edu.jas.poly
Class AlgebraicNumberRing<C extends GcdRingElem<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

public class AlgebraicNumberRing<C extends GcdRingElem<C>>
extends java.lang.Object
implements RingFactory<AlgebraicNumber<C>>

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

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

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

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

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.
boolean	equals(java.lang.Object b) Comparison with any other object.
AlgebraicNumber<C>	fromInteger(java.math.BigInteger a) Get a AlgebraicNumber element from a BigInteger value.
AlgebraicNumber<C>	fromInteger(long a) Get a AlgebraicNumber element from a long value.
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.
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.
java.lang.String	toString() Get the String representation as RingFactory.

Methods inherited from class java.lang.Object

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

Field Detail

ring

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

Ring part of the factory data structure.

modul

public final GenPolynomial<C extends GcdRingElem<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

copy

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

Copy AlgebraicNumber element c.

Specified by:

copy in interface ElemFactory<AlgebraicNumber<C extends GcdRingElem<C>>>

Parameters:

c -

Returns:

a copy of c.

getZERO

public AlgebraicNumber<C> getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<AlgebraicNumber<C extends GcdRingElem<C>>>

Returns:

0 as AlgebraicNumber.

getONE

public AlgebraicNumber<C> getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<AlgebraicNumber<C extends GcdRingElem<C>>>

Returns:

1 as AlgebraicNumber.

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

isCommutative in interface MonoidFactory<AlgebraicNumber<C extends GcdRingElem<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<AlgebraicNumber<C extends GcdRingElem<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<AlgebraicNumber<C extends GcdRingElem<C>>>

Returns:

true if modul is prime, else false.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<AlgebraicNumber<C extends GcdRingElem<C>>>

Returns:

characteristic of this ring.

fromInteger

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

Get a AlgebraicNumber element from a BigInteger value.

Specified by:

fromInteger in interface ElemFactory<AlgebraicNumber<C extends GcdRingElem<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<AlgebraicNumber<C extends GcdRingElem<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()

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<AlgebraicNumber<C extends GcdRingElem<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<AlgebraicNumber<C extends GcdRingElem<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<AlgebraicNumber<C extends GcdRingElem<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<AlgebraicNumber<C extends GcdRingElem<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 algortihm.

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.