edu.jas.poly

Class AlgebraicNumber<C extends RingElem<C>>

java.lang.Object

edu.jas.poly.AlgebraicNumber<C>

All Implemented Interfaces:

AbelianGroupElem<AlgebraicNumber<C>>, Element<AlgebraicNumber<C>>, GcdRingElem<AlgebraicNumber<C>>, MonoidElem<AlgebraicNumber<C>>, RingElem<AlgebraicNumber<C>>, java.io.Serializable, java.lang.Comparable<AlgebraicNumber<C>>

public class AlgebraicNumber<C extends RingElem<C>>
extends java.lang.Object
implements GcdRingElem<AlgebraicNumber<C>>

Algebraic number class. Based on GenPolynomial with RingElem interface. Objects of this class are immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected int	isunit Flag to remember if this algebraic number is a unit. -1 is unknown, 1 is unit, 0 not a unit.
AlgebraicNumberRing<C>	ring Ring part of the data structure.
GenPolynomial<C>	val Value part of the element data structure.

Constructor Summary

Constructors

Constructor and Description
AlgebraicNumber(AlgebraicNumberRing<C> r) The constructor creates a AlgebraicNumber object from a GenPolynomial object module.
AlgebraicNumber(AlgebraicNumberRing<C> r, GenPolynomial<C> a) The constructor creates a AlgebraicNumber object from AlgebraicNumberRing modul and a GenPolynomial value.

Method Summary

Modifier and Type	Method and Description
AlgebraicNumber<C>	abs() AlgebraicNumber absolute value.
int	compareTo(AlgebraicNumber<C> b) AlgebraicNumber comparison.
AlgebraicNumber<C>	copy() Copy this.
AlgebraicNumber<C>	divide(AlgebraicNumber<C> S) AlgebraicNumber division.
AlgebraicNumber<C>[]	egcd(AlgebraicNumber<C> S) AlgebraicNumber extended greatest common divisor.
boolean	equals(java.lang.Object b) Comparison with any other object.
AlgebraicNumberRing<C>	factory() Get the corresponding element factory.
AlgebraicNumber<C>	gcd(AlgebraicNumber<C> S) AlgebraicNumber greatest common divisor.
GenPolynomial<C>	getVal() Get the value part.
int	hashCode() Hash code for this AlgebraicNumber.
AlgebraicNumber<C>	inverse() AlgebraicNumber inverse.
boolean	isONE() Is AlgebraicNumber one.
boolean	isRootOfUnity() Is AlgebraicNumber a root of unity.
boolean	isUnit() Is AlgebraicNumber unit.
boolean	isZERO() Is AlgebraicNumber zero.
AlgebraicNumber<C>	monic() AlgebraicNumber monic.
AlgebraicNumber<C>	multiply(AlgebraicNumber<C> S) AlgebraicNumber multiplication.
AlgebraicNumber<C>	multiply(C c) AlgebraicNumber multiplication.
AlgebraicNumber<C>	multiply(GenPolynomial<C> c) AlgebraicNumber multiplication.
AlgebraicNumber<C>	negate() AlgebraicNumber negate.
AlgebraicNumber<C>[]	quotientRemainder(AlgebraicNumber<C> S) Quotient and remainder by division of this by S.
AlgebraicNumber<C>	remainder(AlgebraicNumber<C> S) AlgebraicNumber remainder.
int	signum() AlgebraicNumber signum.
AlgebraicNumber<C>	subtract(AlgebraicNumber<C> S) AlgebraicNumber subtraction.
AlgebraicNumber<C>	sum(AlgebraicNumber<C> S) AlgebraicNumber summation.
AlgebraicNumber<C>	sum(C c) AlgebraicNumber summation.
AlgebraicNumber<C>	sum(GenPolynomial<C> c) AlgebraicNumber summation.
java.lang.String	toScript() Get a scripting compatible string representation.
java.lang.String	toScriptFactory() Get a scripting compatible string representation of the factory.
java.lang.String	toString() Get the String representation as RingElem.

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface edu.jas.structure.RingElem

leftGcd, rightGcd

Methods inherited from interface edu.jas.structure.MonoidElem

leftDivide, leftRemainder, power, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Field Detail

ring

public final AlgebraicNumberRing<C extends RingElem<C>> ring

Ring part of the data structure.

val

public final GenPolynomial<C extends RingElem<C>> val

Value part of the element data structure.

isunit

protected int isunit

Flag to remember if this algebraic number is a unit. -1 is unknown, 1 is unit, 0 not a unit.

Constructor Detail

AlgebraicNumber

public AlgebraicNumber(AlgebraicNumberRing<C> r,
                       GenPolynomial<C> a)

The constructor creates a AlgebraicNumber object from AlgebraicNumberRing modul and a GenPolynomial value.

Parameters:

r - ring AlgebraicNumberRing.

a - value GenPolynomial.

AlgebraicNumber

public AlgebraicNumber(AlgebraicNumberRing<C> r)

The constructor creates a AlgebraicNumber object from a GenPolynomial object module.

Parameters:

r - ring AlgebraicNumberRing.

Method Detail

getVal

public GenPolynomial<C> getVal()

Get the value part.

Returns:

val.

factory

public AlgebraicNumberRing<C> factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<AlgebraicNumber<C extends RingElem<C>>>

Returns:

factory for this Element.

See Also:

Element.factory()

copy

public AlgebraicNumber<C> copy()

Copy this.

Specified by:

copy in interface Element<AlgebraicNumber<C extends RingElem<C>>>

Returns:

Creates and returns a copy of this Element.

See Also:

Element.copy()

isZERO

public boolean isZERO()

Is AlgebraicNumber zero.

Specified by:

isZERO in interface AbelianGroupElem<AlgebraicNumber<C extends RingElem<C>>>

Returns:

If this is 0 then true is returned, else false.

See Also:

AbelianGroupElem.isZERO()

isONE

public boolean isONE()

Is AlgebraicNumber one.

Specified by:

isONE in interface MonoidElem<AlgebraicNumber<C extends RingElem<C>>>

Returns:

If this is 1 then true is returned, else false.

See Also:

MonoidElem.isONE()

isUnit

public boolean isUnit()

Is AlgebraicNumber unit.

Specified by:

isUnit in interface MonoidElem<AlgebraicNumber<C extends RingElem<C>>>

Returns:

If this is a unit then true is returned, else false.

See Also:

MonoidElem.isUnit()

isRootOfUnity

public boolean isRootOfUnity()

Is AlgebraicNumber a root of unity.

Returns:

true if |this**i| == 1, for some 0 < i ≤ deg(modul), else false.

toString

public java.lang.String toString()

Get the String representation as RingElem.

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 Element<AlgebraicNumber<C extends RingElem<C>>>

Returns:

script compatible representation for this Element.

See Also:

Element.toScript()

toScriptFactory

public java.lang.String toScriptFactory()

Get a scripting compatible string representation of the factory.

Specified by:

toScriptFactory in interface Element<AlgebraicNumber<C extends RingElem<C>>>

Returns:

script compatible representation for this ElemFactory.

See Also:

Element.toScriptFactory()

compareTo

public int compareTo(AlgebraicNumber<C> b)

AlgebraicNumber comparison.

Specified by:

compareTo in interface Element<AlgebraicNumber<C extends RingElem<C>>>

Specified by:

compareTo in interface java.lang.Comparable<AlgebraicNumber<C extends RingElem<C>>>

Parameters:

b - AlgebraicNumber.

Returns:

sign(this-b).

equals

public boolean equals(java.lang.Object b)

Comparison with any other object.

Specified by:

equals in interface Element<AlgebraicNumber<C extends RingElem<C>>>

Overrides:

equals in class java.lang.Object

Returns:

true if this is equal to b, else false.

See Also:

Object.equals(java.lang.Object)

hashCode

public int hashCode()

Hash code for this AlgebraicNumber.

Specified by:

hashCode in interface Element<AlgebraicNumber<C extends RingElem<C>>>

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

abs

public AlgebraicNumber<C> abs()

AlgebraicNumber absolute value.

Specified by:

abs in interface AbelianGroupElem<AlgebraicNumber<C extends RingElem<C>>>

Returns:

the absolute value of this.

See Also:

AbelianGroupElem.abs()

sum

public AlgebraicNumber<C> sum(AlgebraicNumber<C> S)

AlgebraicNumber summation.

Specified by:

sum in interface AbelianGroupElem<AlgebraicNumber<C extends RingElem<C>>>

Parameters:

S - AlgebraicNumber.

Returns:

this+S.

sum

public AlgebraicNumber<C> sum(GenPolynomial<C> c)

AlgebraicNumber summation.

Parameters:

c - coefficient.

Returns:

this+c.

sum

public AlgebraicNumber<C> sum(C c)

AlgebraicNumber summation.

Parameters:

c - polynomial.

Returns:

this+c.

negate

public AlgebraicNumber<C> negate()

AlgebraicNumber negate.

Specified by:

negate in interface AbelianGroupElem<AlgebraicNumber<C extends RingElem<C>>>

Returns:

-this.

See Also:

AbelianGroupElem.negate()

signum

public int signum()

AlgebraicNumber signum.

Specified by:

signum in interface AbelianGroupElem<AlgebraicNumber<C extends RingElem<C>>>

Returns:

signum(this).

See Also:

AbelianGroupElem.signum()

subtract

public AlgebraicNumber<C> subtract(AlgebraicNumber<C> S)

AlgebraicNumber subtraction.

Specified by:

subtract in interface AbelianGroupElem<AlgebraicNumber<C extends RingElem<C>>>

Parameters:

S - AlgebraicNumber.

Returns:

this-S.

divide

public AlgebraicNumber<C> divide(AlgebraicNumber<C> S)

AlgebraicNumber division.

Specified by:

divide in interface MonoidElem<AlgebraicNumber<C extends RingElem<C>>>

Parameters:

S - AlgebraicNumber.

Returns:

this/S.

inverse

public AlgebraicNumber<C> inverse()

AlgebraicNumber inverse.

Specified by:

inverse in interface MonoidElem<AlgebraicNumber<C extends RingElem<C>>>

Returns:

S with S = 1/this if defined.

Throws:

NotInvertibleException - if the element is not invertible.

See Also:

MonoidElem.inverse()

remainder

public AlgebraicNumber<C> remainder(AlgebraicNumber<C> S)

AlgebraicNumber remainder.

Specified by:

remainder in interface MonoidElem<AlgebraicNumber<C extends RingElem<C>>>

Parameters:

S - AlgebraicNumber.

Returns:

this - (this/S)*S.

quotientRemainder

public AlgebraicNumber<C>[] quotientRemainder(AlgebraicNumber<C> S)

Quotient and remainder by division of this by S.

Specified by:

quotientRemainder in interface MonoidElem<AlgebraicNumber<C extends RingElem<C>>>

Parameters:

S - a AlgebraicNumber

Returns:

[this/S, this - (this/S)*S].

multiply

public AlgebraicNumber<C> multiply(AlgebraicNumber<C> S)

AlgebraicNumber multiplication.

Specified by:

multiply in interface MonoidElem<AlgebraicNumber<C extends RingElem<C>>>

Parameters:

S - AlgebraicNumber.

Returns:

this*S.

multiply

public AlgebraicNumber<C> multiply(C c)

AlgebraicNumber multiplication.

Parameters:

c - coefficient.

Returns:

this*c.

multiply

public AlgebraicNumber<C> multiply(GenPolynomial<C> c)

AlgebraicNumber multiplication.

Parameters:

c - polynomial.

Returns:

this*c.

monic

public AlgebraicNumber<C> monic()

AlgebraicNumber monic.

Returns:

this with monic value part.

gcd

public AlgebraicNumber<C> gcd(AlgebraicNumber<C> S)

AlgebraicNumber greatest common divisor.

Specified by:

gcd in interface RingElem<AlgebraicNumber<C extends RingElem<C>>>

Parameters:

S - AlgebraicNumber.

Returns:

gcd(this,S).

egcd

public AlgebraicNumber<C>[] egcd(AlgebraicNumber<C> S)

AlgebraicNumber extended greatest common divisor.

Specified by:

egcd in interface RingElem<AlgebraicNumber<C extends RingElem<C>>>

Parameters:

S - AlgebraicNumber.

Returns:

[ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).