEN, HALF_UP, UNNECESSARY, or UP
  - floorMod
```
public Rational floorMod(Rational moduloValue)
```
    Returns this value modded by the given rational. The sign of returned result is the same sign as the modulo value (following Java's pattern for the Math.floorMod function).
    
    Parameters:
    moduloValue - the modulo value
    
    Returns:
    the value of this rational, modulo the given value
    
    Throws:
    
    java.lang.ArithmeticException - if the moduloValue is zero
  - floorMod
```
public Rational floorMod(java.math.BigInteger moduloValue)
```
    Returns this value modded by the given big integer. The sign of returned result is the same sign as the modulo value (following Java's pattern for the Math.floorMod function).
    
    Parameters:
    moduloValue - the modulo value
    
    Returns:
    the value of this rational, modulo the given value
    
    Throws:
    
    java.lang.ArithmeticException - if the moduloValue is zero
  - floorMod
```
public Rational floorMod(java.math.BigDecimal moduloValue)
```
    Returns this value modded by the given big decimal. The sign of returned result is the same sign as the modulo value (following Java's pattern for the Math.floorMod function).
    
    Parameters:
    moduloValue - the modulo value
    
    Returns:
    the value of this rational, modulo the given value
    
    Throws:
    
    java.lang.ArithmeticException - if the moduloValue is zero
  - floorMod
```
public Rational floorMod(long moduloValue)
```
    Returns this value modded by the given long. The sign of returned result is the same sign as the modulo value (following Java's pattern for the Math.floorMod function).
    
    Parameters:
    moduloValue - the modulo value
    
    Returns:
    the value of this rational, modulo the given value
    
    Throws:
    
    java.lang.ArithmeticException - if the moduloValue is zero
  - mod
```
public Rational mod(Rational m)
```
    Returns this value modded by the given rational. The sign of returned result is the same sign as this rational number (following Java's pattern for the % operator).
    
    Parameters:
    m - the modulo value
    
    Returns:
    the value of this rational, modulo the given value
    
    Throws:
    
    java.lang.ArithmeticException - if the moduloValue is zero
  - mod
```
public Rational mod(java.math.BigInteger moduloValue)
```
    Returns this value modded by the given big integer. The sign of returned result is the same sign as this rational number (following Java's pattern for the % operator).
    
    Parameters:
    moduloValue - the modulo value
    
    Returns:
    the value of this rational, modulo the given value
    
    Throws:
    
    java.lang.ArithmeticException - if the moduloValue is zero
  - mod
```
public Rational mod(java.math.BigDecimal moduloValue)
```
    Returns this value modded by the given big decimal. The sign of returned result is the same sign as this rational number (following Java's pattern for the % operator).
    
    Parameters:
    moduloValue - the modulo value
    
    Returns:
    the value of this rational, modulo the given value
    
    Throws:
    
    java.lang.ArithmeticException - if the moduloValue is zero
  - mod
```
public Rational mod(long moduloValue)
```
    Returns this value modded by the given long. The sign of returned result is the same sign as this rational number (following Java's pattern for the % operator).
    
    Parameters:
    moduloValue - the modulo value
    
    Returns:
    the value of this rational, modulo the given value
    
    Throws:
    
    java.lang.ArithmeticException - if the moduloValue is zero
  - pow
```
public Rational pow(int n)
```
    Raise this rational to the N-th power.
    
    Parameters:
    n - the power to raise the rational to
    
    Returns:
    the rational raised to the N-th power
  - sign
```
public int sign()
```
    Returns the sign of this rational.
    
    Returns:
    the sign of the rational (-1 if negative, 0 if zero, 1 if positive)
  - min
```
public static Rational min(Rational... rationals)
```
    Takes the minimum of the rationals.
    
    Parameters:
    rationals - an arbitrary number of rationals
    
    Returns:
    the minimum of the rationals
    
    Throws:
    
    java.lang.IllegalArgumentException - if no rationals are passed in
  - min
```
public static Rational min(java.lang.Iterable<Rational> rationals)
```
    Takes the minimum of the rationals.
    
    Parameters:
    rationals - an iterable of rationals (e.g., a list)
    
    Returns:
    the minimum of the rationals
    
    Throws:
    
    java.lang.IllegalArgumentException - if no rationals are passed in
  - max
```
public static Rational max(Rational... rationals)
```
    Takes the maximum of the rationals.
    
    Parameters:
    rationals - an arbitrary number of rationals
    
    Returns:
    the maximum of the rationals
    
    Throws:
    
    java.lang.IllegalArgumentException - if no rationals are passed in
  - max
```
public static Rational max(java.lang.Iterable<Rational> rationals)
```
    Takes the maximum of the rationals.
    
    Parameters:
    rationals - an iterable of rationals (e.g., a list)
    
    Returns:
    the maximum of the rationals
    
    Throws:
    
    java.lang.IllegalArgumentException - if no rationals are passed in
  - sum
```
public static Rational sum(Rational... rationals)
```
    Convenience method to sum an arbitrary number of rationals.
    
    Parameters:
    rationals - an arbitrary number of rationals
    
    Returns:
    the sum of the rationals
    
    Throws:
    
    java.lang.IllegalArgumentException - if no rationals are passed in
  - sum
```
public static Rational sum(java.lang.Iterable<Rational> rationals)
```
    Convenience method to sum an iterable of rationals.
    
    Parameters:
    rationals - an iterable of rationals (e.g., a list)
    
    Returns:
    the sum of the rationals
    
    Throws:
    
    java.lang.IllegalArgumentException - if no rationals are passed in
  - product
```
public static Rational product(Rational... rationals)
```
    Convenience method to multiply an arbitrary number of rationals.
    
    Parameters:
    rationals - an arbitrary number of rationals
    
    Returns:
    the product of the rationals
    
    Throws:
    
    java.lang.IllegalArgumentException - if no rationals are passed in
  - product
```
public static Rational product(java.lang.Iterable<Rational> rationals)
```
    Convenience method to multiply an arbitrary number of rationals.
    
    Parameters:
    rationals - an iterable of rationals (e.g., a list)
    
    Returns:
    the product of the rationals
    
    Throws:
    
    java.lang.IllegalArgumentException - if no rationals are passed in
  - bigDecimalValue
```
public java.math.BigDecimal bigDecimalValue()
```
    Converts this rational to a big decimal, throwing an exception if the division results in a non-terminating decimal expansion.
    
    Returns:
    the rational as a BigDecimal
    
    Throws:
    
    java.lang.ArithmeticException - if the quotient does not have a terminating decimal expansion
  - bigDecimalValue
```
public java.math.BigDecimal bigDecimalValue(java.math.MathContext mc)
```
    Converts this rational to a big decimal, using the math context for rounding.
    
    Parameters:
    mc - the math context to use for rounding
    
    Returns:
    the rational as a BigDecimal, rounding according to the math context
    
    Throws:
    
    java.lang.ArithmeticException - if the quotient does not have a terminating decimal expansion and the math context has either 1.) a precision of 0 (meaning exact precision) or 2.) a rounding mode of UNNECESSARY
  - byteValue
```
public byte byteValue()
```
    Returns the rational as a byte (rounding down). If the result is too big to fit in a byte, only the low-order 8 bits are returned. May result in loss of precision, magnitude, and even wrong sign.
    
    Overrides:
    
    byteValue in class java.lang.Number
    
    Returns:
    the rational as a byte
  - doubleValue
```
public double doubleValue()
```
    Returns the rational as a double. Does so by converting it to a big decimal with sufficiently high precision and calling BigDecimal's doubleValue() method. Note that:
    1. if the number has a magnitude greater than what double can hold, positive or negative infinity will be used (depending on the sign)
    2. the conversion may lose precision
    Specified by:
    
    doubleValue in class java.lang.Number
    
    Returns:
    the rational as a double
    See Also:
    BigDecimal.doubleValue()
  - floatValue
```
public float floatValue()
```
    Returns the rational as a float. Does so by converting it to a big decimal with sufficiently high precision and calling BigDecimal's floatValue() method. Note that:
    1. if the number has a magnitude greater than what float can hold, positive or negative infinity will be used (depending on the sign)
    2. the conversion may lose precision
    Specified by:
    
    floatValue in class java.lang.Number
    
    Returns:
    the rational as a float
    See Also:
    BigDecimal.floatValue(), doubleValue()
  - intValue
```
public int intValue()
```
    Returns the rational as an integer (rounding down). If the result is too big to fit in an int, only the low-order 32 bits are returned. May result in loss of precision, magnitude, and even wrong sign.
    
    Specified by:
    
    intValue in class java.lang.Number
    
    Returns:
    the rational as an integer
  - longValue
```
public long longValue()
```
    Returns the rational as a long (rounding down). If the result is too big to fit in a long, only the low-order 64 bits are returned. May result in loss of precision, magnitude, and even wrong sign.
    
    Specified by:
    
    longValue in class java.lang.Number
    
    Returns:
    the rational as a long
  - shortValue
```
public short shortValue()
```
    Returns the rational as a short (rounding down). If the result is too big to fit in a short, only the low-order 16 bits are returned. May result in loss of precision, magnitude, and even wrong sign.
    
    Overrides:
    
    shortValue in class java.lang.Number
    
    Returns:
    the rational as a short
  - hashCode
```
public int hashCode()
```
    Computes the hash code of the rational.
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    the hash code
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Performs an equality check with the other object.
    
    Overrides:
    
    equals in class java.lang.Object
    
    Returns:
    true if the two objects are equal, false otherwise
  - compareTo
```
public int compareTo(Rational other)
```
    Compares this rational with the other one.
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<Rational>
    
    Parameters:
    other - the other rational
    
    Returns:
    a negative integer, zero, or a positive integer if this rational is less than, equal to, or greater than other
  - toString
```
public java.lang.String toString()
```
    Convert this rational into a string. Zero is represented as "0". Any number with a denominator of 1 is represented by just the numerator.
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    the rational as a string

Class Rational

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ZERO

ONE

ONE_HALF

Constructor Detail

Rational

Rational

Rational

Rational

Rational

Rational

Method Detail

numerator

denominator

add

add

add

add

subtract

subtract

subtract

subtract

multiply

multiply

multiply

multiply

divide

divide

divide

divide

abs

negate

invert

floor

ceiling

round

round

floorMod

floorMod

floorMod

floorMod

mod

mod

mod

mod

pow

sign

min

min

max

max

sum

sum

product

product

bigDecimalValue

bigDecimalValue

byteValue

doubleValue

floatValue

intValue

longValue

shortValue

hashCode

equals

compareTo

toString