edu.jas.structure
Class Local<C extends RingElem<C>>

java.lang.Object
  edu.jas.structure.Local<C>

All Implemented Interfaces:

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

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

Local element based on RingElem pairs. Objects of this class are (nearly) immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Fix me

Not jet working because of monic GBs.

Field Summary

protected C	den Denominator part of the element data structure.
protected int	isunit Flag to remember if this local element is a unit
protected C	num Numerator part of the element data structure.
protected LocalRing<C>	ring Local class factory data structure.

Constructor Summary

	Local(LocalRing<C> r) The constructor creates a Local object from a ring factory.
	Local(LocalRing<C> r, C n) The constructor creates a Local object from a ring factory and a numerator element.
	Local(LocalRing<C> r, C n, C d) The constructor creates a Local object from a ring factory and a numerator and denominator element.
protected	Local(LocalRing<C> r, C n, C d, boolean isred) The constructor creates a Local object from a ring factory and a numerator and denominator element.

Method Summary

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

Local class factory data structure.

num

protected final C extends RingElem<C> num

Numerator part of the element data structure.

den

protected final C extends RingElem<C> den

Denominator part of the element data structure.

isunit

protected int isunit

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

Constructor Detail

Local

public Local(LocalRing<C> r)

The constructor creates a Local object from a ring factory.

Parameters:

r - ring factory.

Local

public Local(LocalRing<C> r,
             C n)

The constructor creates a Local object from a ring factory and a numerator element. The denominator is assumed to be 1.

Parameters:

r - ring factory.

n - numerator.

Local

public Local(LocalRing<C> r,
             C n,
             C d)

The constructor creates a Local object from a ring factory and a numerator and denominator element.

Parameters:

r - ring factory.

n - numerator.

d - denominator.

Local

protected Local(LocalRing<C> r,
                C n,
                C d,
                boolean isred)

The constructor creates a Local object from a ring factory and a numerator and denominator element.

Parameters:

r - ring factory.

n - numerator.

d - denominator.

isred - true if gcd(n,d) == 1, else false.

Method Detail

clone

public Local<C> clone()

Clone this.

Specified by:

clone in interface Element<Local<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 Local zero.

Specified by:

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

See Also:

AbelianGroupElem.isZERO()

Returns:

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

isONE

public boolean isONE()

Is Local one.

Specified by:

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

See Also:

MonoidElem.isONE()

Returns:

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

isUnit

public boolean isUnit()

Is Local unit.

Specified by:

isUnit in interface MonoidElem<Local<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(Local<C> b)

Local comparison.

Specified by:

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

Specified by:

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

Parameters:

b - Local.

Returns:

sign(this-b).

equals

public boolean equals(java.lang.Object b)

Comparison with any other object.

Specified by:

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

Overrides:

hashCode in class java.lang.Object

See Also:

Object.hashCode()

Returns:

the hashCode.

abs

public Local<C> abs()

Local absolute value.

Specified by:

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

See Also:

AbelianGroupElem.abs()

Returns:

the absolute value of this.

sum

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

Local summation.

Specified by:

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

Parameters:

S - Local.

Returns:

this+S.

negate

public Local<C> negate()

Local negate.

Specified by:

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

See Also:

AbelianGroupElem.negate()

Returns:

-this.

signum

public int signum()

Local signum.

Specified by:

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

See Also:

AbelianGroupElem.signum()

Returns:

signum(this).

subtract

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

Local subtraction.

Specified by:

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

Parameters:

S - Local.

Returns:

this-S.

divide

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

Local division.

Specified by:

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

Parameters:

S - Local.

Returns:

this/S.

inverse

public Local<C> inverse()

Local inverse.

Specified by:

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

See Also:

MonoidElem.inverse()

Returns:

S with S = 1/this if defined.

remainder

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

Local remainder.

Specified by:

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

Parameters:

S - Local.

Returns:

this - (this/S)*S.

multiply

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

Local multiplication.

Specified by:

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

Parameters:

S - Local.

Returns:

this*S.

gcd

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

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

Specified by:

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

Parameters:

b - other element.

Returns:

gcd(this,b).

egcd

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

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

Specified by:

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

Parameters:

b - other element.

Returns:

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