edu.jas.root

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

java.lang.Object

edu.jas.root.ComplexAlgebraicRing<C>

All Implemented Interfaces:

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

public class ComplexAlgebraicRing<C extends GcdRingElem<C> & Rational>
extends java.lang.Object
implements RingFactory<ComplexAlgebraicNumber<C>>

Complex 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<Complex<C>>	algebraic Representing AlgebraicNumberRing.
protected ComplexRootsSturm<C>	engine Complex root computation engine.
protected BigRational	eps Epsilon of the isolating rectangle for a complex root.
static int	PRECISION Precision of the isolating rectangle for a complex root.

Constructor Summary

Constructors

Constructor and Description
ComplexAlgebraicRing(GenPolynomial<Complex<C>> m, Rectangle<C> root) The constructor creates a ComplexAlgebraicNumber factory object from a GenPolynomial objects module.
ComplexAlgebraicRing(GenPolynomial<Complex<C>> m, Rectangle<C> root, boolean isField) The constructor creates a ComplexAlgebraicNumber factory object from a GenPolynomial objects module.

Method Summary

Modifier and Type	Method and Description
java.math.BigInteger	characteristic() Characteristic of this ring.
ComplexAlgebraicNumber<C>	copy(ComplexAlgebraicNumber<C> c) Copy ComplexAlgebraicNumber element c.
void	ensureEngine() Ensure engine is initialized.
boolean	equals(java.lang.Object b) Comparison with any other object.
ComplexAlgebraicNumber<C>	fromInteger(java.math.BigInteger a) Get a ComplexAlgebraicNumber element from a BigInteger value.
ComplexAlgebraicNumber<C>	fromInteger(long a) Get a ComplexAlgebraicNumber element from a long value.
java.util.List<ComplexAlgebraicNumber<C>>	generators() Get a list of the generating elements.
BigRational	getEps() Get epsilon.
ComplexAlgebraicNumber<C>	getGenerator() Get the generating element.
ComplexAlgebraicNumber<C>	getIMAG() Get the i element.
ComplexAlgebraicNumber<C>	getONE() Get the one element.
Rectangle<C>	getRoot() Get rectangle for the complex root.
ComplexAlgebraicNumber<C>	getZERO() Get the zero element.
int	hashCode() Hash code for this ComplexAlgebraicNumber.
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.
ComplexAlgebraicNumber<C>	parse(java.io.Reader r) Parse ComplexAlgebraicNumber from Reader.
ComplexAlgebraicNumber<C>	parse(java.lang.String s) Parse ComplexAlgebraicNumber from String.
ComplexAlgebraicNumber<C>	random(int n) ComplexAlgebraicNumber random.
ComplexAlgebraicNumber<C>	random(int n, java.util.Random rnd) ComplexAlgebraicNumber 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(Rectangle<C> v) Set a refined rectangle for the complex 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<Complex<C extends GcdRingElem<C> & Rational>> algebraic

Representing AlgebraicNumberRing.

eps

protected BigRational eps

Epsilon of the isolating rectangle for a complex root.

PRECISION

public static final int PRECISION

Precision of the isolating rectangle for a complex root.

engine

protected ComplexRootsSturm<C extends GcdRingElem<C> & Rational> engine

Complex root computation engine.

Constructor Detail

ComplexAlgebraicRing

public ComplexAlgebraicRing(GenPolynomial<Complex<C>> m,
                            Rectangle<C> root)

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

Parameters:

m - module GenPolynomial<C>.

root - isolating rectangle for a complex root.

ComplexAlgebraicRing

public ComplexAlgebraicRing(GenPolynomial<Complex<C>> m,
                            Rectangle<C> root,
                            boolean isField)

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

Parameters:

m - module GenPolynomial<C>.

root - isolating rectangle for a complex root.

isField - indicator if m is prime.

Method Detail

setRoot

public void setRoot(Rectangle<C> v)

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

Parameters:

v - rectangle.

getRoot

public Rectangle<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()

Refine root.

ensureEngine

public void ensureEngine()

Ensure engine is initialized.

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<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>

Returns:

true if this structure is finite, else false.

See Also:

ElemFactory.isFinite()

copy

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

Copy ComplexAlgebraicNumber element c.

Specified by:

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

Parameters:

c -

Returns:

a copy of c.

getZERO

public ComplexAlgebraicNumber<C> getZERO()

Get the zero element.

Specified by:

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

Returns:

0 as ComplexAlgebraicNumber.

getONE

public ComplexAlgebraicNumber<C> getONE()

Get the one element.

Specified by:

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

Returns:

1 as ComplexAlgebraicNumber.

getIMAG

public ComplexAlgebraicNumber<C> getIMAG()

Get the i element.

Returns:

i as ComplexAlgebraicNumber.

getGenerator

public ComplexAlgebraicNumber<C> getGenerator()

Get the generating element.

Returns:

alpha as ComplexAlgebraicNumber.

generators

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

Get a list of the generating elements.

Specified by:

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

Returns:

characteristic of this ring.

fromInteger

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

Get a ComplexAlgebraicNumber element from a BigInteger value.

Specified by:

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

Parameters:

a - BigInteger.

Returns:

a ComplexAlgebraicNumber.

fromInteger

public ComplexAlgebraicNumber<C> fromInteger(long a)

Get a ComplexAlgebraicNumber element from a long value.

Specified by:

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

Parameters:

a - long.

Returns:

a ComplexAlgebraicNumber.

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<ComplexAlgebraicNumber<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 ComplexAlgebraicNumber.

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

random

public ComplexAlgebraicNumber<C> random(int n)

ComplexAlgebraicNumber random.

Specified by:

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

Parameters:

n - such that 0 ≤ v ≤ (2ⁿ-1).

Returns:

a random integer mod modul.

random

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

ComplexAlgebraicNumber random.

Specified by:

random in interface ElemFactory<ComplexAlgebraicNumber<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 ComplexAlgebraicNumber<C> parse(java.lang.String s)

Parse ComplexAlgebraicNumber from String.

Specified by:

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

Parameters:

s - String.

Returns:

ComplexAlgebraicNumber from s.

parse

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

Parse ComplexAlgebraicNumber from Reader.

Specified by:

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

Parameters:

r - Reader.

Returns:

next ComplexAlgebraicNumber from r.