Class LocalRing<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.application.LocalRing<C>

All Implemented Interfaces:

AbelianGroupFactory<Local<C>>, ElemFactory<Local<C>>, MonoidFactory<Local<C>>, QuotPairFactory<GenPolynomial<C>, Local<C>>, RingFactory<Local<C>>, Serializable

public class LocalRing<C extends GcdRingElem<C>>
extends Object
implements RingFactory<Local<C>>, QuotPairFactory<GenPolynomial<C>, Local<C>>

Local ring class based on GenPolynomial with RingElem interface. Objects of this class are effective immutable.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected final GreatestCommonDivisor<C>	engine	Greatest common divisor engine for coefficient content and primitive parts.
final Ideal<C>	ideal	Polynomial ideal for localization.
protected int	isField	Indicator if this ring is a field.
private static final org.apache.logging.log4j.Logger	logger
final GenPolynomialRing<C>	ring	Polynomial ring of the factory.

Constructor Summary

Constructors

Constructor	Description
LocalRing(Ideal<C> i)	The constructor creates a LocalRing object from an Ideal.

Method Summary

Modifier and Type	Method	Description
BigInteger	characteristic()	Characteristic of this ring.
Local<C>	copy(Local<C> c)	Copy Local element c.
Local<C>	create(GenPolynomial<C> n)	Create from numerator.
Local<C>	create(GenPolynomial<C> n, GenPolynomial<C> d)	Create from numerator, denominator pair.
boolean	equals(Object b)	Comparison with any other object.
Local<C>	fromInteger(long a)	Get a Local element from a long value.
Local<C>	fromInteger(BigInteger a)	Get a Local element from a BigInteger value.
List<Local<C>>	generators()	Get a list of the generating elements.
Local<C>	getONE()	Get the one element.
Local<C>	getZERO()	Get the zero element.
int	hashCode()	Hash code for this local 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.
GenPolynomialRing<C>	pairFactory()	Factory for base elements.
Local<C>	parse(Reader r)	Parse Local from Reader.
Local<C>	parse(String s)	Parse Local from String.
Local<C>	random(int n)	Local random.
Local<C>	random(int k, int l, int d, float q)	Generate a random residum polynomial.
Local<C>	random(int n, Random rnd)	Local random.
String	toScript()	Get a scripting compatible string representation.
String	toString()	Get the String representation as RingFactory.

Methods inherited from class Object

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

Methods inherited from interface ElemFactory

valueOf

Field Details

logger

private static final org.apache.logging.log4j.Logger logger

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 localization.

ring

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

Polynomial ring of the factory.

isField

protected int isField

Indicator if this ring is a field.

Constructor Details

LocalRing

public LocalRing(Ideal<C> i)

The constructor creates a LocalRing object from an Ideal.

Parameters:

i - localization polynomial ideal.

Method Details

pairFactory

public GenPolynomialRing<C> pairFactory()

Factory for base elements.

Specified by:

pairFactory in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>, Local<C extends GcdRingElem<C>>>

create

public Local<C> create(GenPolynomial<C> n)

Create from numerator.

Specified by:

create in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>, Local<C extends GcdRingElem<C>>>

create

public Local<C> create(GenPolynomial<C> n,
 GenPolynomial<C> d)

Create from numerator, denominator pair.

Specified by:

create in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>, Local<C extends GcdRingElem<C>>>

isFinite

public boolean isFinite()

Is this structure finite or infinite.

Specified by:

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

Returns:

true if this structure is finite, else false.

See Also:

• ElemFactory.isFinite()

copy

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

Copy Local element c.

Specified by:

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

Parameters:

c -

Returns:

a copy of c.

getZERO

public Local<C> getZERO()

Get the zero element.

Specified by:

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

Returns:

0 as Local.

getONE

public Local<C> getONE()

Get the one element.

Specified by:

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

Returns:

1 as Local.

generators

public List<Local<C>> generators()

Get a list of the generating elements.

Specified by:

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

Returns:

false.

characteristic

public BigInteger characteristic()

Characteristic of this ring.

Specified by:

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

Returns:

characteristic of this ring.

fromInteger

public Local<C> fromInteger(BigInteger a)

Get a Local element from a BigInteger value.

Specified by:

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

Parameters:

a - BigInteger.

Returns:

a Local.

fromInteger

public Local<C> fromInteger(long a)

Get a Local element from a long value.

Specified by:

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

Parameters:

a - long.

Returns:

a Local.

toString

public String toString()

Get the String representation as RingFactory.

Overrides:

toString in class Object

See Also:

• Object.toString()

toScript

public String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface ElemFactory<C extends GcdRingElem<C>>

Returns:

script compatible representation for this ElemFactory.

See Also:

• ElemFactory.toScript()

equals

public boolean equals(Object b)

Comparison with any other object.

Overrides:

equals in class Object

See Also:

• Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this local ring.

Overrides:

hashCode in class Object

See Also:

• Object.hashCode()

random

public Local<C> random(int n)

Local random.

Specified by:

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

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

Returns:

a random residue element.

random

public Local<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 Local<C> random(int n,
 Random rnd)

Local random.

Specified by:

random in interface ElemFactory<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 Local<C> parse(String s)

Parse Local from String.

Specified by:

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

Parameters:

s - String.

Returns:

Local from s.

parse

public Local<C> parse(Reader r)

Parse Local from Reader.

Specified by:

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

Parameters:

r - Reader.

Returns:

next Local from r.