BigRational

java.lang.Object
- edu.jas.arith.BigRational

All Implemented Interfaces:

Rational, AbelianGroupElem<BigRational>, AbelianGroupFactory<BigRational>, Element<BigRational>, ElemFactory<BigRational>, GcdRingElem<BigRational>, MonoidElem<BigRational>, MonoidFactory<BigRational>, RingElem<BigRational>, RingFactory<BigRational>, java.io.Serializable, java.lang.Comparable<BigRational>, java.lang.Iterable<BigRational>
```
public final class BigRational
extends java.lang.Object
implements GcdRingElem<BigRational>, RingFactory<BigRational>, Rational, java.lang.Iterable<BigRational>
```
Immutable arbitrary-precision rational numbers. BigRational class based on BigInteger and implementing the RingElem interface. BigInteger is from java.math in the implementation. The SAC2 static methods are also provided.

Author:

Heinz Kredel

See Also:
Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`java.math.BigInteger`	`den` Denominator part of the data structure.
`java.math.BigInteger`	`num` Numerator part of the data structure.
`static BigRational`	`ONE` The Constant 1.
`static BigRational`	`ZERO` The Constant 0.

Constructor Summary

Constructors
Modifier	Constructor and Description
	`BigRational()` Constructor for a BigRational with no arguments.
	`BigRational(java.math.BigInteger n)` Constructor for a BigRational from math.BigIntegers.
	`BigRational(BigInteger n)` Constructor for a BigRational from jas.arith.BigIntegers.
`protected`	`BigRational(java.math.BigInteger n, java.math.BigInteger d)` Constructor for a BigRational from math.BigIntegers.
	`BigRational(BigInteger n, BigInteger d)` Constructor for a BigRational from jas.arith.BigIntegers.
	`BigRational(long n)` Constructor for a BigRational from longs.
	`BigRational(long n, long d)` Constructor for a BigRational from longs.
	`BigRational(java.lang.String s)` Constructor for a BigRational from String.

Method Summary

Methods
Modifier and Type	Method and Description
`BigRational`	`abs()` Rational number absolute value.
`java.math.BigInteger`	`characteristic()` Characteristic of this ring.
`int`	`compareTo(BigRational S)` Rational number comparison.
`BigRational`	`copy()` Clone this.
`BigRational`	`copy(BigRational c)` Copy BigRational element c.
`java.math.BigInteger`	`denominator()` Get the denominator.
`BigRational`	`divide(BigRational S)` Rational number quotient.
`BigRational[]`	`egcd(BigRational S)` BigRational extended greatest common divisor.
`boolean`	`equals(java.lang.Object b)` Comparison with any other object.
`BigRational`	`factory()` Get the corresponding element factory.
`BigRational`	`fromInteger(java.math.BigInteger a)` Get a BigRational element from a math.BigInteger.
`BigRational`	`fromInteger(BigInteger a)` Get a BigRational element from a arith.BigInteger.
`BigRational`	`fromInteger(long a)` Get a BigRational element from a long.
`BigRational`	`gcd(BigRational S)` Rational number greatest common divisor.
`java.util.List<BigRational>`	`generators()` Get a list of the generating elements.
`BigRational`	`getONE()` Get the one element.
`BigRational`	`getRational()` Return a BigRational approximation of this Element.
`BigRational`	`getZERO()` Get the zero element.
`int`	`hashCode()` Hash code for this BigRational.
`BigRational`	`inverse()` Rational number inverse.
`boolean`	`isAssociative()` Query if this ring is associative.
`boolean`	`isCommutative()` Query if this ring is commutative.
`boolean`	`isField()` Query if this ring is a field.
`boolean`	`isFinite()` Is this structure finite or infinite.
`boolean`	`isONE()` Is BigRational one.
`boolean`	`isUnit()` Is BigRational unit.
`boolean`	`isZERO()` Is BigRational zero.
`java.util.Iterator<BigRational>`	`iterator()` Get a BigRational iterator.
`BigRational`	`multiply(BigRational S)` Rational number product.
`BigRational`	`negate()` Rational number negative.
`java.math.BigInteger`	`numerator()` Get the numerator.
`BigRational`	`parse(java.io.Reader r)` Parse rational number from Reader.
`BigRational`	`parse(java.lang.String s)` Parse rational number from String.
`BigRational`	`random(int n)` Rational number, random.
`BigRational`	`random(int n, java.util.Random rnd)` Rational number, random.
`static BigRational`	`reduction(java.math.BigInteger n, java.math.BigInteger d)` Rational number reduction to lowest terms.
`BigRational`	`remainder(BigRational S)` Rational number remainder.
`static BigRational`	`RNABS(BigRational R)` Rational number absolute value.
`static int`	`RNCOMP(BigRational R, BigRational S)` Rational number comparison.
`static java.math.BigInteger`	`RNDEN(BigRational R)` Rational number denominator.
`static BigRational`	`RNDIF(BigRational R, BigRational S)` Rational number difference.
`static void`	`RNDWR(BigRational R, int NL)` Rational number decimal write.
`static BigRational`	`RNINT(java.math.BigInteger A)` Rational number from integer.
`static BigRational`	`RNINV(BigRational R)` Rational number inverse.
`static BigRational`	`RNNEG(BigRational R)` Rational number negative.
`static java.math.BigInteger`	`RNNUM(BigRational R)` Rational number numerator.
`static BigRational`	`RNPROD(BigRational R, BigRational S)` Rational number product.
`static BigRational`	`RNQ(BigRational R, BigRational S)` Rational number quotient.
`static BigRational`	`RNRAND(int NL)` Rational number, random.
`static BigRational`	`RNRED(java.math.BigInteger n, java.math.BigInteger d)` Rational number reduction to lowest terms.
`static int`	`RNSIGN(BigRational R)` Rational number sign.
`static BigRational`	`RNSUM(BigRational R, BigRational S)` Rational number sum.
`void`	`setAllIterator()` Set the iteration algorithm to all elements.
`void`	`setDuplicatesIterator()` Set the iteration algorithm to allow duplicate elements.
`void`	`setNoDuplicatesIterator()` Set the iteration algorithm to no duplicate elements.
`void`	`setNonNegativeIterator()` Set the iteration algorithm to non-negative elements.
`int`	`signum()` Rational number sign.
`BigRational`	`subtract(BigRational S)` Rational number difference.
`BigRational`	`sum(BigRational S)` Rational number sum.
`java.lang.String`	`toScript()` Get a scripting compatible string representation.
`java.lang.String`	`toScriptFactory()` Get a scripting compatible string representation of the factory.
`java.lang.String`	`toString()` Get the string representation.
`java.lang.String`	`toString(int n)` Get the decimal string representation with given precision.
`java.util.Iterator<BigRational>`	`uniqueIterator()` Get a BigRational iterator with no duplicates.
`static BigRational`	`valueOf(java.math.BigInteger a)` Get a BigRational element from a math.BigInteger.
`static BigRational`	`valueOf(long a)` Get a BigRational element from a long.

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

- Field Detail
  - num
```
public final java.math.BigInteger num
```
    Numerator part of the data structure.
  - den
```
public final java.math.BigInteger den
```
    Denominator part of the data structure.
  - ZERO
```
public static final BigRational ZERO
```
    The Constant 0.
  - ONE
```
public static final BigRational ONE
```
    The Constant 1.
- Constructor Detail
  - BigRational
```
protected BigRational(java.math.BigInteger n,
           java.math.BigInteger d)
```
    Constructor for a BigRational from math.BigIntegers.
    
    Parameters:
    n - math.BigInteger.
    d - math.BigInteger.
  - BigRational
```
public BigRational(java.math.BigInteger n)
```
    Constructor for a BigRational from math.BigIntegers.
    
    Parameters:
    n - math.BigInteger.
  - BigRational
```
public BigRational(BigInteger n)
```
    Constructor for a BigRational from jas.arith.BigIntegers.
    
    Parameters:
    n - edu.jas.arith.BigInteger.
  - BigRational
```
public BigRational(BigInteger n,
           BigInteger d)
```
    Constructor for a BigRational from jas.arith.BigIntegers.
    
    Parameters:
    n - edu.jas.arith.BigInteger.
    d - edu.jas.arith.BigInteger.
  - BigRational
```
public BigRational(long n,
           long d)
```
    Constructor for a BigRational from longs.
    
    Parameters:
    n - long.
    d - long.
  - BigRational
```
public BigRational(long n)
```
    Constructor for a BigRational from longs.
    
    Parameters:
    n - long.
  - BigRational
```
public BigRational()
```
    Constructor for a BigRational with no arguments.
  - BigRational
```
public BigRational(java.lang.String s)
            throws java.lang.NumberFormatException
```
    Constructor for a BigRational from String.
    
    Parameters:
    s - String.
    
    Throws:
    
    java.lang.NumberFormatException
- Method Detail
  - factory
```
public BigRational factory()
```
    Get the corresponding element factory.
    
    Specified by:
    
    factory in interface Element<BigRational>
    
    Returns:
    factory for this Element.
    See Also:
    Element.factory()
  - generators
```
public java.util.List<BigRational> generators()
```
    Get a list of the generating elements.
    
    Specified by:
    
    generators in interface ElemFactory<BigRational>
    
    Returns:
    list of generators for the algebraic structure.
    See Also:
    ElemFactory.generators()
  - isFinite
```
public boolean isFinite()
```
    Is this structure finite or infinite.
    
    Specified by:
    
    isFinite in interface ElemFactory<BigRational>
    
    Returns:
    true if this structure is finite, else false.
    See Also:
    ElemFactory.isFinite()
  - copy
```
public BigRational copy()
```
    Clone this.
    
    Specified by:
    
    copy in interface Element<BigRational>
    
    Returns:
    Creates and returns a copy of this Element.
    See Also:
    Object.clone()
  - copy
```
public BigRational copy(BigRational c)
```
    Copy BigRational element c.
    
    Specified by:
    
    copy in interface ElemFactory<BigRational>
    
    Parameters:
    c - BigRational.
    
    Returns:
    a copy of c.
  - getRational
```
public BigRational getRational()
```
    Return a BigRational approximation of this Element.
    
    Specified by:
    
    getRational in interface Rational
    
    Returns:
    a BigRational approximation of this.
    See Also:
    Rational.getRational()
  - numerator
```
public java.math.BigInteger numerator()
```
    Get the numerator.
    
    Returns:
    num.
  - denominator
```
public java.math.BigInteger denominator()
```
    Get the denominator.
    
    Returns:
    den.
  - toString
```
public java.lang.String toString()
```
    Get the string representation.
    
    Overrides:
    
    toString in class java.lang.Object
    
    See Also:
    Object.toString()
  - toString
```
public java.lang.String toString(int n)
```
    Get the decimal string representation with given precision.
    
    Parameters:
    n - precission.
    
    Returns:
    decimal approximation.
  - toScript
```
public java.lang.String toScript()
```
    Get a scripting compatible string representation.
    
    Specified by:
    
    toScript in interface Element<BigRational>
    
    Specified by:
    
    toScript in interface ElemFactory<BigRational>
    
    Returns:
    script compatible representation for this Element.
    See Also:
    Element.toScript()
  - toScriptFactory
```
public java.lang.String toScriptFactory()
```
    Get a scripting compatible string representation of the factory.
    
    Specified by:
    
    toScriptFactory in interface Element<BigRational>
    
    Returns:
    script compatible representation for this ElemFactory.
    See Also:
    Element.toScriptFactory()
  - getZERO
```
public BigRational getZERO()
```
    Get the zero element.
    
    Specified by:
    
    getZERO in interface AbelianGroupFactory<BigRational>
    
    Returns:
    0 as BigRational.
  - getONE
```
public BigRational getONE()
```
    Get the one element.
    
    Specified by:
    
    getONE in interface MonoidFactory<BigRational>
    
    Returns:
    1 as BigRational.
  - isCommutative
```
public boolean isCommutative()
```
    Query if this ring is commutative.
    
    Specified by:
    
    isCommutative in interface MonoidFactory<BigRational>
    
    Returns:
    true.
  - isAssociative
```
public boolean isAssociative()
```
    Query if this ring is associative.
    
    Specified by:
    
    isAssociative in interface MonoidFactory<BigRational>
    
    Returns:
    true.
  - isField
```
public boolean isField()
```
    Query if this ring is a field.
    
    Specified by:
    
    isField in interface RingFactory<BigRational>
    
    Returns:
    true.
  - characteristic
```
public java.math.BigInteger characteristic()
```
    Characteristic of this ring.
    
    Specified by:
    
    characteristic in interface RingFactory<BigRational>
    
    Returns:
    characteristic of this ring.
  - fromInteger
```
public BigRational fromInteger(java.math.BigInteger a)
```
    Get a BigRational element from a math.BigInteger.
    
    Specified by:
    
    fromInteger in interface ElemFactory<BigRational>
    
    Parameters:
    a - math.BigInteger.
    
    Returns:
    BigRational from a.
  - fromInteger
```
public BigRational fromInteger(BigInteger a)
```
    Get a BigRational element from a arith.BigInteger.
    
    Parameters:
    a - arith.BigInteger.
    
    Returns:
    BigRational from a.
  - valueOf
```
public static BigRational valueOf(java.math.BigInteger a)
```
    Get a BigRational element from a math.BigInteger.
    
    Parameters:
    a - math.BigInteger.
    
    Returns:
    BigRational from a.
  - fromInteger
```
public BigRational fromInteger(long a)
```
    Get a BigRational element from a long.
    
    Specified by:
    
    fromInteger in interface ElemFactory<BigRational>
    
    Parameters:
    a - long.
    
    Returns:
    BigRational from a.
  - valueOf
```
public static BigRational valueOf(long a)
```
    Get a BigRational element from a long.
    
    Parameters:
    a - long.
    
    Returns:
    BigRational from a.
  - isZERO
```
public boolean isZERO()
```
    Is BigRational zero.
    
    Specified by:
    
    isZERO in interface AbelianGroupElem<BigRational>
    
    Returns:
    If this is 0 then true is returned, else false.
    See Also:
    AbelianGroupElem.isZERO()
  - isONE
```
public boolean isONE()
```
    Is BigRational one.
    
    Specified by:
    
    isONE in interface MonoidElem<BigRational>
    
    Returns:
    If this is 1 then true is returned, else false.
    See Also:
    MonoidElem.isONE()
  - isUnit
```
public boolean isUnit()
```
    Is BigRational unit.
    
    Specified by:
    
    isUnit in interface MonoidElem<BigRational>
    
    Returns:
    If this is a unit then true is returned, else false.
    See Also:
    MonoidElem.isUnit()
  - equals
```
public boolean equals(java.lang.Object b)
```
    Comparison with any other object.
    
    Specified by:
    
    equals in interface Element<BigRational>
    
    Overrides:
    
    equals in class java.lang.Object
    
    Returns:
    true if this is equal to b, else false.
    See Also:
    Object.equals(java.lang.Object)
  - hashCode
```
public int hashCode()
```
    Hash code for this BigRational.
    
    Specified by:
    
    hashCode in interface Element<BigRational>
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    the hashCode.
    See Also:
    Object.hashCode()
  - RNRED
```
public static BigRational RNRED(java.math.BigInteger n,
                java.math.BigInteger d)
```
    Rational number reduction to lowest terms.
    
    Parameters:
    n - BigInteger.
    d - BigInteger.
    
    Returns:
    a/b ~ n/d, gcd(a,b) = 1, b > 0.
  - reduction
```
public static BigRational reduction(java.math.BigInteger n,
                    java.math.BigInteger d)
```
    Rational number reduction to lowest terms.
    
    Parameters:
    n - BigInteger.
    d - BigInteger.
    
    Returns:
    a/b ~ n/d, gcd(a,b) = 1, b > 0.
  - abs
```
public BigRational abs()
```
    Rational number absolute value.
    
    Specified by:
    
    abs in interface AbelianGroupElem<BigRational>
    
    Returns:
    the absolute value of this.
    See Also:
    AbelianGroupElem.abs()
  - RNABS
```
public static BigRational RNABS(BigRational R)
```
    Rational number absolute value.
    
    Parameters:
    R - is a rational number.
    
    Returns:
    the absolute value of R.
  - compareTo
```
public int compareTo(BigRational S)
```
    Rational number comparison.
    
    Specified by:
    
    compareTo in interface Element<BigRational>
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<BigRational>
    
    Parameters:
    S - BigRational.
    
    Returns:
    SIGN(this-S).
  - RNCOMP
```
public static int RNCOMP(BigRational R,
         BigRational S)
```
    Rational number comparison.
    
    Parameters:
    R - BigRational.
    S - BigRational.
    
    Returns:
    SIGN(R-S).
  - RNDEN
```
public static java.math.BigInteger RNDEN(BigRational R)
```
    Rational number denominator.
    
    Parameters:
    R - BigRational.
    
    Returns:
    R.denominator().
  - subtract
```
public BigRational subtract(BigRational S)
```
    Rational number difference.
    
    Specified by:
    
    subtract in interface AbelianGroupElem<BigRational>
    
    Parameters:
    S - BigRational.
    
    Returns:
    this-S.
  - RNDIF
```
public static BigRational RNDIF(BigRational R,
                BigRational S)
```
    Rational number difference.
    
    Parameters:
    R - BigRational.
    S - BigRational.
    
    Returns:
    R-S.
  - RNDWR
```
public static void RNDWR(BigRational R,
         int NL)
```
    Rational number decimal write. R is a rational number. n is a non-negative integer. R is approximated by a decimal fraction D with n decimal digits following the decimal point and D is written in the output stream. The inaccuracy of the approximation is at most (1/2)*10**-n.
    
    Parameters:
    R -
    NL -
  - RNINT
```
public static BigRational RNINT(java.math.BigInteger A)
```
    Rational number from integer.
    
    Parameters:
    A - BigInteger.
    
    Returns:
    A/1.
  - inverse
```
public BigRational inverse()
```
    Rational number inverse.
    
    Specified by:
    
    inverse in interface MonoidElem<BigRational>
    
    Returns:
    1/this.
    See Also:
    MonoidElem.inverse()
  - RNINV
```
public static BigRational RNINV(BigRational R)
```
    Rational number inverse.
    
    Parameters:
    R - BigRational.
    
    Returns:
    1/R.
  - negate
```
public BigRational negate()
```
    Rational number negative.
    
    Specified by:
    
    negate in interface AbelianGroupElem<BigRational>
    
    Returns:
    -this.
    See Also:
    AbelianGroupElem.negate()
  - RNNEG
```
public static BigRational RNNEG(BigRational R)
```
    Rational number negative.
    
    Parameters:
    R - BigRational.
    
    Returns:
    -R.
  - RNNUM
```
public static java.math.BigInteger RNNUM(BigRational R)
```
    Rational number numerator.
    
    Parameters:
    R - BigRational.
    
    Returns:
    R.numerator().
  - multiply
```
public BigRational multiply(BigRational S)
```
    Rational number product.
    
    Specified by:
    
    multiply in interface MonoidElem<BigRational>
    
    Parameters:
    S - BigRational.
    
    Returns:
    this*S.
  - RNPROD
```
public static BigRational RNPROD(BigRational R,
                 BigRational S)
```
    Rational number product.
    
    Parameters:
    R - BigRational.
    S - BigRational.
    
    Returns:
    R*S.
  - divide
```
public BigRational divide(BigRational S)
```
    Rational number quotient.
    
    Specified by:
    
    divide in interface MonoidElem<BigRational>
    
    Parameters:
    S - BigRational.
    
    Returns:
    this/S.
  - RNQ
```
public static BigRational RNQ(BigRational R,
              BigRational S)
```
    Rational number quotient.
    
    Parameters:
    R - BigRational.
    S - BigRational.
    
    Returns:
    R/S.
  - remainder
```
public BigRational remainder(BigRational S)
```
    Rational number remainder.
    
    Specified by:
    
    remainder in interface MonoidElem<BigRational>
    
    Parameters:
    S - BigRational.
    
    Returns:
    this-(this/S)*S
  - random
```
public BigRational random(int n)
```
    Rational number, random. Random integers A, B and a random sign s are generated using BigInteger(n,random) and random.nextBoolen(). Then R = s*A/(B+1), reduced to lowest terms.
    
    Specified by:
    
    random in interface ElemFactory<BigRational>
    
    Parameters:
    n - such that 0 ≤ A, B ≤ (2ⁿ-1).
    
    Returns:
    a random BigRational.
  - random
```
public BigRational random(int n,
                 java.util.Random rnd)
```
    Rational number, random. Random integers A, B and a random sign s are generated using BigInteger(n,random) and random.nextBoolen(). Then R = s*A/(B+1), reduced to lowest terms.
    
    Specified by:
    
    random in interface ElemFactory<BigRational>
    
    Parameters:
    n - such that 0 ≤ A, B ≤ (2ⁿ-1).
    rnd - is a source for random bits.
    
    Returns:
    a random BigRational.
  - RNRAND
```
public static BigRational RNRAND(int NL)
```
    Rational number, random. Random integers A, B and a random sign s are generated using BigInteger(n,random) and random.nextBoolen(). Then R = s*A/(B+1), reduced to lowest terms.
    
    Parameters:
    NL - such that 0 ≤ A, B ≤ (2ⁿ-1).
    
    Returns:
    a random BigRational.
  - signum
```
public int signum()
```
    Rational number sign.
    
    Specified by:
    
    signum in interface AbelianGroupElem<BigRational>
    
    Returns:
    the sign of this.
    See Also:
    AbelianGroupElem.signum()
  - RNSIGN
```
public static int RNSIGN(BigRational R)
```
    Rational number sign.
    
    Parameters:
    R - BigRational.
    
    Returns:
    R.signum().
  - sum
```
public BigRational sum(BigRational S)
```
    Rational number sum.
    
    Specified by:
    
    sum in interface AbelianGroupElem<BigRational>
    
    Parameters:
    S - BigRational.
    
    Returns:
    this+S.
  - RNSUM
```
public static BigRational RNSUM(BigRational R,
                BigRational S)
```
    Rational number sum.
    
    Parameters:
    R - BigRational.
    S - BigRational.
    
    Returns:
    R+S.
  - parse
```
public BigRational parse(java.lang.String s)
```
    Parse rational number from String.
    
    Specified by:
    
    parse in interface ElemFactory<BigRational>
    
    Parameters:
    s - String.
    
    Returns:
    BigRational from s.
  - parse
```
public BigRational parse(java.io.Reader r)
```
    Parse rational number from Reader.
    
    Specified by:
    
    parse in interface ElemFactory<BigRational>
    
    Parameters:
    r - Reader.
    
    Returns:
    next BigRational from r.
  - gcd
```
public BigRational gcd(BigRational S)
```
    Rational number greatest common divisor.
    
    Specified by:
    
    gcd in interface RingElem<BigRational>
    
    Parameters:
    S - BigRational.
    
    Returns:
    gcd(this,S).
  - egcd
```
public BigRational[] egcd(BigRational S)
```
    BigRational extended greatest common divisor.
    
    Specified by:
    
    egcd in interface RingElem<BigRational>
    
    Parameters:
    S - BigRational.
    
    Returns:
    [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).
  - setAllIterator
```
public void setAllIterator()
```
    Set the iteration algorithm to all elements.
  - setNonNegativeIterator
```
public void setNonNegativeIterator()
```
    Set the iteration algorithm to non-negative elements.
  - setNoDuplicatesIterator
```
public void setNoDuplicatesIterator()
```
    Set the iteration algorithm to no duplicate elements.
  - setDuplicatesIterator
```
public void setDuplicatesIterator()
```
    Set the iteration algorithm to allow duplicate elements.
  - iterator
```
public java.util.Iterator<BigRational> iterator()
```
    Get a BigRational iterator.
    
    Specified by:
    
    iterator in interface java.lang.Iterable<BigRational>
    
    Returns:
    a iterator over all rationals.
  - uniqueIterator
```
public java.util.Iterator<BigRational> uniqueIterator()
```
    Get a BigRational iterator with no duplicates.
    
    Returns:
    a iterator over all rationals without duplicates.

Class BigRational

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

num

den

ZERO

ONE

Constructor Detail

BigRational

BigRational

BigRational

BigRational

BigRational

BigRational

BigRational

BigRational

Method Detail

factory

generators

isFinite

copy

copy

getRational

numerator

denominator

toString

toString

toScript

toScriptFactory

getZERO

getONE

isCommutative

isAssociative

isField

characteristic

fromInteger

fromInteger

valueOf

fromInteger

valueOf

isZERO

isONE

isUnit

equals

hashCode

RNRED

reduction

abs

RNABS

compareTo

RNCOMP

RNDEN

subtract

RNDIF

RNDWR

RNINT

inverse

RNINV

negate

RNNEG

RNNUM

multiply

RNPROD

divide

RNQ

remainder

random

random

RNRAND

signum

RNSIGN

sum

RNSUM

parse

parse

gcd

egcd