Package edu.jas.arith

Class ModIntegerRing

java.lang.Object

edu.jas.arith.ModIntegerRing

All Implemented Interfaces:

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

public final class ModIntegerRing
extends java.lang.Object
implements ModularRingFactory<ModInteger>, java.lang.Iterable<ModInteger>

ModIntegerRing factory with RingFactory interface. Effectively immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
java.math.BigInteger	modul	Module part of the factory data structure.

Constructor Summary

Constructors

Constructor	Description
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.
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.

Method Summary

Modifier and Type	Method	Description
java.math.BigInteger	characteristic()	Characteristic of this ring.
ModInteger	chineseRemainder(ModInteger c, ModInteger ci, ModInteger a)	ModInteger chinese remainder algorithm.
static java.util.List<ModInteger>	chineseRemainder(ModInteger m1, ModInteger m2, java.util.List<ModInteger> L1, java.util.List<ModInteger> L2)	Modular integer list chinese remainder algorithm. m1 and m2 are positive integers, with GCD(m1,m2)=1 and m=m1*m2 less than beta.
ModInteger	copy(ModInteger c)	Copy ModInteger element c.
ModInteger	create(long c)	Create ModInteger element c.
ModInteger	create(java.lang.String c)	Create ModInteger element c.
ModInteger	create(java.math.BigInteger c)	Create ModInteger element c.
boolean	equals(java.lang.Object b)	Comparison with any other object.
ModInteger	fromInteger(long a)	Get a ModInteger element from a long value.
ModInteger	fromInteger(java.math.BigInteger a)	Get a ModInteger element from a BigInteger value.
java.util.List<ModInteger>	generators()	Get a list of the generating elements.
BigInteger	getIntegerModul()	Get the module part as BigInteger.
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.
boolean	isFinite()	Is this structure finite or infinite.
java.util.Iterator<ModInteger>	iterator()	Get a ModInteger iterator.
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	toScript()	Get a scripting compatible string representation.
java.lang.String	toString()	Get the String representation.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface edu.jas.structure.ElemFactory

valueOf

Methods inherited from interface java.lang.Iterable

forEach, spliterator

Field Detail

modul

public final java.math.BigInteger modul

Module part of the factory data structure.

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.

getIntegerModul

public BigInteger getIntegerModul()

Get the module part as BigInteger.

Specified by:

getIntegerModul in interface ModularRingFactory<ModInteger>

Returns:

modul.

create

public ModInteger create(java.math.BigInteger c)

Create ModInteger element c.

Parameters:

c -

Returns:

a ModInteger of c.

create

public ModInteger create(long c)

Create ModInteger element c.

Parameters:

c -

Returns:

a ModInteger of c.

create

public ModInteger create(java.lang.String c)

Create ModInteger element c.

Parameters:

c -

Returns:

a ModInteger of c.

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.

generators

public java.util.List<ModInteger> generators()

Get a list of the generating elements.

Specified by:

generators in interface ElemFactory<ModInteger>

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<ModInteger>

Returns:

true if this structure is finite, else false.

See Also:

ElemFactory.isFinite()

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()

toScript

public java.lang.String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface ElemFactory<ModInteger>

Returns:

script compatible representation for this ElemFactory.

See Also:

ElemFactory.toScript()

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.

Specified by:

chineseRemainder in interface ModularRingFactory<ModInteger>

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.

chineseRemainder

public static java.util.List<ModInteger> chineseRemainder(ModInteger m1,
                                                          ModInteger m2,
                                                          java.util.List<ModInteger> L1,
                                                          java.util.List<ModInteger> L2)

Modular integer list chinese remainder algorithm. m1 and m2 are positive integers, with GCD(m1,m2)=1 and m=m1*m2 less than beta. L1 and L2 are lists of elements of Z(m1) and Z(m2) respectively. L is a list of all a in Z(m) such that a is congruent to a1 modulo m1 and a is congruent to a2 modulo m2 with a1 in L1 and a2 in L2. This is a factory method. Assert c.modul ≥ a.modul and c.modul * a.modul = this.modul.

Parameters:

m1 - modular integer.

m2 - other modular integer.

Returns:

L list of congruences.

iterator

public java.util.Iterator<ModInteger> iterator()

Get a ModInteger iterator.

Specified by:

iterator in interface java.lang.Iterable<ModInteger>

Returns:

a iterator over all modular integers in this ring.