Package edu.jas.poly

Class AlgebraicNumberRing<C extends RingElem<C>>

java.lang.Object

edu.jas.poly.AlgebraicNumberRing<C>

All Implemented Interfaces:

AbelianGroupFactory<AlgebraicNumber<C>>, ElemFactory<AlgebraicNumber<C>>, MonoidFactory<AlgebraicNumber<C>>, RingFactory<AlgebraicNumber<C>>, java.io.Serializable, java.lang.Iterable<AlgebraicNumber<C>>

public class AlgebraicNumberRing<C extends RingElem<C>>
extends java.lang.Object
implements RingFactory<AlgebraicNumber<C>>, java.lang.Iterable<AlgebraicNumber<C>>

Algebraic number factory. Based on GenPolynomial factory with RingElem interface. Objects of this class are immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected int	isField	Indicator if this ring is a field
GenPolynomial<C>	modul	Module part of the factory data structure.
GenPolynomialRing<C>	ring	Ring part of the factory data structure.

Constructor Summary

Constructors

Constructor	Description
AlgebraicNumberRing(GenPolynomial<C> m)	The constructor creates a AlgebraicNumber factory object from a GenPolynomial objects module.
AlgebraicNumberRing(GenPolynomial<C> m, boolean isField)	The constructor creates a AlgebraicNumber factory object from a GenPolynomial objects module.

Method Summary

Modifier and Type	Method	Description
java.math.BigInteger	characteristic()	Characteristic of this ring.
AlgebraicNumber<C>	chineseRemainder(AlgebraicNumber<C> c, AlgebraicNumber<C> ci, AlgebraicNumber<C> a)	AlgebraicNumber chinese remainder algorithm.
AlgebraicNumber<C>	copy(AlgebraicNumber<C> c)	Copy AlgebraicNumber element c.
int	depth()	Depth of extension field tower.
boolean	equals(java.lang.Object b)	Comparison with any other object.
long	extensionDegree()	Degree of extension field.
AlgebraicNumber<C>	fillFromInteger(long a)	Get a AlgebraicNumber element from a long value.
AlgebraicNumber<C>	fillFromInteger(java.math.BigInteger a)	Get an AlgebraicNumber element from a BigInteger value.
AlgebraicNumber<C>	fromInteger(long a)	Get a AlgebraicNumber element from a long value.
AlgebraicNumber<C>	fromInteger(java.math.BigInteger a)	Get a AlgebraicNumber element from a BigInteger value.
java.util.List<AlgebraicNumber<C>>	generators()	Get a list of the generating elements.
int	getField()	Get the internal field indicator.
AlgebraicNumber<C>	getGenerator()	Get the generating element.
GenPolynomial<C>	getModul()	Get the module part.
AlgebraicNumber<C>	getONE()	Get the one element.
AlgebraicNumber<C>	getZERO()	Get the zero element.
int	hashCode()	Hash code for this AlgebraicNumber.
AlgebraicNumber<C>	interpolate(AlgebraicNumber<C> c, C ci, C am, C a)	AlgebraicNumber interpolation algorithm.
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<AlgebraicNumber<C>>	iterator()	Get a AlgebraicNumber iterator.
AlgebraicNumber<C>	parse(java.io.Reader r)	Parse AlgebraicNumber from Reader.
AlgebraicNumber<C>	parse(java.lang.String s)	Parse AlgebraicNumber from String.
AlgebraicNumber<C>	random(int n)	AlgebraicNumber random.
AlgebraicNumber<C>	random(int n, java.util.Random rnd)	AlgebraicNumber random.
void	setField(boolean field)	Set field property of this ring.
java.lang.String	toScript()	Get a scripting compatible string representation.
java.lang.String	toString()	Get the String representation as RingFactory.
long	totalExtensionDegree()	Total degree of nested extension fields.

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

ring

public final GenPolynomialRing<C extends RingElem<C>> ring

Ring part of the factory data structure.

modul

public final GenPolynomial<C extends RingElem<C>> modul

Module part of the factory data structure.

isField

protected int isField

Indicator if this ring is a field

Constructor Detail

AlgebraicNumberRing

public AlgebraicNumberRing(GenPolynomial<C> m)

The constructor creates a AlgebraicNumber factory object from a GenPolynomial objects module.

Parameters:

m - module GenPolynomial.

AlgebraicNumberRing

public AlgebraicNumberRing(GenPolynomial<C> m,
                           boolean isField)

The constructor creates a AlgebraicNumber factory object from a GenPolynomial objects module.

Parameters:

m - module GenPolynomial.

isField - indicator if m is prime.

Method Detail

getModul

public GenPolynomial<C> getModul()

Get the module part.

Returns:

modul.

copy

public AlgebraicNumber<C> copy(AlgebraicNumber<C> c)

Copy AlgebraicNumber element c.

Specified by:

copy in interface ElemFactory<C extends RingElem<C>>

Parameters:

c - algebraic number to copy.

Returns:

a copy of c.

getZERO

public AlgebraicNumber<C> getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<C extends RingElem<C>>

Returns:

0 as AlgebraicNumber.

getONE

public AlgebraicNumber<C> getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<C extends RingElem<C>>

Returns:

1 as AlgebraicNumber.

getGenerator

public AlgebraicNumber<C> getGenerator()

Get the generating element.

Returns:

alpha as AlgebraicNumber.

generators

public java.util.List<AlgebraicNumber<C>> generators()

Get a list of the generating elements.

Specified by:

generators in interface ElemFactory<C extends RingElem<C>>

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<C extends RingElem<C>>

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<C extends RingElem<C>>

Returns:

true if this ring is commutative, else false.

isAssociative

public boolean isAssociative()

Query if this ring is associative.

Specified by:

isAssociative in interface MonoidFactory<C extends RingElem<C>>

Returns:

true if this ring is associative, else false.

isField

public boolean isField()

Query if this ring is a field.

Specified by:

isField in interface RingFactory<C extends RingElem<C>>

Returns:

true if modul is prime, else false.

setField

public void setField(boolean field)

Set field property of this ring.

Parameters:

field - true, if this ring is determined to be a field, false, if it is determined that it is not a field.

getField

public int getField()

Get the internal field indicator.

Returns:

internal field indicator.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<C extends RingElem<C>>

Returns:

characteristic of this ring.

fillFromInteger

public AlgebraicNumber<C> fillFromInteger(java.math.BigInteger a)

Get an AlgebraicNumber element from a BigInteger value. If a = a_k p^k + ... + a_0 p^0 then b = a_k x^k + ... + a_0 x^0, where p = characteristic( this ).

Parameters:

a - BigInteger.

Returns:

b an AlgebraicNumber.

fillFromInteger

public AlgebraicNumber<C> fillFromInteger(long a)

Get a AlgebraicNumber element from a long value.

Parameters:

a - long.

Returns:

a AlgebraicNumber.

fromInteger

public AlgebraicNumber<C> fromInteger(java.math.BigInteger a)

Get a AlgebraicNumber element from a BigInteger value.

Specified by:

fromInteger in interface ElemFactory<C extends RingElem<C>>

Parameters:

a - BigInteger.

Returns:

a AlgebraicNumber.

fromInteger

public AlgebraicNumber<C> fromInteger(long a)

Get a AlgebraicNumber element from a long value.

Specified by:

fromInteger in interface ElemFactory<C extends RingElem<C>>

Parameters:

a - long.

Returns:

a AlgebraicNumber.

toString

public java.lang.String toString()

Get the String representation as RingFactory.

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<C extends RingElem<C>>

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 AlgebraicNumber.

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

random

public AlgebraicNumber<C> random(int n)

AlgebraicNumber random.

Specified by:

random in interface ElemFactory<C extends RingElem<C>>

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

Returns:

a random integer mod modul.

random

public AlgebraicNumber<C> random(int n,
                                 java.util.Random rnd)

AlgebraicNumber random.

Specified by:

random in interface ElemFactory<C extends RingElem<C>>

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

rnd - is a source for random bits.

Returns:

a random integer mod modul.

parse

public AlgebraicNumber<C> parse(java.lang.String s)

Parse AlgebraicNumber from String.

Specified by:

parse in interface ElemFactory<C extends RingElem<C>>

Parameters:

s - String.

Returns:

AlgebraicNumber from s.

parse

public AlgebraicNumber<C> parse(java.io.Reader r)

Parse AlgebraicNumber from Reader.

Specified by:

parse in interface ElemFactory<C extends RingElem<C>>

Parameters:

r - Reader.

Returns:

next AlgebraicNumber from r.

chineseRemainder

public AlgebraicNumber<C> chineseRemainder(AlgebraicNumber<C> c,
                                           AlgebraicNumber<C> ci,
                                           AlgebraicNumber<C> a)

AlgebraicNumber chinese remainder algorithm. Assert deg(c.modul) ≥ deg(a.modul) and c.modul * a.modul = this.modul.

Parameters:

c - AlgebraicNumber.

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

a - other AlgebraicNumber.

Returns:

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

interpolate

public AlgebraicNumber<C> interpolate(AlgebraicNumber<C> c,
                                      C ci,
                                      C am,
                                      C a)

AlgebraicNumber interpolation algorithm. Assert deg(c.modul) ≥ deg(A.modul) and c.modul * A.modul = this.modul. Special case with deg(A.modul) == 1. Similar algorithm as chinese remainder algorithm.

Parameters:

c - AlgebraicNumber.

ci - inverse of (c.modul)(a) in ring of A.

am - trailing base coefficient of modul of other AlgebraicNumber A.

a - value of other AlgebraicNumber A.

Returns:

S, with S(c) == c and S(A) == a.

depth

public int depth()

Depth of extension field tower.

Returns:

number of nested algebraic extension fields

extensionDegree

public long extensionDegree()

Degree of extension field.

Returns:

degree of this algebraic extension field

totalExtensionDegree

public long totalExtensionDegree()

Total degree of nested extension fields.

Returns:

degree of tower of algebraic extension fields

iterator

public java.util.Iterator<AlgebraicNumber<C>> iterator()

Get a AlgebraicNumber iterator. Note: Only for finite field coefficients or fields which are iterable.

Specified by:

iterator in interface java.lang.Iterable<C extends RingElem<C>>

Returns:

a iterator over all algebraic numbers in this ring.