Package edu.jas.application

Class SolvableLocalResidueRing<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.application.SolvableLocalResidueRing<C>

All Implemented Interfaces:

AbelianGroupFactory<SolvableLocalResidue<C>>, ElemFactory<SolvableLocalResidue<C>>, MonoidFactory<SolvableLocalResidue<C>>, QuotPairFactory<GenPolynomial<C>,SolvableLocalResidue<C>>, RingFactory<SolvableLocalResidue<C>>, java.io.Serializable

public class SolvableLocalResidueRing<C extends GcdRingElem<C>>
extends java.lang.Object
implements RingFactory<SolvableLocalResidue<C>>, QuotPairFactory<GenPolynomial<C>,SolvableLocalResidue<C>>

SolvableLocalResidue ring factory for SolvableLocalResidue based on GenSolvablePolynomial with GcdRingElem interface. Objects of this class are immutable. It represents the "classical quotient ring modulo an ideal".

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected SolvableGroebnerBaseAbstract<C>	bb	Groebner base engine.
SolvableSyzygyAbstract<C>	engine	Syzygy engine of the factory.
GreatestCommonDivisorAbstract<C>	fdengine	FD engine of the factory.
SolvableIdeal<C>	ideal	Solvable polynomial ideal for the reduction.
protected int	isField	Indicator if this ring is a field.
GenSolvablePolynomialRing<C>	ring	Solvable polynomial ring of the factory.

Constructor Summary

Constructors

Constructor	Description
SolvableLocalResidueRing(SolvableIdeal<C> i)	The constructor creates a SolvableLocalResidueRing object from a SolvableIdeal.

Method Summary

Modifier and Type	Method	Description
java.math.BigInteger	characteristic()	Characteristic of this ring.
SolvableLocalResidue<C>	copy(SolvableLocalResidue<C> c)	Copy SolvableLocalResidue element c.
SolvableLocalResidue<C>	create(GenPolynomial<C> n)	Create from numerator.
SolvableLocalResidue<C>	create(GenPolynomial<C> n, GenPolynomial<C> d)	Create from numerator, denominator pair.
boolean	equals(java.lang.Object b)	Comparison with any other object.
SolvableLocalResidue<C>	fromInteger(long a)	Get a SolvableLocalResidue element from a long value.
SolvableLocalResidue<C>	fromInteger(java.math.BigInteger a)	Get a SolvableLocalResidue element from a BigInteger value.
java.util.List<SolvableLocalResidue<C>>	generators()	Get a list of the generating elements.
SolvableLocalResidue<C>	getONE()	Get the one element.
SolvableLocalResidue<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.
GenSolvablePolynomialRing<C>	pairFactory()	Factory for base elements.
SolvableLocalResidue<C>	parse(java.io.Reader r)	Parse SolvableLocalResidue from Reader.
SolvableLocalResidue<C>	parse(java.lang.String s)	Parse SolvableLocalResidue from String.
SolvableLocalResidue<C>	random(int n)	SolvableLocalResidue random.
SolvableLocalResidue<C>	random(int k, int l, int d, float q)	Generate a random quotient.
SolvableLocalResidue<C>	random(int n, java.util.Random rnd)	SolvableLocalResidue 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

Methods inherited from interface edu.jas.structure.ElemFactory

valueOf

Field Detail

ring

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

Solvable polynomial ring of the factory.

ideal

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

Solvable polynomial ideal for the reduction.

engine

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

Syzygy engine of the factory.

fdengine

public final GreatestCommonDivisorAbstract<C extends GcdRingElem<C>> fdengine

FD engine of the factory.

bb

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

Groebner base engine.

isField

protected int isField

Indicator if this ring is a field.

Constructor Detail

SolvableLocalResidueRing

public SolvableLocalResidueRing(SolvableIdeal<C> i)

The constructor creates a SolvableLocalResidueRing object from a SolvableIdeal.

Parameters:

i - ideal in solvable polynomial ring.

Method Detail

pairFactory

public GenSolvablePolynomialRing<C> pairFactory()

Factory for base elements.

Specified by:

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

create

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

Create from numerator.

Specified by:

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

create

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

Create from numerator, denominator pair.

Specified by:

create in interface QuotPairFactory<GenPolynomial<C extends GcdRingElem<C>>,SolvableLocalResidue<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.

copy

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

Copy SolvableLocalResidue element c.

Specified by:

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

Parameters:

c -

Returns:

a copy of c.

getZERO

public SolvableLocalResidue<C> getZERO()

Get the zero element.

Specified by:

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

Returns:

0 as SolvableLocalResidue.

getONE

public SolvableLocalResidue<C> getONE()

Get the one element.

Specified by:

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

Returns:

1 as SolvableLocalResidue.

generators

public java.util.List<SolvableLocalResidue<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.

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 java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

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

Returns:

characteristic of this ring.

fromInteger

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

Get a SolvableLocalResidue element from a BigInteger value.

Specified by:

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

Parameters:

a - BigInteger.

Returns:

a SolvableLocalResidue.

fromInteger

public SolvableLocalResidue<C> fromInteger(long a)

Get a SolvableLocalResidue element from a long value.

Specified by:

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

Parameters:

a - long.

Returns:

a SolvableLocalResidue.

toString

public java.lang.String toString()

Get the String representation as RingFactory.

Overrides:

toString in class java.lang.Object

toScript

public java.lang.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.

equals

public boolean equals(java.lang.Object b)

Comparison with any other object.

Overrides:

equals in class java.lang.Object

hashCode

public int hashCode()

Hash code for this quotient ring.

Overrides:

hashCode in class java.lang.Object

random

public SolvableLocalResidue<C> random(int n)

SolvableLocalResidue random.

Specified by:

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

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

Returns:

a random quotient element.

random

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

Generate a random quotient.

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.

random

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

SolvableLocalResidue 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 SolvableLocalResidue<C> parse(java.lang.String s)

Parse SolvableLocalResidue 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:

SolvableLocalResidue from s.

parse

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

Parse SolvableLocalResidue from Reader.

Specified by:

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

Parameters:

r - Reader.

Returns:

next SolvableLocalResidue from r.