java.lang.Object
- cc.redberry.rings.Rationals<E>

All Implemented Interfaces:

IParser<Rational<E>>, Stringifiable<Rational<E>>, Ring<Rational<E>>, Serializable, Iterable<Rational<E>>, Comparator<Rational<E>>
```
public final class Rationals<E>
extends Object
implements Ring<Rational<E>>
```
The ring of rationals (Q).

Since:

1.0

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type Field Description

Ring<E> ring
Ring that numerator and denominator belongs to

Constructor Summary

Constructors
Constructor Description

Rationals(Ring<E> ring)

Method Summary

Modifier and Type	Method	Description
`Rational<E>`	`add(Rational<E> a, Rational<E> b)`	Add two elements
`BigInteger`	`cardinality()`	Returns the number of elements in this ring (cardinality) or null if ring is infinite
`BigInteger`	`characteristic()`	Returns characteristic of this ring
`int`	`compare(Rational<E> o1, Rational<E> o2)`
`Rational<E>`	`copy(Rational<E> element)`	Makes a deep copy of the specified element (for immutable instances the same reference returned).
`Rational<E>[]`	`createArray(int length)`	Creates generic array of ring elements of specified length
`Rational<E>[][]`	`createArray2d(int length)`	Creates 2d array of ring elements of specified length
`Rational<E>[][]`	`createArray2d(int m, int n)`	Creates 2d array of ring elements of specified shape
`Rational<E>[]`	`divideAndRemainder(Rational<E> dividend, Rational<E> divider)`	Returns quotient and remainder of `dividend / divider`
`boolean`	`equals(Object o)`
`FactorDecomposition<Rational<E>>`	`factor(Rational<E> element)`	Factor specified element
`FactorDecomposition<Rational<E>>`	`factorSquareFree(Rational<E> element)`	Square-free factorization of specified element
`Rational<E>`	`gcd(Rational<E> a, Rational<E> b)`	Returns the greatest common divisor of two elements
`Rational<E>`	`getNegativeOne()`	Returns negative unit element of this ring (minus one)
`Rational<E>`	`getOne()`	Returns unit element of this ring (one)
`Rational<E>`	`getZero()`	Returns zero element of this ring
`int`	`hashCode()`
`boolean`	`isEuclideanRing()`	Returns whether this ring is a Euclidean ring
`boolean`	`isField()`	Returns whether this ring is a field
`boolean`	`isOne(Rational<E> element)`	Tests whether specified element is one (exactly)
`boolean`	`isPerfectPower()`	Returns whether the cardinality is a perfect power (p^k with k > 1)
`boolean`	`isUnit(Rational<E> element)`	Tests whether specified element is a ring unit
`boolean`	`isZero(Rational<E> element)`	Tests whether specified element is zero
`Iterator<Rational<E>>`	`iterator()`	Returns iterator over ring elements (for finite rings, otherwise throws exception)
`Rational<E>`	`mk(long num, long den)`	Gives rational with a given numerator and denominator
`Rational<E>`	`mk(E num, E den)`	Gives rational with a given numerator and denominator
`Rational<E>`	`mkDenominator(long den)`	Gives rational with a given denominator and unit numerator
`Rational<E>`	`mkDenominator(E den)`	Gives rational with a given denominator and unit numerator
`Rational<E>`	`mkNumerator(long num)`	Gives rational with a given numerator and unit denominator
`Rational<E>`	`mkNumerator(E num)`	Gives rational with a given numerator and unit denominator
`Rational<E>`	`multiply(Rational<E> a, Rational<E> b)`	Multiplies two elements
`Rational<E>`	`negate(Rational<E> element)`	Negates the given element
`BigInteger`	`perfectPowerBase()`	Returns `base` so that `cardinality == base^exponent` or null if cardinality is not finite
`BigInteger`	`perfectPowerExponent()`	Returns `exponent` so that `cardinality == base^exponent` or null if cardinality is not finite
`Rational<E>`	`randomElement(org.apache.commons.math3.random.RandomGenerator rnd)`	Returns a random element from this ring
`Rational<E>`	`randomElementTree(org.apache.commons.math3.random.RandomGenerator rnd)`	If this ring has a complicated nested structure, this method guaranties that the resulting random element will reflect ring complicated structure, i.e.
`Rational<E>`	`reciprocal(Rational<E> element)`	Gives the inverse element `element ^ (-1)`
`int`	`signum(Rational<E> element)`	Returns -1 if `element < 0`, 0 if `element == 0` and 1 if `element > 0`, where comparison is specified by `Comparator.compare(Object, Object)`
`Rational<E>`	`subtract(Rational<E> a, Rational<E> b)`	Subtracts `b` from `a`
`String`	`toString()`
`String`	`toString(IStringifier<Rational<E>> stringifier)`	convert this to string with the use of stringifier
`Rational<E>`	`valueOf(long val)`	Returns ring element associated with specified `long`
`Rational<E>`	`valueOf(Rational<E> val)`	Converts a value from other ring to this ring.
`Rational<E>`	`valueOfBigInteger(BigInteger val)`	Returns ring element associated with specified integer

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

Methods inherited from interface java.util.Comparator
reversed, thenComparing, thenComparing, thenComparing, thenComparingDouble, thenComparingInt, thenComparingLong

Methods inherited from interface java.lang.Iterable
forEach, spliterator

Methods inherited from interface cc.redberry.rings.Ring
abs, add, addMutable, createArray, createArray, createArray, createZeroesArray, createZeroesArray2d, decrement, divideExact, divideExactMutable, divideOrNull, extendedGCD, factorial, fillZeros, firstBezoutCoefficient, gcd, gcd, increment, isFinite, isFiniteField, isMinusOne, isUnitOrZero, lcm, lcm, lcm, max, min, multiply, multiply, multiply, multiplyMutable, negateMutable, parse, pow, pow, pow, quotient, randomElement, randomElementTree, randomNonZeroElement, remainder, setToValueOf, subtractMutable, valueOf

- Field Detail
  - ring
```
public final Ring<E> ring
```
    Ring that numerator and denominator belongs to
- Constructor Detail
  - Rationals
```
public Rationals(Ring<E> ring)
```
- Method Detail
  - mkNumerator
```
public Rational<E> mkNumerator(E num)
```
    Gives rational with a given numerator and unit denominator
  - mkNumerator
```
public Rational<E> mkNumerator(long num)
```
    Gives rational with a given numerator and unit denominator
  - mkDenominator
```
public Rational<E> mkDenominator(E den)
```
    Gives rational with a given denominator and unit numerator
  - mkDenominator
```
public Rational<E> mkDenominator(long den)
```
    Gives rational with a given denominator and unit numerator
  - mk
```
public Rational<E> mk(E num,
                      E den)
```
    Gives rational with a given numerator and denominator
  - mk
```
public Rational<E> mk(long num,
                      long den)
```
    Gives rational with a given numerator and denominator
  - isField
```
public boolean isField()
```
    Description copied from interface: Ring
    
    Returns whether this ring is a field
    
    Specified by:
    
    isField in interface Ring<E>
    
    Returns:
    
    whether this ring is a field
  - isEuclideanRing
```
public boolean isEuclideanRing()
```
    Description copied from interface: Ring
    
    Returns whether this ring is a Euclidean ring
    
    Specified by:
    
    isEuclideanRing in interface Ring<E>
    
    Returns:
    
    whether this ring is a Euclidean ring
  - cardinality
```
public BigInteger cardinality()
```
    Description copied from interface: Ring
    
    Returns the number of elements in this ring (cardinality) or null if ring is infinite
    
    Specified by:
    
    cardinality in interface Ring<E>
    
    Returns:
    
    the number of elements in this ring (cardinality) or null if ring is infinite
  - characteristic
```
public BigInteger characteristic()
```
    Description copied from interface: Ring
    
    Returns characteristic of this ring
    
    Specified by:
    
    characteristic in interface Ring<E>
    
    Returns:
    
    characteristic of this ring
  - isPerfectPower
```
public boolean isPerfectPower()
```
    Description copied from interface: Ring
    
    Returns whether the cardinality is a perfect power (p^k with k > 1)
    
    Specified by:
    
    isPerfectPower in interface Ring<E>
    
    Returns:
    
    whether the cardinality is a perfect power (p^k with k > 1)
  - perfectPowerBase
```
public BigInteger perfectPowerBase()
```
    Description copied from interface: Ring
    
    Returns base so that cardinality == base^exponent or null if cardinality is not finite
    
    Specified by:
    
    perfectPowerBase in interface Ring<E>
    
    Returns:
    
    base so that cardinality == base^exponent or null if cardinality is not finite
  - perfectPowerExponent
```
public BigInteger perfectPowerExponent()
```
    Description copied from interface: Ring
    
    Returns exponent so that cardinality == base^exponent or null if cardinality is not finite
    
    Specified by:
    
    perfectPowerExponent in interface Ring<E>
    
    Returns:
    
    exponent so that cardinality == base^exponent or null if cardinality is not finite
  - add
```
public Rational<E> add(Rational<E> a,
                       Rational<E> b)
```
    Description copied from interface: Ring
    
    Add two elements
    
    Specified by:
    
    add in interface Ring<E>
    
    Parameters:
    
    a - the first element
    
    b - the second element
    
    Returns:
    
    a + b
  - subtract
```
public Rational<E> subtract(Rational<E> a,
                            Rational<E> b)
```
    Description copied from interface: Ring
    
    Subtracts b from a
    
    Specified by:
    
    subtract in interface Ring<E>
    
    Parameters:
    
    a - the first element
    
    b - the second element
    
    Returns:
    
    a - b
  - multiply
```
public Rational<E> multiply(Rational<E> a,
                            Rational<E> b)
```
    Description copied from interface: Ring
    
    Multiplies two elements
    
    Specified by:
    
    multiply in interface Ring<E>
    
    Parameters:
    
    a - the first element
    
    b - the second element
    
    Returns:
    
    a * b
  - negate
```
public Rational<E> negate(Rational<E> element)
```
    Description copied from interface: Ring
    
    Negates the given element
    
    Specified by:
    
    negate in interface Ring<E>
    
    Parameters:
    
    element - the ring element
    
    Returns:
    
    -val
  - signum
```
public int signum(Rational<E> element)
```
    Description copied from interface: Ring
    
    Returns -1 if element < 0, 0 if element == 0 and 1 if element > 0, where comparison is specified by Comparator.compare(Object, Object)
    
    Specified by:
    
    signum in interface Ring<E>
    
    Parameters:
    
    element - the element
    
    Returns:
    
    -1 if element < 0, 0 if element == 0 and 1 otherwise
  - divideAndRemainder
```
public Rational<E>[] divideAndRemainder(Rational<E> dividend,
                                        Rational<E> divider)
```
    Description copied from interface: Ring
    
    Returns quotient and remainder of dividend / divider
    
    Specified by:
    
    divideAndRemainder in interface Ring<E>
    
    Parameters:
    
    dividend - the dividend
    
    divider - the divider
    
    Returns:
    
    {quotient, remainder}
  - reciprocal
```
public Rational<E> reciprocal(Rational<E> element)
```
    Description copied from interface: Ring
    
    Gives the inverse element element ^ (-1)
    
    Specified by:
    
    reciprocal in interface Ring<E>
    
    Parameters:
    
    element - the element
    
    Returns:
    
    element ^ (-1)
  - gcd
```
public Rational<E> gcd(Rational<E> a,
                       Rational<E> b)
```
    Description copied from interface: Ring
    
    Returns the greatest common divisor of two elements
    
    Specified by:
    
    gcd in interface Ring<E>
    
    Parameters:
    
    a - the first element
    
    b - the second element
    
    Returns:
    
    gcd
  - factorSquareFree
```
public FactorDecomposition<Rational<E>> factorSquareFree(Rational<E> element)
```
    Description copied from interface: Ring
    
    Square-free factorization of specified element
    
    Specified by:
    
    factorSquareFree in interface Ring<E>
  - factor
```
public FactorDecomposition<Rational<E>> factor(Rational<E> element)
```
    Description copied from interface: Ring
    
    Factor specified element
    
    Specified by:
    
    factor in interface Ring<E>
  - getZero
```
public Rational<E> getZero()
```
    Description copied from interface: Ring
    
    Returns zero element of this ring
    
    Specified by:
    
    getZero in interface Ring<E>
    
    Returns:
    
    0
  - getOne
```
public Rational<E> getOne()
```
    Description copied from interface: Ring
    
    Returns unit element of this ring (one)
    
    Specified by:
    
    getOne in interface Ring<E>
    
    Returns:
    
    1
  - isZero
```
public boolean isZero(Rational<E> element)
```
    Description copied from interface: Ring
    
    Tests whether specified element is zero
    
    Specified by:
    
    isZero in interface Ring<E>
    
    Parameters:
    
    element - the ring element
    
    Returns:
    
    whether specified element is zero
  - isOne
```
public boolean isOne(Rational<E> element)
```
    Description copied from interface: Ring
    
    Tests whether specified element is one (exactly)
    
    Specified by:
    
    isOne in interface Ring<E>
    
    Parameters:
    
    element - the ring element
    
    Returns:
    
    whether specified element is exactly one
    
    See Also:
    
    Ring.isUnit(Object)
  - isUnit
```
public boolean isUnit(Rational<E> element)
```
    Description copied from interface: Ring
    
    Tests whether specified element is a ring unit
    
    Specified by:
    
    isUnit in interface Ring<E>
    
    Parameters:
    
    element - the ring element
    
    Returns:
    
    whether specified element is a ring unit
    
    See Also:
    
    Ring.isOne(Object)
  - valueOf
```
public Rational<E> valueOf(long val)
```
    Description copied from interface: Ring
    
    Returns ring element associated with specified long
    
    Specified by:
    
    valueOf in interface Ring<E>
    
    Parameters:
    
    val - machine integer
    
    Returns:
    
    ring element associated with specified long
  - valueOfBigInteger
```
public Rational<E> valueOfBigInteger(BigInteger val)
```
    Description copied from interface: Ring
    
    Returns ring element associated with specified integer
    
    Specified by:
    
    valueOfBigInteger in interface Ring<E>
    
    Parameters:
    
    val - integer
    
    Returns:
    
    ring element associated with specified integer
  - copy
```
public Rational<E> copy(Rational<E> element)
```
    Description copied from interface: Ring
    
    Makes a deep copy of the specified element (for immutable instances the same reference returned).
    
    Specified by:
    
    copy in interface Ring<E>
    
    Parameters:
    
    element - the element
    
    Returns:
    
    deep copy of specified element
  - valueOf
```
public Rational<E> valueOf(Rational<E> val)
```
    Description copied from interface: Ring
    
    Converts a value from other ring to this ring. The result is not guarantied to be a new instance (i.e. val == valueOf(val) is possible).
    
    Specified by:
    
    valueOf in interface Ring<E>
    
    Parameters:
    
    val - some element from any ring
    
    Returns:
    
    this ring element associated with specified val
  - createArray2d
```
public Rational<E>[][] createArray2d(int length)
```
    Description copied from interface: Ring
    
    Creates 2d array of ring elements of specified length
    
    Specified by:
    
    createArray2d in interface Ring<E>
    
    Parameters:
    
    length - array length
    
    Returns:
    
    2d array of ring elements of specified length
  - createArray2d
```
public Rational<E>[][] createArray2d(int m,
                                     int n)
```
    Description copied from interface: Ring
    
    Creates 2d array of ring elements of specified shape
    
    Specified by:
    
    createArray2d in interface Ring<E>
    
    Parameters:
    
    m - result length
    
    n - length of each array in the result
    
    Returns:
    
    2d array E[m][n]
  - compare
```
public int compare(Rational<E> o1,
                   Rational<E> o2)
```
    Specified by:
    
    compare in interface Comparator<E>
  - getNegativeOne
```
public Rational<E> getNegativeOne()
```
    Description copied from interface: Ring
    
    Returns negative unit element of this ring (minus one)
    
    Specified by:
    
    getNegativeOne in interface Ring<E>
    
    Returns:
    
    -1
  - createArray
```
public Rational<E>[] createArray(int length)
```
    Description copied from interface: Ring
    
    Creates generic array of ring elements of specified length
    
    Specified by:
    
    createArray in interface Ring<E>
    
    Parameters:
    
    length - array length
    
    Returns:
    
    array of ring elements of specified length
  - randomElement
```
public Rational<E> randomElement(org.apache.commons.math3.random.RandomGenerator rnd)
```
    Description copied from interface: Ring
    
    Returns a random element from this ring
    
    Specified by:
    
    randomElement in interface Ring<E>
    
    Parameters:
    
    rnd - the source of randomness
    
    Returns:
    
    random element from this ring
  - randomElementTree
```
public Rational<E> randomElementTree(org.apache.commons.math3.random.RandomGenerator rnd)
```
    Description copied from interface: Ring
    
    If this ring has a complicated nested structure, this method guaranties that the resulting random element will reflect ring complicated structure, i.e. the result will be roughly as complicated as the ring is
    
    Specified by:
    
    randomElementTree in interface Ring<E>
    
    Returns:
    
    random element from this ring
  - iterator
```
public Iterator<Rational<E>> iterator()
```
    Description copied from interface: Ring
    
    Returns iterator over ring elements (for finite rings, otherwise throws exception)
    
    Specified by:
    
    iterator in interface Iterable<E>
    
    Specified by:
    
    iterator in interface Ring<E>
  - equals
```
public boolean equals(Object o)
```
    Specified by:
    
    equals in interface Comparator<E>
    
    Overrides:
    
    equals in class Object
  - hashCode
```
public int hashCode()
```
    Overrides:
    
    hashCode in class Object
  - toString
```
public String toString(IStringifier<Rational<E>> stringifier)
```
    Description copied from interface: Stringifiable
    
    convert this to string with the use of stringifier
    
    Specified by:
    
    toString in interface Stringifiable<E>
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object

Class Rationals<E>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface java.util.Comparator

Methods inherited from interface java.lang.Iterable

Methods inherited from interface cc.redberry.rings.Ring

Field Detail

ring

Constructor Detail

Rationals

Method Detail

mkNumerator

mkNumerator

mkDenominator

mkDenominator

mk

mk

isField

isEuclideanRing

cardinality

characteristic

isPerfectPower

perfectPowerBase

perfectPowerExponent

add

subtract

multiply

negate

signum

divideAndRemainder

reciprocal

gcd

factorSquareFree

factor

getZero

getOne

isZero

isOne

isUnit

valueOf

valueOfBigInteger

copy

valueOf

createArray2d

createArray2d

compare

getNegativeOne

createArray

randomElement

randomElementTree

iterator

equals

hashCode

toString

toString