Class QuotientRing<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.ufd.QuotientRing<C>

All Implemented Interfaces:

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

public class QuotientRing<C extends GcdRingElem<C>>
extends Object
implements RingFactory<Quotient<C>>, QuotPairFactory<GenPolynomial<C>, Quotient<C>>

Quotient ring factory based on GenPolynomial with RingElem interface. Objects of this class are immutable.

See Also:

• Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static enum	QuotientRing.QuoNorm	Quotient polynomial normalization, simplification.

Field Summary

Fields

Modifier and Type	Field	Description
final GreatestCommonDivisor<C>	engine	GCD engine of the factory.
private static final org.apache.logging.log4j.Logger	logger
static final QuotientRing.QuoNorm	quoNorm	Default quotient polynomial normalization, simplification.
final GenPolynomialRing<C>	ring	Polynomial ring of the factory.
final boolean	ufdGCD	Use GCD of package edu.jas.ufd.

Constructor Summary

Constructors

Constructor	Description
QuotientRing(GenPolynomialRing<C> r)	The constructor creates a QuotientRing object from a GenPolynomialRing.
QuotientRing(GenPolynomialRing<C> r, boolean ufdGCD)	The constructor creates a QuotientRing object from a GenPolynomialRing.

Method Summary

Modifier and Type	Method	Description
BigInteger	characteristic()	Characteristic of this ring.
Quotient<C>	copy(Quotient<C> c)	Copy Quotient element c.
Quotient<C>	create(GenPolynomial<C> n)	Create from numerator.
Quotient<C>	create(GenPolynomial<C> n, GenPolynomial<C> d)	Create from numerator, denominator pair.
protected GenPolynomial<C>	divide(GenPolynomial<C> n, GenPolynomial<C> d)	Divide.
boolean	equals(Object b)	Comparison with any other object.
long	extensionDegree()	Degree of extension field.
Quotient<C>	fromInteger(long a)	Get a Quotient element from a long value.
Quotient<C>	fromInteger(BigInteger a)	Get a Quotient element from a BigInteger value.
protected GenPolynomial<C>	gcd(GenPolynomial<C> n, GenPolynomial<C> d)	Greatest common divisor.
List<Quotient<C>>	generators()	Get a list of the generating elements.
Quotient<C>	getONE()	Get the one element.
Quotient<C>	getZERO()	Get the zero element.
int	hashCode()	Hash code for this quotient 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.
Quotient<C>	parse(Reader r)	Parse Quotient from Reader.
Quotient<C>	parse(String s)	Parse Quotient from String.
Quotient<C>	random(int n)	Quotient random.
Quotient<C>	random(int k, int l, int d, float q)	Generate a random quotient polynomial.
Quotient<C>	random(int n, Random rnd)	Quotient 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

quoNorm

public static final QuotientRing.QuoNorm quoNorm

Default quotient polynomial normalization, simplification.

ring

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

Polynomial ring of the factory.

engine

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

GCD engine of the factory.

ufdGCD

public final boolean ufdGCD

Use GCD of package edu.jas.ufd.

Constructor Details

QuotientRing

public QuotientRing(GenPolynomialRing<C> r)

The constructor creates a QuotientRing object from a GenPolynomialRing.

Parameters:

r - polynomial ring.

QuotientRing

public QuotientRing(GenPolynomialRing<C> r,
 boolean ufdGCD)

The constructor creates a QuotientRing object from a GenPolynomialRing.

Parameters:

r - polynomial ring.

ufdGCD - flag, if syzygy or gcd based algorithm used for engine.

Method Details

pairFactory

public GenPolynomialRing<C> pairFactory()

Factory for base elements.

Specified by:

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

create

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

Create from numerator.

Specified by:

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

create

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

Create from numerator, denominator pair.

Specified by:

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

divide

protected GenPolynomial<C> divide(GenPolynomial<C> n,
 GenPolynomial<C> d)

Divide.

Parameters:

n - first polynomial.

d - second polynomial.

Returns:

divide(n,d)

gcd

protected GenPolynomial<C> gcd(GenPolynomial<C> n,
 GenPolynomial<C> d)

Greatest common divisor.

Parameters:

n - first polynomial.

d - second polynomial.

Returns:

gcd(n,d)

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 Quotient<C> copy(Quotient<C> c)

Copy Quotient element c.

Specified by:

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

Parameters:

c -

Returns:

a copy of c.

getZERO

public Quotient<C> getZERO()

Get the zero element.

Specified by:

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

Returns:

0 as Quotient.

getONE

public Quotient<C> getONE()

Get the one element.

Specified by:

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

Returns:

1 as Quotient.

generators

public List<Quotient<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:

true.

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 Quotient<C> fromInteger(BigInteger a)

Get a Quotient element from a BigInteger value.

Specified by:

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

Parameters:

a - BigInteger.

Returns:

a Quotient.

fromInteger

public Quotient<C> fromInteger(long a)

Get a Quotient element from a long value.

Specified by:

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

Parameters:

a - long.

Returns:

a Quotient.

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 quotient ring.

Overrides:

hashCode in class Object

See Also:

• Object.hashCode()

random

public Quotient<C> random(int n)

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

Generate a random quotient 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 quotient polynomial.

random

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

Quotient 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 quotient element.

parse

public Quotient<C> parse(String s)

Parse Quotient from String. Syntax: "{ polynomial | polynomial }" or "{ polynomial }" or " polynomial | polynomial " or " polynomial "

Specified by:

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

Parameters:

s - String.

Returns:

Quotient from s.

parse

public Quotient<C> parse(Reader r)

Parse Quotient from Reader.

Specified by:

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

Parameters:

r - Reader.

Returns:

next Quotient from r.

extensionDegree

public long extensionDegree()

Degree of extension field.

Returns:

degree of this extension field, -1 for transcendental extension.