edu.jas.poly
Class AlgebraicNumber<C extends GcdRingElem<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.Cloneable, java.lang.Comparable<AlgebraicNumber<C>>

public class AlgebraicNumber<C extends GcdRingElem<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

protected int	isunit Flag to remember if this algebraic number is a unit
AlgebraicNumberRing<C>	ring Ring part of the data structure.
GenPolynomial<C>	val Value part of the element data structure.

Constructor Summary

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

AlgebraicNumber<C>	abs() AlgebraicNumber absolute value.
AlgebraicNumber<C>	clone() Clone this.
int	compareTo(AlgebraicNumber<C> b) AlgebraicNumber comparison.
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.
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	isUnit() Is AlgebraicNumber unit.
boolean	isZERO() Is AlgebraicNumber zero.
AlgebraicNumber<C>	monic() AlgebraicNumber monic.
AlgebraicNumber<C>	multiply(AlgebraicNumber<C> S) AlgebraicNumber multiplication.
AlgebraicNumber<C>	negate() AlgebraicNumber negate.
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.
java.lang.String	toString() Get the String representation as RingElem.

Methods inherited from class java.lang.Object

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

Field Detail

ring

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

Ring part of the data structure.

val

public final GenPolynomial<C extends GcdRingElem<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.

clone

public AlgebraicNumber<C> clone()

Clone this.

Specified by:

clone in interface Element<AlgebraicNumber<C extends GcdRingElem<C>>>

Overrides:

clone in class java.lang.Object

See Also:

Object.clone()

Returns:

Creates and returns a copy of this Elemnt.

isZERO

public boolean isZERO()

Is AlgebraicNumber zero.

Specified by:

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

See Also:

AbelianGroupElem.isZERO()

Returns:

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

isONE

public boolean isONE()

Is AlgebraicNumber one.

Specified by:

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

See Also:

MonoidElem.isONE()

Returns:

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

isUnit

public boolean isUnit()

Is AlgebraicNumber unit.

Specified by:

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

See Also:

MonoidElem.isUnit()

Returns:

If this is a unit then true is returned, 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()

compareTo

public int compareTo(AlgebraicNumber<C> b)

AlgebraicNumber comparison.

Specified by:

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

Specified by:

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

Overrides:

equals in class java.lang.Object

See Also:

Object.equals(java.lang.Object)

Returns:

true if this is equal to b, else false.

hashCode

public int hashCode()

Hash code for this AlgebraicNumber.

Specified by:

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

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

Returns:

the hashCode.

abs

public AlgebraicNumber<C> abs()

AlgebraicNumber absolute value.

Specified by:

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

See Also:

AbelianGroupElem.abs()

Returns:

the absolute value of this.

sum

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

AlgebraicNumber summation.

Specified by:

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

Parameters:

S - AlgebraicNumber.

Returns:

this+S.

negate

public AlgebraicNumber<C> negate()

AlgebraicNumber negate.

Specified by:

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

See Also:

AbelianGroupElem.negate()

Returns:

-this.

signum

public int signum()

AlgebraicNumber signum.

Specified by:

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

See Also:

AbelianGroupElem.signum()

Returns:

signum(this).

subtract

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

AlgebraicNumber subtraction.

Specified by:

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

Parameters:

S - AlgebraicNumber.

Returns:

this/S.

inverse

public AlgebraicNumber<C> inverse()

AlgebraicNumber inverse.

Specified by:

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

Throws:

NotInvertibleException - if the element is not invertible.

See Also:

MonoidElem.inverse()

Returns:

S with S = 1/this if defined.

remainder

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

AlgebraicNumber remainder.

Specified by:

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

Parameters:

S - AlgebraicNumber.

Returns:

this - (this/S)*S.

multiply

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

AlgebraicNumber multiplication.

Specified by:

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

Parameters:

S - AlgebraicNumber.

Returns:

this*S.

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 GcdRingElem<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 GcdRingElem<C>>>

Parameters:

S - AlgebraicNumber.

Returns:

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