edu.jas.arith

Class 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.

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

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.