edu.jas.arith

Class ModIntRing

java.lang.Object

edu.jas.arith.ModIntRing

All Implemented Interfaces:

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

public final class ModIntRing
extends java.lang.Object
implements ModularRingFactory<ModInt>, java.lang.Iterable<ModInt>

ModIntRing 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_INT maximal representable integer.
int	modul Module part of the factory data structure.

Constructor Summary

Constructors

Constructor and Description
ModIntRing(java.math.BigInteger m) The constructor creates a ModIntRing object from a BigInteger converted to int as module part.
ModIntRing(java.math.BigInteger m, boolean isField) The constructor creates a ModIntRing object from a BigInteger converted to int as module part.
ModIntRing(int m) The constructor creates a ModIntRing object from a int integer as module part.
ModIntRing(int m, boolean isField) The constructor creates a ModIntRing object from a int integer as module part.
ModIntRing(java.lang.Integer m) The constructor creates a ModIntRing object from a Int integer as module part.
ModIntRing(java.lang.Integer m, boolean isField) The constructor creates a ModIntRing object from a Int integer as module part.
ModIntRing(java.lang.String m) The constructor creates a ModIntRing object from a String object as module part.
ModIntRing(java.lang.String m, boolean isField) The constructor creates a ModIntRing 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<ModInt>	chineseRemainder(ModInt m1, ModInt m2, java.util.List<ModInt> L1, java.util.List<ModInt> 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.
ModInt	chineseRemainder(ModInt c, ModInt ci, ModInt a) ModInt chinese remainder algorithm.
ModInt	copy(ModInt c) Copy ModInt element c.
ModInt	create(java.math.BigInteger c) Create ModInt element c.
ModInt	create(int c) Create ModInt element c.
ModInt	create(java.lang.String c) Create ModInt element c.
boolean	equals(java.lang.Object b) Comparison with any other object.
ModInt	fromInteger(java.math.BigInteger a) Get a ModInt element from a BigInteger value.
ModInt	fromInteger(int a) Get a ModInt element from a int value.
ModInt	fromInteger(long a) Get a ModInt element from a long value.
java.util.List<ModInt>	generators() Get a list of the generating elements.
BigInteger	getIntegerModul() Get the module part as BigInteger.
int	getIntModul() Get the module part as int.
java.math.BigInteger	getModul() Get the module part as BigInteger.
ModInt	getONE() Get the one element.
ModInt	getZERO() Get the zero element.
int	hashCode() Hash code for this ModIntRing.
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<ModInt>	iterator() Get a ModInt iterator.
ModInt	parse(java.io.Reader r) Parse ModInt from Reader.
ModInt	parse(java.lang.String s) Parse ModInt from String.
ModInt	random(int n) ModInt random.
ModInt	random(int n, java.util.Random rnd) ModInt 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 int modul

Module part of the factory data structure.

MAX_INT

public static final java.math.BigInteger MAX_INT

maximal representable integer.

Constructor Detail

ModIntRing

public ModIntRing(int m)

The constructor creates a ModIntRing object from a int integer as module part.

Parameters:

m - int integer.

ModIntRing

public ModIntRing(int m,
                  boolean isField)

The constructor creates a ModIntRing object from a int integer as module part.

Parameters:

m - int integer.

isField - indicator if m is prime.

ModIntRing

public ModIntRing(java.lang.Integer m)

The constructor creates a ModIntRing object from a Int integer as module part.

Parameters:

m - Int integer.

ModIntRing

public ModIntRing(java.lang.Integer m,
                  boolean isField)

The constructor creates a ModIntRing object from a Int integer as module part.

Parameters:

m - Int integer.

isField - indicator if m is prime.

ModIntRing

public ModIntRing(java.math.BigInteger m)

The constructor creates a ModIntRing object from a BigInteger converted to int as module part.

Parameters:

m - java.math.BigInteger.

ModIntRing

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

The constructor creates a ModIntRing object from a BigInteger converted to int as module part.

Parameters:

m - java.math.BigInteger.

isField - indicator if m is prime.

ModIntRing

public ModIntRing(java.lang.String m)

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

Parameters:

m - String.

ModIntRing

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

The constructor creates a ModIntRing 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.

getIntModul

public int getIntModul()

Get the module part as int.

Returns:

modul.

getIntegerModul

public BigInteger getIntegerModul()

Get the module part as BigInteger.

Specified by:

getIntegerModul in interface ModularRingFactory<ModInt>

Returns:

modul.

create

public ModInt create(java.math.BigInteger c)

Create ModInt element c.

Parameters:

c -

Returns:

a ModInt of c.

create

public ModInt create(int c)

Create ModInt element c.

Parameters:

c -

Returns:

a ModInt of c.

create

public ModInt create(java.lang.String c)

Create ModInt element c.

Parameters:

c -

Returns:

a ModInt of c.

copy

public ModInt copy(ModInt c)

Copy ModInt element c.

Specified by:

copy in interface ElemFactory<ModInt>

Parameters:

c -

Returns:

a copy of c.

getZERO

public ModInt getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<ModInt>

Returns:

0 as ModInt.

getONE

public ModInt getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<ModInt>

Returns:

1 as ModInt.

generators

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

Get a list of the generating elements.

Specified by:

generators in interface ElemFactory<ModInt>

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<ModInt>

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<ModInt>

Returns:

true.

isAssociative

public boolean isAssociative()

Query if this ring is associative.

Specified by:

isAssociative in interface MonoidFactory<ModInt>

Returns:

true.

isField

public boolean isField()

Query if this ring is a field.

Specified by:

isField in interface RingFactory<ModInt>

Returns:

true if module is prime, else false.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<ModInt>

Returns:

characteristic of this ring.

fromInteger

public ModInt fromInteger(java.math.BigInteger a)

Get a ModInt element from a BigInteger value.

Specified by:

fromInteger in interface ElemFactory<ModInt>

Parameters:

a - BigInteger.

Returns:

a ModInt.

fromInteger

public ModInt fromInteger(int a)

Get a ModInt element from a int value.

Parameters:

a - int.

Returns:

a ModInt.

fromInteger

public ModInt fromInteger(long a)

Get a ModInt element from a long value.

Specified by:

fromInteger in interface ElemFactory<ModInt>

Parameters:

a - lon.

Returns:

a ModInt.

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<ModInt>

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 ModIntRing.

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

random

public ModInt random(int n)

ModInt random.

Specified by:

random in interface ElemFactory<ModInt>

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

Returns:

a random integer mod modul.

random

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

ModInt random.

Specified by:

random in interface ElemFactory<ModInt>

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

rnd - is a source for random bits.

Returns:

a random integer mod modul.

parse

public ModInt parse(java.lang.String s)

Parse ModInt from String.

Specified by:

parse in interface ElemFactory<ModInt>

Parameters:

s - String.

Returns:

ModInt from s.

parse

public ModInt parse(java.io.Reader r)

Parse ModInt from Reader.

Specified by:

parse in interface ElemFactory<ModInt>

Parameters:

r - Reader.

Returns:

next ModInt from r.

chineseRemainder

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

ModInt 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<ModInt>

Parameters:

c - ModInt.

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

a - other ModInt.

Returns:

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

chineseRemainder

public static java.util.List<ModInt> chineseRemainder(ModInt m1,
                                                      ModInt m2,
                                                      java.util.List<ModInt> L1,
                                                      java.util.List<ModInt> 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 - ModInt.

m2 - other ModInt.

Returns:

L list of congruences.

iterator

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

Get a ModInt iterator.

Specified by:

iterator in interface java.lang.Iterable<ModInt>

Returns:

a iterator over all modular integers in this ring.