edu.jas.application
Class Residue<C extends RingElem<C>>

java.lang.Object
  edu.jas.application.Residue<C>

All Implemented Interfaces:

AbelianGroupElem<Residue<C>>, Element<Residue<C>>, MonoidElem<Residue<C>>, RingElem<Residue<C>>, java.io.Serializable, java.lang.Cloneable, java.lang.Comparable<Residue<C>>

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

Residue ring element based on GenPolynomial with RingElem interface. Objects of this class are (nearly) immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

protected int	isunit Flag to remember if this residue element is a unit
protected ResidueRing<C>	ring Residue class factory data structure.
protected GenPolynomial<C>	val Value part of the element data structure.

Constructor Summary

Residue(ResidueRing<C> r)
The constructor creates a Residue object from a ring factory.

Residue(ResidueRing<C> r, GenPolynomial<C> a)
The constructor creates a Residue object from a ring factory and a polynomial.

Residue(ResidueRing<C> r, GenPolynomial<C> a, int u)
The constructor creates a Residue object from a ring factory, a polynomial and an indicator if a is a unit.

Method Summary

Residue<C>	abs() Residue absolute value.
Residue<C>	clone() Clone this.
int	compareTo(Residue<C> b) Residue comparison.
Residue<C>	divide(Residue<C> S) Residue division.
Residue<C>[]	egcd(Residue<C> b) Extended greatest common divisor.
boolean	equals(java.lang.Object b) Comparison with any other object.
Residue<C>	gcd(Residue<C> b) Greatest common divisor.
int	hashCode() Hash code for this local.
Residue<C>	inverse() Residue inverse.
boolean	isONE() Is Residue one.
boolean	isUnit() Is Residue unit.
boolean	isZERO() Is Residue zero.
Residue<C>	monic() Residue monic.
Residue<C>	multiply(Residue<C> S) Residue multiplication.
Residue<C>	negate() Residue negate.
Residue<C>	remainder(Residue<C> S) Residue remainder.
int	signum() Residue signum.
Residue<C>	subtract(Residue<C> S) Residue subtraction.
Residue<C>	sum(Residue<C> S) Residue 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

protected final ResidueRing<C extends RingElem<C>> ring

Residue class factory data structure.

val

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

Value part of the element data structure.

isunit

protected int isunit

Flag to remember if this residue element is a unit. -1 is unknown, 1 is unit, 0 not a unit.

Constructor Detail

Residue

public Residue(ResidueRing<C> r)

The constructor creates a Residue object from a ring factory.

Parameters:

r - ring factory.

Residue

public Residue(ResidueRing<C> r,
               GenPolynomial<C> a)

The constructor creates a Residue object from a ring factory and a polynomial.

Parameters:

r - ring factory.

a - polynomial list.

Residue

public Residue(ResidueRing<C> r,
               GenPolynomial<C> a,
               int u)

The constructor creates a Residue object from a ring factory, a polynomial and an indicator if a is a unit.

Parameters:

r - ring factory.

a - polynomial list.

u - isunit indicator, -1, 0, 1.

Method Detail

clone

public Residue<C> clone()

Clone this.

Specified by:

clone in interface Element<Residue<C extends RingElem<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 Residue zero.

Specified by:

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

See Also:

AbelianGroupElem.isZERO()

Returns:

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

isONE

public boolean isONE()

Is Residue one.

Specified by:

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

See Also:

MonoidElem.isONE()

Returns:

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

isUnit

public boolean isUnit()

Is Residue unit.

Specified by:

isUnit in interface MonoidElem<Residue<C extends RingElem<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(Residue<C> b)

Residue comparison.

Specified by:

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

Specified by:

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

Parameters:

b - Residue.

Returns:

sign(this-b).

equals

public boolean equals(java.lang.Object b)

Comparison with any other object.

Specified by:

equals in interface Element<Residue<C extends RingElem<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 local.

Specified by:

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

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

Returns:

the hashCode.

abs

public Residue<C> abs()

Residue absolute value.

Specified by:

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

See Also:

AbelianGroupElem.abs()

Returns:

the absolute value of this.

sum

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

Residue summation.

Specified by:

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

Parameters:

S - Residue.

Returns:

this+S.

negate

public Residue<C> negate()

Residue negate.

Specified by:

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

See Also:

AbelianGroupElem.negate()

Returns:

-this.

signum

public int signum()

Residue signum.

Specified by:

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

See Also:

AbelianGroupElem.signum()

Returns:

signum(this).

subtract

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

Residue subtraction.

Specified by:

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

Parameters:

S - Residue.

Returns:

this-S.

divide

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

Residue division.

Specified by:

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

Parameters:

S - Residue.

Returns:

this/S.

inverse

public Residue<C> inverse()

Residue inverse.

Specified by:

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

See Also:

MonoidElem.inverse()

Returns:

S with S = 1/this if defined.

remainder

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

Residue remainder.

Specified by:

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

Parameters:

S - Residue.

Returns:

this - (this/S)*S.

multiply

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

Residue multiplication.

Specified by:

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

Parameters:

S - Residue.

Returns:

this*S.

monic

public Residue<C> monic()

Residue monic.

Returns:

this with monic value part.

gcd

public Residue<C> gcd(Residue<C> b)

Greatest common divisor. Note: Not implemented, throws RuntimeException.

Specified by:

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

Parameters:

b - other element.

Returns:

gcd(this,b).

egcd

public Residue<C>[] egcd(Residue<C> b)

Extended greatest common divisor. Note: Not implemented, throws RuntimeException.

Specified by:

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

Parameters:

b - other element.

Returns:

[ gcd(this,b), c1, c2 ] with c1*this + c2*b = gcd(this,b).