Package edu.jas.poly

Class Residue<C extends RingElem<C>>

java.lang.Object

edu.jas.poly.Residue<C>

All Implemented Interfaces:

AbelianGroupElem<Residue<C>>, Element<Residue<C>>, MonoidElem<Residue<C>>, RingElem<Residue<C>>, Serializable, Comparable<Residue<C>>

public class Residue<C extends RingElem<C>>
extends Object
implements RingElem<Residue<C>>

Residue element based on RingElem residue. Objects of this class are (nearly) immutable.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
private static final boolean	debug
protected int	isunit	Flag to remember if this residue element is a unit.
private static final org.apache.logging.log4j.Logger	logger
protected final ResidueRing<C>	ring	Residue class factory data structure.
protected final C	val	Value part of the element data structure.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	Description
Residue<C>	abs()	Residue absolute value.
int	compareTo(Residue<C> b)	Residue comparison.
Residue<C>	copy()	Copy this.
Residue<C>	divide(Residue<C> S)	Residue division.
Residue<C>[]	egcd(Residue<C> b)	Extended greatest common divisor.
boolean	equals(Object b)	Comparison with any other object.
ResidueRing<C>	factory()	Get the corresponding element factory.
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>	multiply(Residue<C> S)	Residue multiplication.
Residue<C>	negate()	Residue negate.
Residue<C>[]	quotientRemainder(Residue<C> S)	Quotient and remainder by division of this by S.
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.
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 java.lang.Object

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

Methods inherited from interface edu.jas.structure.MonoidElem

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

Methods inherited from interface edu.jas.structure.RingElem

leftGcd, rightGcd

Field Details

logger

private static final org.apache.logging.log4j.Logger logger

debug

private static final boolean debug

ring

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

Residue class factory data structure.

val

protected final 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 Details

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,
 C a)

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

Parameters:

r - ring factory.

a - ring element.

Residue

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

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

Parameters:

r - ring factory.

a - ring element.

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

Method Details

factory

public ResidueRing<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()

copy

public Residue<C> copy()

Copy this.

Specified by:

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

Returns:

Creates and returns a copy of this Element.

See Also:

• Element.copy()

isZERO

public boolean isZERO()

Is Residue 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 Residue 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 Residue 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(Residue<C> b)

Residue comparison.

Specified by:

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

Specified by:

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

Parameters:

b - Residue.

Returns:

sign(this-b), 0 means that this and b are equivalent in this residue class ring.

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 means that this and b are equivalent in this residue class ring.

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 Residue<C> abs()

Residue absolute value.

Specified by:

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

Returns:

the absolute value of this.

See Also:

• AbelianGroupElem.abs()

sum

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

Residue summation.

Specified by:

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

Parameters:

S - Residue.

Returns:

this+S.

negate

public Residue<C> negate()

Residue negate.

Specified by:

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

Returns:

-this.

See Also:

• AbelianGroupElem.negate()

signum

public int signum()

Residue signum.

Specified by:

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

Returns:

signum(this).

See Also:

• AbelianGroupElem.signum()

subtract

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

Residue subtraction.

Specified by:

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

Parameters:

S - Residue.

Returns:

this/S.

inverse

public Residue<C> inverse()

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

Residue remainder.

Specified by:

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

Parameters:

S - Residue.

Returns:

this - (this/S)*S.

quotientRemainder

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

Quotient and remainder by division of this by S.

Specified by:

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

Parameters:

S - a Residue

Returns:

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

multiply

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

Residue multiplication.

Specified by:

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

Parameters:

S - Residue.

Returns:

this*S.

gcd

public Residue<C> gcd(Residue<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 Residue<C>[] egcd(Residue<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).