Class RealAlgebraicRing<C extends GcdRingElem<C> & Rational>

java.lang.Object

edu.jas.application.RealAlgebraicRing<C>

All Implemented Interfaces:

AbelianGroupFactory<RealAlgebraicNumber<C>>, ElemFactory<RealAlgebraicNumber<C>>, MonoidFactory<RealAlgebraicNumber<C>>, RingFactory<RealAlgebraicNumber<C>>, Serializable

public class RealAlgebraicRing<C extends GcdRingElem<C> & Rational>
extends Object
implements RingFactory<RealAlgebraicNumber<C>>

Real algebraic number factory class based on bi-variate real algebraic numbers. Objects of this class are immutable with the exception of the isolating intervals. Bi-variate ideal implementation is in version 3614 2011-04-28 09:20:34Z.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
(package private) final ResidueRing<C>	algebraic	Representing ResidueRing.
protected BigRational	eps	Epsilon of the isolating rectangle for a complex root.
private static final org.apache.logging.log4j.Logger	logger
final int	PRECISION	Precision of the isolating rectangle for a complex root.
final RealAlgebraicRing<RealAlgebraicNumber<C>>	realRing	Recursive real root ring.
(package private) RealRootTuple<C>	root	Isolating intervals for the real algebraic roots of the real and imaginary part.
(package private) final IdealWithUniv<C>	univs	Representing ideal with univariate polynomials IdealWithUniv.

Constructor Summary

Constructors

Constructor	Description
RealAlgebraicRing(IdealWithUniv<C> m, ResidueRing<C> a, RealRootTuple<C> r)	The constructor creates a RealAlgebraicNumber factory object from a IdealWithUniv, ResidueRing and a root tuple.
RealAlgebraicRing(IdealWithUniv<C> m, RealRootTuple<C> root)	The constructor creates a RealAlgebraicNumber factory object from a IdealWithUniv and a root tuple.
RealAlgebraicRing(IdealWithUniv<C> m, RealRootTuple<C> root, boolean isField)	The constructor creates a RealAlgebraicNumber factory object from a IdealWithUniv and a root tuple.

Method Summary

Modifier and Type	Method	Description
BigInteger	characteristic()	Characteristic of this ring.
RealAlgebraicNumber<C>	copy(RealAlgebraicNumber<C> c)	Copy RealAlgebraicNumber element c.
boolean	equals(Object b)	Comparison with any other object.
RealAlgebraicNumber<C>	fromInteger(long a)	Get a RealAlgebraicNumber element from a long value.
RealAlgebraicNumber<C>	fromInteger(BigInteger a)	Get a RealAlgebraicNumber element from a BigInteger value.
List<RealAlgebraicNumber<C>>	generators()	Get a list of the generating elements.
BigRational	getEps()	Get epsilon.
RealAlgebraicNumber<C>	getONE()	Get the one element.
RealRootTuple<C>	getRoot()	Get rectangle for the complex root.
RealAlgebraicNumber<C>	getZERO()	Get the zero element.
int	hashCode()	Hash code for this RealAlgebraicNumber.
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.
RealAlgebraicNumber<C>	parse(Reader r)	Parse RealAlgebraicNumber from Reader.
RealAlgebraicNumber<C>	parse(String s)	Parse RealAlgebraicNumber from String.
RealAlgebraicNumber<C>	random(int n)	RealAlgebraicNumber random.
RealAlgebraicNumber<C>	random(int n, Random rnd)	RealAlgebraicNumber random.
void	refineRoot(BigRational e)	Refine root.
void	setEps(C e)	Set a new epsilon.
void	setEps(BigRational e)	Set a new epsilon.
void	setField(boolean isField)	Assert that this ring is a field.
void	setRoot(RealRootTuple<C> v)	Set a refined rectangle for the complex root.
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

univs

final IdealWithUniv<C extends GcdRingElem<C> & Rational> univs

Representing ideal with univariate polynomials IdealWithUniv.

algebraic

final ResidueRing<C extends GcdRingElem<C> & Rational> algebraic

Representing ResidueRing.

root

RealRootTuple<C extends GcdRingElem<C> & Rational> root

Isolating intervals for the real algebraic roots of the real and imaginary part. Note: intervals may shrink eventually.

realRing

public final RealAlgebraicRing<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>> realRing

Recursive real root ring.

eps

protected BigRational eps

Epsilon of the isolating rectangle for a complex root.

PRECISION

public final int PRECISION

Precision of the isolating rectangle for a complex root.

See Also:

• Constant Field Values

logger

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

Constructor Details

RealAlgebraicRing

public RealAlgebraicRing(IdealWithUniv<C> m,
 ResidueRing<C> a,
 RealRootTuple<C> r)

The constructor creates a RealAlgebraicNumber factory object from a IdealWithUniv, ResidueRing and a root tuple.

Parameters:

m - module IdealWithUniv<C>.

a - module ResidueRing<C>.

r - isolating rectangle for a complex root.

RealAlgebraicRing

public RealAlgebraicRing(IdealWithUniv<C> m,
 RealRootTuple<C> root)

The constructor creates a RealAlgebraicNumber factory object from a IdealWithUniv and a root tuple.

Parameters:

m - module IdealWithUniv<C>.

root - isolating rectangle for a complex root.

RealAlgebraicRing

public RealAlgebraicRing(IdealWithUniv<C> m,
 RealRootTuple<C> root,
 boolean isField)

The constructor creates a RealAlgebraicNumber factory object from a IdealWithUniv and a root tuple.

Parameters:

m - module IdealWithUniv<C>.

root - isolating rectangle for a complex root.

isField - indicator if m is maximal.

Method Details

setRoot

public void setRoot(RealRootTuple<C> v)

Set a refined rectangle for the complex root. Note: rectangle may shrink eventually.

Parameters:

v - rectangle.

getRoot

public RealRootTuple<C> getRoot()

Get rectangle for the complex root.

Returns:

v rectangle.

getEps

public BigRational getEps()

Get epsilon.

Returns:

epsilon.

setEps

public void setEps(C e)

Set a new epsilon.

Parameters:

e - epsilon.

setEps

public void setEps(BigRational e)

Set a new epsilon.

Parameters:

e - epsilon.

refineRoot

public void refineRoot(BigRational e)

Refine root.

Parameters:

e - epsilon.

isFinite

public boolean isFinite()

Is this structure finite or infinite.

Specified by:

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

Returns:

true if this structure is finite, else false.

See Also:

• ElemFactory.isFinite()

copy

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

Copy RealAlgebraicNumber element c.

Specified by:

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

Parameters:

c -

Returns:

a copy of c.

getZERO

public RealAlgebraicNumber<C> getZERO()

Get the zero element.

Specified by:

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

Returns:

0 as RealAlgebraicNumber.

getONE

public RealAlgebraicNumber<C> getONE()

Get the one element.

Specified by:

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

Returns:

1 as RealAlgebraicNumber.

generators

public List<RealAlgebraicNumber<C>> generators()

Get a list of the generating elements.

Specified by:

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

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> & Rational>

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> & Rational>

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> & Rational>

Returns:

true if algebraic is prime, else false.

setField

public void setField(boolean isField)

Assert that this ring is a field.

Parameters:

isField - true if this ring is a field, else false.

characteristic

public BigInteger characteristic()

Characteristic of this ring.

Specified by:

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

Returns:

characteristic of this ring.

fromInteger

public RealAlgebraicNumber<C> fromInteger(BigInteger a)

Get a RealAlgebraicNumber element from a BigInteger value.

Specified by:

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

Parameters:

a - BigInteger.

Returns:

a RealAlgebraicNumber.

fromInteger

public RealAlgebraicNumber<C> fromInteger(long a)

Get a RealAlgebraicNumber element from a long value.

Specified by:

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

Parameters:

a - long.

Returns:

a RealAlgebraicNumber.

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> & Rational>

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 RealAlgebraicNumber.

Overrides:

hashCode in class Object

See Also:

• Object.hashCode()

random

public RealAlgebraicNumber<C> random(int n)

RealAlgebraicNumber random.

Specified by:

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

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

Returns:

a random integer mod modul.

random

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

RealAlgebraicNumber random.

Specified by:

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

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

rnd - is a source for random bits.

Returns:

a random integer mod modul.

parse

public RealAlgebraicNumber<C> parse(String s)

Parse RealAlgebraicNumber from String.

Specified by:

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

Parameters:

s - String.

Returns:

RealAlgebraicNumber from s.

parse

public RealAlgebraicNumber<C> parse(Reader r)

Parse RealAlgebraicNumber from Reader.

Specified by:

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

Parameters:

r - Reader.

Returns:

next RealAlgebraicNumber from r.