edu.jas.application

Class ResidueRing<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.application.ResidueRing<C>

All Implemented Interfaces:

AbelianGroupFactory<Residue<C>>, ElemFactory<Residue<C>>, MonoidFactory<Residue<C>>, RingFactory<Residue<C>>, java.io.Serializable

public class ResidueRing<C extends GcdRingElem<C>>
extends java.lang.Object
implements RingFactory<Residue<C>>

Residue ring factory based on GenPolynomial with RingFactory interface. Objects of this class are immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected GreatestCommonDivisor<C>	engine Greatest common divisor engine for coefficient content and primitive parts.
Ideal<C>	ideal Polynomial ideal for the reduction.
protected int	isField Indicator if this ring is a field.
GenPolynomialRing<C>	ring Polynomial ring of the factory.

Constructor Summary

Constructors

Constructor and Description
ResidueRing(Ideal<C> i) The constructor creates a ResidueRing object from an Ideal.
ResidueRing(Ideal<C> i, boolean isMaximal) The constructor creates a ResidueRing object from an Ideal.

Method Summary

Methods

Modifier and Type	Method and Description
java.math.BigInteger	characteristic() Characteristic of this ring.
Residue<C>	copy(Residue<C> c) Copy Residue element c.
boolean	equals(java.lang.Object b) Comparison with any other object.
Residue<C>	fromInteger(java.math.BigInteger a) Get a Residue element from a BigInteger value.
Residue<C>	fromInteger(long a) Get a Residue element from a long value.
java.util.List<Residue<C>>	generators() Get a list of the generating elements.
Residue<C>	getONE() Get the one element.
Residue<C>	getZERO() Get the zero element.
int	hashCode() Hash code for this residue ring.
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.
Residue<C>	parse(java.io.Reader r) Parse Residue from Reader.
Residue<C>	parse(java.lang.String s) Parse Residue from String.
Residue<C>	random(int n) Residue random.
Residue<C>	random(int k, int l, int d, float q) Generate a random residum polynomial.
Residue<C>	random(int n, java.util.Random rnd) Residue random.
java.lang.String	toScript() Get a scripting compatible string representation.
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

engine

protected final GreatestCommonDivisor<C extends GcdRingElem<C>> engine

Greatest common divisor engine for coefficient content and primitive parts.

ideal

public final Ideal<C extends GcdRingElem<C>> ideal

Polynomial ideal for the reduction.

ring

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

Polynomial ring of the factory. Shortcut to ideal.list.ring.

isField

protected int isField

Indicator if this ring is a field.

Constructor Detail

ResidueRing

public ResidueRing(Ideal<C> i)

The constructor creates a ResidueRing object from an Ideal.

Parameters:

i - polynomial ideal.

ResidueRing

public ResidueRing(Ideal<C> i,
           boolean isMaximal)

The constructor creates a ResidueRing object from an Ideal.

Parameters:

i - polynomial ideal.

isMaximal - true, if ideal is maxmal.

Method Detail

isFinite

public boolean isFinite()

Is this structure finite or infinite.

Specified by:

isFinite in interface ElemFactory<Residue<C extends GcdRingElem<C>>>

Returns:

true if this structure is finite, else false.

See Also:

ElemFactory.isFinite()

copy

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

Copy Residue element c.

Specified by:

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

Parameters:

c -

Returns:

a copy of c.

getZERO

public Residue<C> getZERO()

Get the zero element.

Specified by:

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

Returns:

0 as Residue.

getONE

public Residue<C> getONE()

Get the one element.

Specified by:

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

Returns:

1 as Residue.

generators

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

Get a list of the generating elements.

Specified by:

generators in interface ElemFactory<Residue<C extends GcdRingElem<C>>>

Returns:

list of generators for the algebraic structure.

See Also:

ElemFactory.generators()

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

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

Returns:

false.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

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

Returns:

characteristic of this ring.

fromInteger

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

Get a Residue element from a BigInteger value.

Specified by:

fromInteger in interface ElemFactory<Residue<C extends GcdRingElem<C>>>

Parameters:

a - BigInteger.

Returns:

a Residue.

fromInteger

public Residue<C> fromInteger(long a)

Get a Residue element from a long value.

Specified by:

fromInteger in interface ElemFactory<Residue<C extends GcdRingElem<C>>>

Parameters:

a - long.

Returns:

a Residue.

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<Residue<C extends GcdRingElem<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 residue ring.

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

random

public Residue<C> random(int n)

Residue random.

Specified by:

random in interface ElemFactory<Residue<C extends GcdRingElem<C>>>

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

Returns:

a random residue element.

random

public Residue<C> random(int k,
                int l,
                int d,
                float q)

Generate a random residum polynomial.

Parameters:

k - bitsize of random coefficients.

l - number of terms.

d - maximal degree in each variable.

q - density of nozero exponents.

Returns:

a random residue polynomial.

random

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

Residue random.

Specified by:

random in interface ElemFactory<Residue<C extends GcdRingElem<C>>>

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

rnd - is a source for random bits.

Returns:

a random residue element.

parse

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

Parse Residue from String.

Specified by:

parse in interface ElemFactory<Residue<C extends GcdRingElem<C>>>

Parameters:

s - String.

Returns:

Residue from s.

parse

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

Parse Residue from Reader.

Specified by:

parse in interface ElemFactory<Residue<C extends GcdRingElem<C>>>

Parameters:

r - Reader.

Returns:

next Residue from r.