edu.jas.application

Class WordResidueRing<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.application.WordResidueRing<C>

All Implemented Interfaces:

AbelianGroupFactory<WordResidue<C>>, ElemFactory<WordResidue<C>>, MonoidFactory<WordResidue<C>>, QuotPairFactory<GenWordPolynomial<C>,WordResidue<C>>, RingFactory<WordResidue<C>>, ValueFactory<GenWordPolynomial<C>,WordResidue<C>>, java.io.Serializable

public class WordResidueRing<C extends GcdRingElem<C>>
extends java.lang.Object
implements RingFactory<WordResidue<C>>, QuotPairFactory<GenWordPolynomial<C>,WordResidue<C>>, ValueFactory<GenWordPolynomial<C>,WordResidue<C>>

WordResidue ring factory based on GenWordPolynomialRing with GcdRingFactory interface. Objects of this class are immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected WordGroebnerBaseAbstract<C>	bb Groebner base engine.
WordIdeal<C>	ideal Word polynomial ideal for the reduction.
protected int	isField Indicator if this ring is a field.
GenWordPolynomialRing<C>	ring Polynomial ring of the factory.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
java.math.BigInteger	characteristic() Characteristic of this ring.
WordResidue<C>	copy(WordResidue<C> c) Copy WordResidue element c.
WordResidue<C>	create(GenWordPolynomial<C> n) Create from numerator.
WordResidue<C>	create(GenWordPolynomial<C> n, GenWordPolynomial<C> d) Create from numerator, denominator pair.
boolean	equals(java.lang.Object b) Comparison with any other object.
WordResidue<C>	fromInteger(java.math.BigInteger a) Get a WordResidue element from a BigInteger value.
WordResidue<C>	fromInteger(long a) Get a WordResidue element from a long value.
java.util.List<WordResidue<C>>	generators() Get a list of the generating elements.
WordResidue<C>	getONE() Get the one element.
WordResidue<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.
GenWordPolynomialRing<C>	pairFactory() Factory for base elements.
WordResidue<C>	parse(java.io.Reader r) Parse WordResidue from Reader.
WordResidue<C>	parse(java.lang.String s) Parse WordResidue from String.
WordResidue<C>	random(int n) WordResidue random.
WordResidue<C>	random(int k, int l, int d) Generate a random residum polynomial.
WordResidue<C>	random(int n, java.util.Random rnd) WordResidue random.
java.lang.String	toScript() Get a scripting compatible string representation.
java.lang.String	toString() Get the String representation as RingFactory.
GenWordPolynomialRing<C>	valueFactory() Factory for base elements.

Methods inherited from class java.lang.Object

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

Field Detail

bb

protected final WordGroebnerBaseAbstract<C extends GcdRingElem<C>> bb

Groebner base engine.

ideal

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

Word polynomial ideal for the reduction.

ring

public final GenWordPolynomialRing<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

WordResidueRing

public WordResidueRing(WordIdeal<C> i)

The constructor creates a WordResidueRing object from an Ideal.

Parameters:

i - polynomial ideal.

WordResidueRing

public WordResidueRing(WordIdeal<C> i,
                       boolean isMaximal)

The constructor creates a WordResidueRing object from an WordIdeal.

Parameters:

i - solvable polynomial ideal.

isMaximal - true, if ideal is maxmal.

Method Detail

pairFactory

public GenWordPolynomialRing<C> pairFactory()

Factory for base elements.

Specified by:

pairFactory in interface QuotPairFactory<GenWordPolynomial<C extends GcdRingElem<C>>,WordResidue<C extends GcdRingElem<C>>>

valueFactory

public GenWordPolynomialRing<C> valueFactory()

Factory for base elements.

Specified by:

valueFactory in interface ValueFactory<GenWordPolynomial<C extends GcdRingElem<C>>,WordResidue<C extends GcdRingElem<C>>>

create

public WordResidue<C> create(GenWordPolynomial<C> n)

Create from numerator.

Specified by:

create in interface QuotPairFactory<GenWordPolynomial<C extends GcdRingElem<C>>,WordResidue<C extends GcdRingElem<C>>>

Specified by:

create in interface ValueFactory<GenWordPolynomial<C extends GcdRingElem<C>>,WordResidue<C extends GcdRingElem<C>>>

create

public WordResidue<C> create(GenWordPolynomial<C> n,
                             GenWordPolynomial<C> d)

Create from numerator, denominator pair.

Specified by:

create in interface QuotPairFactory<GenWordPolynomial<C extends GcdRingElem<C>>,WordResidue<C extends GcdRingElem<C>>>

isFinite

public boolean isFinite()

Is this structure finite or infinite.

Specified by:

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

Returns:

true if this structure is finite, else false.

See Also:

ElemFactory.isFinite()

copy

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

Copy WordResidue element c.

Specified by:

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

Parameters:

c -

Returns:

a copy of c.

getZERO

public WordResidue<C> getZERO()

Get the zero element.

Specified by:

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

Returns:

0 as WordResidue.

getONE

public WordResidue<C> getONE()

Get the one element.

Specified by:

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

Returns:

1 as WordResidue.

generators

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

Get a list of the generating elements.

Specified by:

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

Returns:

false.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

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

Returns:

characteristic of this ring.

fromInteger

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

Get a WordResidue element from a BigInteger value.

Specified by:

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

Parameters:

a - BigInteger.

Returns:

a WordResidue.

fromInteger

public WordResidue<C> fromInteger(long a)

Get a WordResidue element from a long value.

Specified by:

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

Parameters:

a - long.

Returns:

a WordResidue.

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<WordResidue<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 WordResidue<C> random(int n)

WordResidue random.

Specified by:

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

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

Returns:

a random residue element.

random

public WordResidue<C> random(int k,
                             int l,
                             int d)

Generate a random residum polynomial.

Parameters:

k - bitsize of random coefficients.

l - number of terms.

d - maximal degree in each variable.

Returns:

a random residue polynomial.

random

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

WordResidue random.

Specified by:

random in interface ElemFactory<WordResidue<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 WordResidue<C> parse(java.lang.String s)

Parse WordResidue from String.

Specified by:

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

Parameters:

s - String.

Returns:

WordResidue from s.

parse

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

Parse WordResidue from Reader.

Specified by:

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

Parameters:

r - Reader.

Returns:

next WordResidue from r.