edu.jas.application

Class Local<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.application.Local<C>

All Implemented Interfaces:

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

public class Local<C extends GcdRingElem<C>>
extends java.lang.Object
implements RingElem<Local<C>>, QuotPair<GenPolynomial<C>>

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

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected GenPolynomial<C>	den Denominator part of the element data structure.
protected int	isunit Flag to remember if this local element is a unit. -1 is unknown, 1 is unit, 0 not a unit.
protected GenPolynomial<C>	num Numerator part of the element data structure.
LocalRing<C>	ring Local class factory data structure.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
Local<C>	abs() Local absolute value.
int	compareTo(Local<C> b) Local comparison.
Local<C>	copy() Clone this.
GenPolynomial<C>	denominator() Denominator.
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.
LocalRing<C>	factory() Get the corresponding element factory.
Local<C>	gcd(Local<C> b) Greatest common divisor.
int	hashCode() Hash code for this local.
Local<C>	inverse() Local inverse.
boolean	isConstant() Is Qoutient a constant.
boolean	isONE() Is Local one.
boolean	isUnit() Is Local unit.
boolean	isZERO() Is Local zero.
Local<C>	monic() Local monic.
Local<C>	multiply(C b) Local multiplication by coefficient.
Local<C>	multiply(ExpVector e) Local multiplication by exponent.
Local<C>	multiply(GenPolynomial<C> b) Local multiplication by GenPolynomial.
Local<C>	multiply(Local<C> S) Local multiplication.
Local<C>	negate() Local negate.
GenPolynomial<C>	numerator() Numerator.
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	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, quotientRemainder, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Field Detail

ring

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

Local class factory data structure.

num

protected final GenPolynomial<C extends GcdRingElem<C>> num

Numerator part of the element data structure.

den

protected final GenPolynomial<C extends GcdRingElem<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,
             GenPolynomial<C> n)

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

Parameters:

r - ring factory.

n - numerator polynomial.

Local

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

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

Parameters:

r - ring factory.

n - numerator polynomial.

d - denominator polynomial.

Local

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

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

Parameters:

r - ring factory.

n - numerator polynomial.

d - denominator polynomial.

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

Method Detail

factory

public LocalRing<C> factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<Local<C extends GcdRingElem<C>>>

Returns:

factory for this Element.

See Also:

Element.factory()

numerator

public GenPolynomial<C> numerator()

Numerator.

Specified by:

numerator in interface QuotPair<GenPolynomial<C extends GcdRingElem<C>>>

See Also:

QuotPair.numerator()

denominator

public GenPolynomial<C> denominator()

Denominator.

Specified by:

denominator in interface QuotPair<GenPolynomial<C extends GcdRingElem<C>>>

See Also:

QuotPair.denominator()

copy

public Local<C> copy()

Clone this.

Specified by:

copy in interface Element<Local<C extends GcdRingElem<C>>>

Returns:

Creates and returns a copy of this Element.

See Also:

Object.clone()

isZERO

public boolean isZERO()

Is Local zero.

Specified by:

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

Returns:

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

See Also:

AbelianGroupElem.isZERO()

isONE

public boolean isONE()

Is Local one.

Specified by:

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

Returns:

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

See Also:

MonoidElem.isONE()

isUnit

public boolean isUnit()

Is Local unit.

Specified by:

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

Returns:

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

See Also:

MonoidElem.isUnit()

isConstant

public boolean isConstant()

Is Qoutient a constant.

Specified by:

isConstant in interface QuotPair<GenPolynomial<C extends GcdRingElem<C>>>

Returns:

true, if this has constant numerator and denominator, 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<Local<C extends GcdRingElem<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<Local<C extends GcdRingElem<C>>>

Returns:

script compatible representation for this ElemFactory.

See Also:

Element.toScriptFactory()

compareTo

public int compareTo(Local<C> b)

Local comparison.

Specified by:

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

Specified by:

compareTo in interface java.lang.Comparable<Local<C extends GcdRingElem<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 GcdRingElem<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 local.

Specified by:

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

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

abs

public Local<C> abs()

Local absolute value.

Specified by:

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

Returns:

the absolute value of this.

See Also:

AbelianGroupElem.abs()

sum

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

Local summation.

Specified by:

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

Parameters:

S - Local.

Returns:

this+S.

negate

public Local<C> negate()

Local negate.

Specified by:

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

Returns:

-this.

See Also:

AbelianGroupElem.negate()

signum

public int signum()

Local signum.

Specified by:

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

Returns:

signum(this).

See Also:

AbelianGroupElem.signum()

subtract

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

Local subtraction.

Specified by:

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

Parameters:

S - Local.

Returns:

this/S.

inverse

public Local<C> inverse()

Local inverse.

Specified by:

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

Returns:

S with S = 1/this if defined.

See Also:

MonoidElem.inverse()

remainder

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

Local remainder.

Specified by:

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

Parameters:

S - Local.

Returns:

this*S.

multiply

public Local<C> multiply(GenPolynomial<C> b)

Local multiplication by GenPolynomial.

Parameters:

b - GenPolynomial.

Returns:

this*b.

multiply

public Local<C> multiply(C b)

Local multiplication by coefficient.

Parameters:

b - coefficient.

Returns:

this*b.

multiply

public Local<C> multiply(ExpVector e)

Local multiplication by exponent.

Parameters:

e - exponent vector.

Returns:

this*b.

monic

public Local<C> monic()

Local monic.

Returns:

this with monic value part.

gcd

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

Greatest common divisor.

Specified by:

gcd in interface RingElem<Local<C extends GcdRingElem<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 UnsupportedOperationException.

Specified by:

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

Parameters:

b - other element.

Returns:

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