Class Local<C extends RingElem<C>>

java.lang.Object

edu.jas.poly.Local<C>

All Implemented Interfaces:

AbelianGroupElem<Local<C>>, Element<Local<C>>, MonoidElem<Local<C>>, QuotPair<C>, RingElem<Local<C>>, Serializable, Comparable<Local<C>>

public class Local<C extends RingElem<C>>
extends Object
implements RingElem<Local<C>>, QuotPair<C>

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

Author:

Heinz Kredel

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected final 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 final C	num	Numerator part of the element data structure.
protected final LocalRing<C>	ring	Local class factory data structure.

Constructor Summary

Constructors

Modifier	Constructor	Description
	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

Modifier and Type	Method	Description
Local<C>	abs()	Local absolute value.
int	compareTo(Local<C> b)	Local comparison.
Local<C>	copy()	Clone this.
C	denominator()	Denominator.
Local<C>	divide(Local<C> S)	Local division.
Local<C>[]	egcd(Local<C> b)	Extended greatest common divisor.
boolean	equals(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 Local a constant.
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.
C	numerator()	Numerator.
Local<C>[]	quotientRemainder(Local<C> S)	Quotient and remainder by division of this by S.
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.
String	toScript()	Get a scripting compatible string representation.
String	toScriptFactory()	Get a scripting compatible string representation of the factory.
String	toString()	Get the String representation as RingElem.

Methods inherited from class Object

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

Methods inherited from interface MonoidElem

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

Methods inherited from interface RingElem

leftGcd, rightGcd

Field Details

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 Details

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 Details

factory

public LocalRing<C> factory()

Get the corresponding element factory.

Specified by:

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

Returns:

factory for this Element.

See Also:

• Element.factory()

numerator

public C numerator()

Numerator.

Specified by:

numerator in interface QuotPair<C extends RingElem<C>>

See Also:

• QuotPair.numerator()

denominator

public C denominator()

Denominator.

Specified by:

denominator in interface QuotPair<C extends RingElem<C>>

See Also:

• QuotPair.denominator()

isConstant

public boolean isConstant()

Is Local a constant. Not implemented.

Specified by:

isConstant in interface QuotPair<C extends RingElem<C>>

copy

public Local<C> copy()

Clone this.

Specified by:

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

Returns:

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

See Also:

• MonoidElem.isUnit()

toString

public String toString()

Get the String representation as RingElem.

Overrides:

toString in class Object

See Also:

• Object.toString()

toScript

public String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface Element<C extends RingElem<C>>

Returns:

script compatible representation for this Element.

See Also:

• Element.toScript()

toScriptFactory

public String toScriptFactory()

Get a scripting compatible string representation of the factory.

Specified by:

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

Specified by:

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

Parameters:

b - Local.

Returns:

sign(this-b).

equals

public boolean equals(Object b)

Comparison with any other object.

Specified by:

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

Overrides:

equals in class Object

Parameters:

b -

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<C extends RingElem<C>>

Overrides:

hashCode in class Object

Returns:

the hashCode.

See Also:

• Object.hashCode()

abs

public Local<C> abs()

Local absolute value.

Specified by:

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

Parameters:

S - Local.

Returns:

this+S.

negate

public Local<C> negate()

Local negate.

Specified by:

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

Returns:

-this.

See Also:

• AbelianGroupElem.negate()

signum

public int signum()

Local signum.

Specified by:

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

Returns:

signum(this).

See Also:

• AbelianGroupElem.signum()

subtract

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

Local subtraction.

Specified by:

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

Parameters:

S - Local.

Returns:

this/S.

inverse

public Local<C> inverse()

Local inverse.

Specified by:

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

Parameters:

S - Local.

Returns:

this - (this/S)*S.

quotientRemainder

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

Quotient and remainder by division of this by S.

Specified by:

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

Parameters:

S - a Local

Returns:

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

multiply

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

Local multiplication.

Specified by:

multiply in interface MonoidElem<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 UnsupportedOperationException.

Specified by:

gcd in interface RingElem<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 UnsupportedOperationException.

Specified by:

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

Parameters:

b - other element.

Returns:

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