edu.jas.arith
Class ModIntegerRing

java.lang.Object
  edu.jas.arith.ModIntegerRing

All Implemented Interfaces:

AbelianGroupFactory<ModInteger>, ElemFactory<ModInteger>, MonoidFactory<ModInteger>, RingFactory<ModInteger>, java.io.Serializable

public final class ModIntegerRing
extends java.lang.Object
implements RingFactory<ModInteger>

ModIntegerRing factory with RingFactory interface. Effectively immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

protected int	certainty Certainty if module is probable prime.
protected int	isField Indicator if this ring is a field.
java.math.BigInteger	modul Module part of the factory data structure.

Constructor Summary

ModIntegerRing(java.math.BigInteger m)
The constructor creates a ModIntegerRing object from a BigInteger object as module part.

ModIntegerRing(java.math.BigInteger m, boolean isField)
The constructor creates a ModIntegerRing object from a BigInteger object as module part.

ModIntegerRing(long m)
The constructor creates a ModIntegerRing object from a long as module part.

ModIntegerRing(long m, boolean isField)
The constructor creates a ModIntegerRing object from a long as module part.

ModIntegerRing(java.lang.String m)
The constructor creates a ModIntegerRing object from a String object as module part.

ModIntegerRing(java.lang.String m, boolean isField)
The constructor creates a ModIntegerRing object from a String object as module part.

Method Summary

java.math.BigInteger	characteristic() Characteristic of this ring.
ModInteger	chineseRemainder(ModInteger c, ModInteger ci, ModInteger a) ModInteger chinese remainder algorithm.
ModInteger	copy(ModInteger c) Copy ModInteger element c.
boolean	equals(java.lang.Object b) Comparison with any other object.
ModInteger	fromInteger(java.math.BigInteger a) Get a ModInteger element from a BigInteger value.
ModInteger	fromInteger(long a) Get a ModInteger element from a long value.
java.math.BigInteger	getModul() Get the module part.
ModInteger	getONE() Get the one element.
ModInteger	getZERO() Get the zero element.
int	hashCode() Hash code for this ModIntegerRing.
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.
ModInteger	parse(java.io.Reader r) Parse ModInteger from Reader.
ModInteger	parse(java.lang.String s) Parse ModInteger from String.
ModInteger	random(int n) ModInteger random.
ModInteger	random(int n, java.util.Random rnd) ModInteger random.
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

modul

public final java.math.BigInteger modul

Module part of the factory data structure.

isField

protected int isField

Indicator if this ring is a field.

certainty

protected int certainty

Certainty if module is probable prime.

Constructor Detail

ModIntegerRing

public ModIntegerRing(java.math.BigInteger m)

The constructor creates a ModIntegerRing object from a BigInteger object as module part.

Parameters:

m - math.BigInteger.

ModIntegerRing

public ModIntegerRing(java.math.BigInteger m,
                      boolean isField)

The constructor creates a ModIntegerRing object from a BigInteger object as module part.

Parameters:

m - math.BigInteger.

isField - indicator if m is prime.

ModIntegerRing

public ModIntegerRing(long m)

The constructor creates a ModIntegerRing object from a long as module part.

Parameters:

m - long.

ModIntegerRing

public ModIntegerRing(long m,
                      boolean isField)

The constructor creates a ModIntegerRing object from a long as module part.

Parameters:

m - long.

isField - indicator if m is prime.

ModIntegerRing

public ModIntegerRing(java.lang.String m)

The constructor creates a ModIntegerRing object from a String object as module part.

Parameters:

m - String.

ModIntegerRing

public ModIntegerRing(java.lang.String m,
                      boolean isField)

The constructor creates a ModIntegerRing object from a String object as module part.

Parameters:

m - String.

isField - indicator if m is prime.

Method Detail

getModul

public java.math.BigInteger getModul()

Get the module part.

Returns:

modul.

copy

public ModInteger copy(ModInteger c)

Copy ModInteger element c.

Specified by:

copy in interface ElemFactory<ModInteger>

Parameters:

c -

Returns:

a copy of c.

getZERO

public ModInteger getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<ModInteger>

Returns:

0 as ModInteger.

getONE

public ModInteger getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<ModInteger>

Returns:

1 as ModInteger.

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

isCommutative in interface MonoidFactory<ModInteger>

Returns:

true.

isAssociative

public boolean isAssociative()

Query if this ring is associative.

Specified by:

isAssociative in interface MonoidFactory<ModInteger>

Returns:

true.

isField

public boolean isField()

Query if this ring is a field.

Specified by:

isField in interface RingFactory<ModInteger>

Returns:

true if module is prime, else false.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<ModInteger>

Returns:

characteristic of this ring.

fromInteger

public ModInteger fromInteger(java.math.BigInteger a)

Get a ModInteger element from a BigInteger value.

Specified by:

fromInteger in interface ElemFactory<ModInteger>

Parameters:

a - BigInteger.

Returns:

a ModInteger.

fromInteger

public ModInteger fromInteger(long a)

Get a ModInteger element from a long value.

Specified by:

fromInteger in interface ElemFactory<ModInteger>

Parameters:

a - long.

Returns:

a ModInteger.

toString

public java.lang.String toString()

Get the String representation.

Overrides:

toString in class java.lang.Object

See Also:

Object.toString()

equals

public boolean equals(java.lang.Object b)

Comparison with any other object.

Overrides:

equals in class java.lang.Object

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this ModIntegerRing.

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

random

public ModInteger random(int n)

ModInteger random.

Specified by:

random in interface ElemFactory<ModInteger>

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

Returns:

a random integer mod modul.

random

public ModInteger random(int n,
                         java.util.Random rnd)

ModInteger random.

Specified by:

random in interface ElemFactory<ModInteger>

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

rnd - is a source for random bits.

Returns:

a random integer mod modul.

parse

public ModInteger parse(java.lang.String s)

Parse ModInteger from String.

Specified by:

parse in interface ElemFactory<ModInteger>

Parameters:

s - String.

Returns:

ModInteger from s.

parse

public ModInteger parse(java.io.Reader r)

Parse ModInteger from Reader.

Specified by:

parse in interface ElemFactory<ModInteger>

Parameters:

r - Reader.

Returns:

next ModInteger from r.

chineseRemainder

public ModInteger chineseRemainder(ModInteger c,
                                   ModInteger ci,
                                   ModInteger a)

ModInteger chinese remainder algorithm. This is a factory method. Assert c.modul >= a.modul and c.modul * a.modul = this.modul.

Parameters:

c - ModInteger.

ci - inverse of c.modul in ring of a.

a - other ModInteger.

Returns:

S, with S mod c.modul == c and S mod a.modul == a.