ModLong

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

All Implemented Interfaces:

Modular, AbelianGroupElem<ModLong>, Element<ModLong>, GcdRingElem<ModLong>, MonoidElem<ModLong>, RingElem<ModLong>, java.io.Serializable, java.lang.Comparable<ModLong>
```
public final class ModLong
extends java.lang.Object
implements GcdRingElem<ModLong>, Modular
```
ModLong class with RingElem interface. Objects of this class are immutable.

Author:

Heinz Kredel

See Also:
ModInteger, Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

ModLongRing ring
ModLongRing reference.

long val
Value part of the element data structure.

Fields
Modifier and Type	Field and Description
`ModLongRing`	`ring` ModLongRing reference.
`long`	`val` Value part of the element data structure.

Constructor Summary

Constructors
Constructor and Description
`ModLong(ModLongRing m)` The constructor creates a 0 ModLong object from a given ModLongRing.
`ModLong(ModLongRing m, java.math.BigInteger a)` The constructor creates a ModLong object from a ModLongRing and a value part.
`ModLong(ModLongRing m, long a)` The constructor creates a ModLong object from a ModLongRing and a long value part.
`ModLong(ModLongRing m, java.lang.Long a)` The constructor creates a ModLong object from a ModLongRing and a Long value part.
`ModLong(ModLongRing m, java.lang.String s)` The constructor creates a ModLong object from a ModLongRing and a String value part.

Method Summary

Methods
Modifier and Type	Method and Description
`ModLong`	`abs()` ModLong absolute value.
`int`	`compareTo(ModLong b)` ModLong comparison.
`ModLong`	`copy()` Clone this.
`ModLong`	`divide(ModLong S)` ModLong divide.
`ModLong[]`	`egcd(ModLong S)` ModInteger extended greatest common divisor.
`boolean`	`equals(java.lang.Object b)` Comparison with any other object.
`ModLongRing`	`factory()` Get the corresponding element factory.
`long`	`gcd(long T, long S)` Long greatest common divisor.
`ModLong`	`gcd(ModLong S)` ModInteger greatest common divisor.
`BigInteger`	`getInteger()` Return a BigInteger from this Element.
`long`	`getModul()` Get the module part.
`BigInteger`	`getSymmetricInteger()` Return a symmetric BigInteger from this Element.
`long`	`getSymmetricVal()` Get the symmetric value part.
`long`	`getVal()` Get the value part.
`int`	`hashCode()` Hash code for this ModLong.
`long[]`	`hegcd(long T, long S)` Long half extended greatest common divisor.
`ModLong`	`inverse()` ModLong inverse.
`boolean`	`isONE()` Is ModLong number one.
`boolean`	`isUnit()` Is ModLong number a unit.
`boolean`	`isZERO()` Is ModLong number zero.
`long`	`modInverse(long T, long m)` Long modular inverse.
`ModLong`	`multiply(ModLong S)` ModLong multiply.
`ModLong`	`negate()` ModLong negative.
`ModLong`	`remainder(ModLong S)` ModLong remainder.
`int`	`signum()` ModLong signum.
`ModLong`	`subtract(ModLong S)` ModLong subtraction.
`ModLong`	`sum(ModLong S)` ModLong summation.
`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.

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

- Field Detail
  - ring
```
public final ModLongRing ring
```
    ModLongRing reference.
  - val
```
public final long val
```
    Value part of the element data structure.
- Constructor Detail
  - ModLong
```
public ModLong(ModLongRing m,
       java.math.BigInteger a)
```
    The constructor creates a ModLong object from a ModLongRing and a value part.
    
    Parameters:
    m - ModLongRing.
    a - math.BigInteger.
  - ModLong
```
public ModLong(ModLongRing m,
       long a)
```
    The constructor creates a ModLong object from a ModLongRing and a long value part.
    
    Parameters:
    m - ModLongRing.
    a - long.
  - ModLong
```
public ModLong(ModLongRing m,
       java.lang.Long a)
```
    The constructor creates a ModLong object from a ModLongRing and a Long value part.
    
    Parameters:
    m - ModLongRing.
    a - Long.
  - ModLong
```
public ModLong(ModLongRing m,
       java.lang.String s)
```
    The constructor creates a ModLong object from a ModLongRing and a String value part.
    
    Parameters:
    m - ModLongRing.
    s - String.
  - ModLong
```
public ModLong(ModLongRing m)
```
    The constructor creates a 0 ModLong object from a given ModLongRing.
    
    Parameters:
    m - ModLongRing.
- Method Detail
  - getVal
```
public long getVal()
```
    Get the value part.
    
    Returns:
    val.
  - getModul
```
public long getModul()
```
    Get the module part.
    
    Returns:
    modul.
  - factory
```
public ModLongRing factory()
```
    Get the corresponding element factory.
    
    Specified by:
    
    factory in interface Element<ModLong>
    
    Returns:
    factory for this Element.
    See Also:
    Element.factory()
  - getSymmetricVal
```
public long getSymmetricVal()
```
    Get the symmetric value part.
    
    Returns:
    val with -modul/2 <= val < modul/2.
  - getInteger
```
public BigInteger getInteger()
```
    Return a BigInteger from this Element.
    
    Specified by:
    
    getInteger in interface Modular
    
    Returns:
    a BigInteger of this.
  - getSymmetricInteger
```
public BigInteger getSymmetricInteger()
```
    Return a symmetric BigInteger from this Element.
    
    Specified by:
    
    getSymmetricInteger in interface Modular
    
    Returns:
    a symmetric BigInteger of this.
  - copy
```
public ModLong copy()
```
    Clone this.
    
    Specified by:
    
    copy in interface Element<ModLong>
    
    Returns:
    Creates and returns a copy of this Element.
    See Also:
    Object.clone()
  - isZERO
```
public boolean isZERO()
```
    Is ModLong number zero.
    
    Specified by:
    
    isZERO in interface AbelianGroupElem<ModLong>
    
    Returns:
    If this is 0 then true is returned, else false.
    See Also:
    AbelianGroupElem.isZERO()
  - isONE
```
public boolean isONE()
```
    Is ModLong number one.
    
    Specified by:
    
    isONE in interface MonoidElem<ModLong>
    
    Returns:
    If this is 1 then true is returned, else false.
    See Also:
    MonoidElem.isONE()
  - isUnit
```
public boolean isUnit()
```
    Is ModLong number a unit.
    
    Specified by:
    
    isUnit in interface MonoidElem<ModLong>
    
    Returns:
    If this is a unit then true is returned, else false.
    See Also:
    MonoidElem.isUnit()
  - toString
```
public java.lang.String toString()
```
    Get the String representation.
    
    Overrides:
    
    toString in class java.lang.Object
    
    See Also:
    Object.toString()
  - toScript
```
public java.lang.String toScript()
```
    Get a scripting compatible string representation.
    
    Specified by:
    
    toScript in interface Element<ModLong>
    
    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<ModLong>
    
    Returns:
    script compatible representation for this ElemFactory.
    See Also:
    Element.toScriptFactory()
  - compareTo
```
public int compareTo(ModLong b)
```
    ModLong comparison.
    
    Specified by:
    
    compareTo in interface Element<ModLong>
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<ModLong>
    
    Parameters:
    b - ModLong.
    
    Returns:
    sign(this-b).
  - equals
```
public boolean equals(java.lang.Object b)
```
    Comparison with any other object.
    
    Specified by:
    
    equals in interface Element<ModLong>
    
    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 ModLong.
    
    Specified by:
    
    hashCode in interface Element<ModLong>
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    the hashCode.
    See Also:
    Object.hashCode()
  - abs
```
public ModLong abs()
```
    ModLong absolute value.
    
    Specified by:
    
    abs in interface AbelianGroupElem<ModLong>
    
    Returns:
    the absolute value of this.
    See Also:
    AbelianGroupElem.abs()
  - negate
```
public ModLong negate()
```
    ModLong negative.
    
    Specified by:
    
    negate in interface AbelianGroupElem<ModLong>
    
    Returns:
    -this.
    See Also:
    AbelianGroupElem.negate()
  - signum
```
public int signum()
```
    ModLong signum.
    
    Specified by:
    
    signum in interface AbelianGroupElem<ModLong>
    
    Returns:
    signum(this).
    See Also:
    AbelianGroupElem.signum()
  - subtract
```
public ModLong subtract(ModLong S)
```
    ModLong subtraction.
    
    Specified by:
    
    subtract in interface AbelianGroupElem<ModLong>
    
    Parameters:
    S - ModLong.
    
    Returns:
    this-S.
  - divide
```
public ModLong divide(ModLong S)
```
    ModLong divide.
    
    Specified by:
    
    divide in interface MonoidElem<ModLong>
    
    Parameters:
    S - ModLong.
    
    Returns:
    this/S.
  - inverse
```
public ModLong inverse()
```
    ModLong inverse.
    
    Specified by:
    
    inverse in interface MonoidElem<ModLong>
    
    Returns:
    S with S=1/this if defined.
    
    Throws:
    
    NotInvertibleException - if the element is not invertible.
    See Also:
    MonoidElem.inverse()
  - remainder
```
public ModLong remainder(ModLong S)
```
    ModLong remainder.
    
    Specified by:
    
    remainder in interface MonoidElem<ModLong>
    
    Parameters:
    S - ModLong.
    
    Returns:
    remainder(this,S).
  - multiply
```
public ModLong multiply(ModLong S)
```
    ModLong multiply.
    
    Specified by:
    
    multiply in interface MonoidElem<ModLong>
    
    Parameters:
    S - ModLong.
    
    Returns:
    this*S.
  - sum
```
public ModLong sum(ModLong S)
```
    ModLong summation.
    
    Specified by:
    
    sum in interface AbelianGroupElem<ModLong>
    
    Parameters:
    S - ModLong.
    
    Returns:
    this+S.
  - gcd
```
public ModLong gcd(ModLong S)
```
    ModInteger greatest common divisor.
    
    Specified by:
    
    gcd in interface RingElem<ModLong>
    
    Parameters:
    S - ModInteger.
    
    Returns:
    [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).
  - egcd
```
public ModLong[] egcd(ModLong S)
```
    ModInteger extended greatest common divisor.
    
    Specified by:
    
    egcd in interface RingElem<ModLong>
    
    Parameters:
    S - ModInteger.
    
    Returns:
    [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).
  - gcd
```
public long gcd(long T,
       long S)
```
    Long greatest common divisor.
    
    Parameters:
    T - long.
    S - long.
    
    Returns:
    gcd(T,S).
  - hegcd
```
public long[] hegcd(long T,
           long S)
```
    Long half extended greatest common divisor.
    
    Parameters:
    T - long.
    S - long.
    
    Returns:
    [ gcd(T,S), a ] with a*T + b*S = gcd(T,S).
  - modInverse
```
public long modInverse(long T,
              long m)
```
    Long modular inverse.
    
    Parameters:
    T - long.
    m - long.
    
    Returns:
    a with with a*T = 1 mod m.

Class ModLong

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ring

val

Constructor Detail

ModLong

ModLong

ModLong

ModLong

ModLong

Method Detail

getVal

getModul

factory

getSymmetricVal

getInteger

getSymmetricInteger

copy

isZERO

isONE

isUnit

toString

toScript

toScriptFactory

compareTo

equals

hashCode

abs

negate

signum

subtract

divide

inverse

remainder

multiply

sum

gcd

egcd

gcd

hegcd

modInverse