edu.jas.root

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

java.lang.Object

edu.jas.root.RealAlgebraicRing<C>

All Implemented Interfaces:

AbelianGroupFactory<RealAlgebraicNumber<C>>, ElemFactory<RealAlgebraicNumber<C>>, MonoidFactory<RealAlgebraicNumber<C>>, RingFactory<RealAlgebraicNumber<C>>, java.io.Serializable

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

Real algebraic number factory class based on AlgebraicNumberRing with RingFactory interface. Objects of this class are immutable with the exception of the isolating intervals.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
AlgebraicNumberRing<C>	algebraic Representing AlgebraicNumberRing.
RealRootsSturm<C>	engine Real root computation engine.
protected BigRational	eps Precision of the isolating interval for a real root.
static int	PRECISION Precision of the isolating rectangle for a complex root.

Constructor Summary

Constructors

Constructor and Description
RealAlgebraicRing(GenPolynomial<C> m, Interval<C> root) The constructor creates a RealAlgebraicNumber factory object from a GenPolynomial objects module.
RealAlgebraicRing(GenPolynomial<C> m, Interval<C> root, boolean isField) The constructor creates a RealAlgebraicNumber factory object from a GenPolynomial objects module.

Method Summary

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

Field Detail

algebraic

public final AlgebraicNumberRing<C extends GcdRingElem<C> & Rational> algebraic

Representing AlgebraicNumberRing.

PRECISION

public static final int PRECISION

Precision of the isolating rectangle for a complex root.

eps

protected BigRational eps

Precision of the isolating interval for a real root.

engine

public final RealRootsSturm<C extends GcdRingElem<C> & Rational> engine

Real root computation engine.

Constructor Detail

RealAlgebraicRing

public RealAlgebraicRing(GenPolynomial<C> m,
                         Interval<C> root)

The constructor creates a RealAlgebraicNumber factory object from a GenPolynomial objects module.

Parameters:

m - module GenPolynomial.

root - isolating interval for a real root.

RealAlgebraicRing

public RealAlgebraicRing(GenPolynomial<C> m,
                         Interval<C> root,
                         boolean isField)

The constructor creates a RealAlgebraicNumber factory object from a GenPolynomial objects module.

Parameters:

m - module GenPolynomial.

root - isolating interval for a real root.

isField - indicator if m is prime.

Method Detail

getRoot

public Interval<C> getRoot()

Get the interval for the real root. Note: interval may shrink later.

Returns:

real root isolating interval

setRoot

public void setRoot(Interval<C> v)

Set a refined interval for the real root. Note: interval may shrink eventually.

Parameters:

v - interval.

getEps

public BigRational getEps()

Get the epsilon.

Returns:

eps.

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()

Refine root.

refineRoot

public void refineRoot(BigRational e)

Refine root.

Parameters:

e - epsilon.

halfInterval

public void halfInterval()

RealAlgebraicRing half interval.

isFinite

public boolean isFinite()

Is this structure finite or infinite.

Specified by:

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

Parameters:

c -

Returns:

a copy of c.

copy

public RealAlgebraicRing<C> copy()

Copy this RealAlgebraicRing.

Returns:

a copy of this.

getZERO

public RealAlgebraicNumber<C> getZERO()

Get the zero element.

Specified by:

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

Returns:

0 as RealAlgebraicNumber.

getONE

public RealAlgebraicNumber<C> getONE()

Get the one element.

Specified by:

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

Returns:

1 as RealAlgebraicNumber.

getGenerator

public RealAlgebraicNumber<C> getGenerator()

Get the generating element.

Returns:

alpha as RealAlgebraicNumber.

generators

public java.util.List<RealAlgebraicNumber<C>> generators()

Get a list of the generating elements.

Specified by:

generators in interface ElemFactory<RealAlgebraicNumber<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<RealAlgebraicNumber<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<RealAlgebraicNumber<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<RealAlgebraicNumber<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 java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

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

Returns:

characteristic of this ring.

fromInteger

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

Get a RealAlgebraicNumber element from a BigInteger value.

Specified by:

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

Parameters:

a - long.

Returns:

a RealAlgebraicNumber.

toString

public java.lang.String toString()

Get the String representation as RingFactory.

Overrides:

toString in class java.lang.Object

See Also:

Object.toString()

toScript

public java.lang.String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface ElemFactory<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>

Returns:

script compatible representation for this ElemFactory.

See Also:

ElemFactory.toScript()

equals

public boolean equals(java.lang.Object b)

Comparison with any other object.

Overrides:

equals in class java.lang.Object

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this RealAlgebraicNumber.

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

random

public RealAlgebraicNumber<C> random(int n)

RealAlgebraicNumber random.

Specified by:

random in interface ElemFactory<RealAlgebraicNumber<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,
                                     java.util.Random rnd)

RealAlgebraicNumber random.

Specified by:

random in interface ElemFactory<RealAlgebraicNumber<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(java.lang.String s)

Parse RealAlgebraicNumber from String.

Specified by:

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

Parameters:

s - String.

Returns:

RealAlgebraicNumber from s.

parse

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

Parse RealAlgebraicNumber from Reader.

Specified by:

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

Parameters:

r - Reader.

Returns:

next RealAlgebraicNumber from r.