Class SolvableResidueRing<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.application.SolvableResidueRing<C>

All Implemented Interfaces:

AbelianGroupFactory<SolvableResidue<C>>, ElemFactory<SolvableResidue<C>>, MonoidFactory<SolvableResidue<C>>, QuotPairFactory<GenPolynomial<C>, SolvableResidue<C>>, RingFactory<SolvableResidue<C>>, ValueFactory<GenPolynomial<C>, SolvableResidue<C>>, Serializable

public class SolvableResidueRing<C extends GcdRingElem<C>>
extends Object
implements RingFactory<SolvableResidue<C>>, QuotPairFactory<GenPolynomial<C>, SolvableResidue<C>>, ValueFactory<GenPolynomial<C>, SolvableResidue<C>>

SolvableResidue ring factory based on GenSolvablePolynomialRing with GcdRingFactory interface. Objects of this class are immutable.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected final SolvableGroebnerBaseAbstract<C>	bb	Groebner base engine.
final SolvableIdeal<C>	ideal	Solvable polynomial ideal for the reduction.
protected int	isField	Indicator if this ring is a field.
private static final org.apache.logging.log4j.Logger	logger
final GenSolvablePolynomialRing<C>	ring	Polynomial ring of the factory.

Constructor Summary

Constructors

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

Method Summary

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

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

bb

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

Groebner base engine.

ideal

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

Solvable polynomial ideal for the reduction.

ring

public final GenSolvablePolynomialRing<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 Details

SolvableResidueRing

public SolvableResidueRing(SolvableIdeal<C> i)

The constructor creates a SolvableResidueRing object from an Ideal.

Parameters:

i - polynomial ideal.

SolvableResidueRing

public SolvableResidueRing(SolvableIdeal<C> i,
 boolean isMaximal)

The constructor creates a SolvableResidueRing object from an SolvableIdeal.

Parameters:

i - solvable polynomial ideal.

isMaximal - true, if ideal is maxmal.

Method Details

pairFactory

public GenSolvablePolynomialRing<C> pairFactory()

Factory for base elements.

Specified by:

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

valueFactory

public GenSolvablePolynomialRing<C> valueFactory()

Factory for base elements.

Specified by:

valueFactory in interface ValueFactory<GenPolynomial<C extends GcdRingElem<C>>, SolvableResidue<C extends GcdRingElem<C>>>

create

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

Create from numerator.

Specified by:

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

Specified by:

create in interface ValueFactory<GenPolynomial<C extends GcdRingElem<C>>, SolvableResidue<C extends GcdRingElem<C>>>

create

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

Create from numerator, denominator pair.

Specified by:

create in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>, SolvableResidue<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 SolvableResidue<C> copy(SolvableResidue<C> c)

Copy SolvableResidue element c.

Specified by:

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

Parameters:

c -

Returns:

a copy of c.

getZERO

public SolvableResidue<C> getZERO()

Get the zero element.

Specified by:

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

Returns:

0 as SolvableResidue.

getONE

public SolvableResidue<C> getONE()

Get the one element.

Specified by:

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

Returns:

1 as SolvableResidue.

generators

public List<SolvableResidue<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 SolvableResidue<C> fromInteger(BigInteger a)

Get a SolvableResidue element from a BigInteger value.

Specified by:

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

Parameters:

a - BigInteger.

Returns:

a SolvableResidue.

fromInteger

public SolvableResidue<C> fromInteger(long a)

Get a SolvableResidue element from a long value.

Specified by:

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

Parameters:

a - long.

Returns:

a SolvableResidue.

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 residue ring.

Overrides:

hashCode in class Object

See Also:

• Object.hashCode()

random

public SolvableResidue<C> random(int n)

SolvableResidue 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 SolvableResidue<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 SolvableResidue<C> random(int n,
 Random rnd)

SolvableResidue 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 SolvableResidue<C> parse(String s)

Parse SolvableResidue from String.

Specified by:

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

Parameters:

s - String.

Returns:

SolvableResidue from s.

parse

public SolvableResidue<C> parse(Reader r)

Parse SolvableResidue from Reader.

Specified by:

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

Parameters:

r - Reader.

Returns:

next SolvableResidue from r.