edu.jas.arith

Class ModLongRing

java.lang.Object

edu.jas.arith.ModLongRing

All Implemented Interfaces:

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

public final class ModLongRing
extends java.lang.Object
implements ModularRingFactory<ModLong>, java.lang.Iterable<ModLong>

ModLongRing factory with RingFactory interface. Effectively immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
static java.math.BigInteger	MAX_LONG maximal representable integer.
long	modul Module part of the factory data structure.

Constructor Summary

Constructors

Constructor and Description
ModLongRing(java.math.BigInteger m) The constructor creates a ModLongRing object from a BigInteger converted to long as module part.
ModLongRing(java.math.BigInteger m, boolean isField) The constructor creates a ModLongRing object from a BigInteger converted to long as module part.
ModLongRing(long m) The constructor creates a ModLongRing object from a long integer as module part.
ModLongRing(java.lang.Long m) The constructor creates a ModLongRing object from a Long integer as module part.
ModLongRing(long m, boolean isField) The constructor creates a ModLongRing object from a long integer as module part.
ModLongRing(java.lang.Long m, boolean isField) The constructor creates a ModLongRing object from a Long integer as module part.
ModLongRing(java.lang.String m) The constructor creates a ModLongRing object from a String object as module part.
ModLongRing(java.lang.String m, boolean isField) The constructor creates a ModLongRing object from a String object as module part.

Method Summary

Modifier and Type	Method and Description
java.math.BigInteger	characteristic() Characteristic of this ring.
static java.util.List<ModLong>	chineseRemainder(ModLong m1, ModLong m2, java.util.List<ModLong> L1, java.util.List<ModLong> L2) Modular digit list chinese remainder algorithm. m1 and m2 are positive beta-integers, with GCD(m1,m2)=1 and m=m1*m2 less than beta.
ModLong	chineseRemainder(ModLong c, ModLong ci, ModLong a) ModLong chinese remainder algorithm.
ModLong	copy(ModLong c) Copy ModLong element c.
ModLong	create(java.math.BigInteger c) Create ModLong element c.
ModLong	create(long c) Create ModLong element c.
ModLong	create(java.lang.String c) Create ModLong element c.
boolean	equals(java.lang.Object b) Comparison with any other object.
ModLong	fromInteger(java.math.BigInteger a) Get a ModLong element from a BigInteger value.
ModLong	fromInteger(long a) Get a ModLong element from a long value.
java.util.List<ModLong>	generators() Get a list of the generating elements.
BigInteger	getIntegerModul() Get the module part as BigInteger.
long	getLongModul() Get the module part as long.
java.math.BigInteger	getModul() Get the module part as BigInteger.
ModLong	getONE() Get the one element.
ModLong	getZERO() Get the zero element.
int	hashCode() Hash code for this ModLongRing.
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<ModLong>	iterator() Get a ModLong iterator.
ModLong	parse(java.io.Reader r) Parse ModLong from Reader.
ModLong	parse(java.lang.String s) Parse ModLong from String.
ModLong	random(int n) ModLong random.
ModLong	random(int n, java.util.Random rnd) ModLong 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 java.lang.Iterable

forEach, spliterator

Field Detail

modul

public final long modul

Module part of the factory data structure.

MAX_LONG

public static final java.math.BigInteger MAX_LONG

maximal representable integer.

Constructor Detail

ModLongRing

public ModLongRing(long m)

The constructor creates a ModLongRing object from a long integer as module part.

Parameters:

m - long integer.

ModLongRing

public ModLongRing(long m,
                   boolean isField)

The constructor creates a ModLongRing object from a long integer as module part.

Parameters:

m - long integer.

isField - indicator if m is prime.

ModLongRing

public ModLongRing(java.lang.Long m)

The constructor creates a ModLongRing object from a Long integer as module part.

Parameters:

m - Long integer.

ModLongRing

public ModLongRing(java.lang.Long m,
                   boolean isField)

The constructor creates a ModLongRing object from a Long integer as module part.

Parameters:

m - Long integer.

isField - indicator if m is prime.

ModLongRing

public ModLongRing(java.math.BigInteger m)

The constructor creates a ModLongRing object from a BigInteger converted to long as module part.

Parameters:

m - java.math.BigInteger.

ModLongRing

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

The constructor creates a ModLongRing object from a BigInteger converted to long as module part.

Parameters:

m - java.math.BigInteger.

isField - indicator if m is prime.

ModLongRing

public ModLongRing(java.lang.String m)

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

Parameters:

m - String.

ModLongRing

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

The constructor creates a ModLongRing 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 as BigInteger.

Returns:

modul.

getLongModul

public long getLongModul()

Get the module part as long.

Returns:

modul.

getIntegerModul

public BigInteger getIntegerModul()

Get the module part as BigInteger.

Specified by:

getIntegerModul in interface ModularRingFactory<ModLong>

Returns:

modul.

create

public ModLong create(java.math.BigInteger c)

Create ModLong element c.

Parameters:

c -

Returns:

a ModLong of c.

create

public ModLong create(long c)

Create ModLong element c.

Parameters:

c -

Returns:

a ModLong of c.

create

public ModLong create(java.lang.String c)

Create ModLong element c.

Parameters:

c -

Returns:

a ModLong of c.

copy

public ModLong copy(ModLong c)

Copy ModLong element c.

Specified by:

copy in interface ElemFactory<ModLong>

Parameters:

c -

Returns:

a copy of c.

getZERO

public ModLong getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<ModLong>

Returns:

0 as ModLong.

getONE

public ModLong getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<ModLong>

Returns:

1 as ModLong.

generators

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

Get a list of the generating elements.

Specified by:

generators in interface ElemFactory<ModLong>

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<ModLong>

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<ModLong>

Returns:

true.

isAssociative

public boolean isAssociative()

Query if this ring is associative.

Specified by:

isAssociative in interface MonoidFactory<ModLong>

Returns:

true.

isField

public boolean isField()

Query if this ring is a field.

Specified by:

isField in interface RingFactory<ModLong>

Returns:

true if module is prime, else false.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<ModLong>

Returns:

characteristic of this ring.

fromInteger

public ModLong fromInteger(java.math.BigInteger a)

Get a ModLong element from a BigInteger value.

Specified by:

fromInteger in interface ElemFactory<ModLong>

Parameters:

a - BigInteger.

Returns:

a ModLong.

fromInteger

public ModLong fromInteger(long a)

Get a ModLong element from a long value.

Specified by:

fromInteger in interface ElemFactory<ModLong>

Parameters:

a - long.

Returns:

a ModLong.

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<ModLong>

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 ModLongRing.

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

random

public ModLong random(int n)

ModLong random.

Specified by:

random in interface ElemFactory<ModLong>

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

Returns:

a random integer mod modul.

random

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

ModLong random.

Specified by:

random in interface ElemFactory<ModLong>

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

rnd - is a source for random bits.

Returns:

a random integer mod modul.

parse

public ModLong parse(java.lang.String s)

Parse ModLong from String.

Specified by:

parse in interface ElemFactory<ModLong>

Parameters:

s - String.

Returns:

ModLong from s.

parse

public ModLong parse(java.io.Reader r)

Parse ModLong from Reader.

Specified by:

parse in interface ElemFactory<ModLong>

Parameters:

r - Reader.

Returns:

next ModLong from r.

chineseRemainder

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

ModLong 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<ModLong>

Parameters:

c - ModLong.

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

a - other ModLong.

Returns:

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

chineseRemainder

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

Modular digit list chinese remainder algorithm. m1 and m2 are positive beta-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 - ModLong.

m2 - other ModLong.

Returns:

L list of congruences.

iterator

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

Get a ModLong iterator.

Specified by:

iterator in interface java.lang.Iterable<ModLong>

Returns:

a iterator over all modular integers in this ring.