Class Residue<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.application.Residue<C>

All Implemented Interfaces:

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

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

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

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected int	isunit	Flag to remember if this residue element is a unit.
final ResidueRing<C>	ring	Residue class factory data structure.
final GenPolynomial<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, 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

Modifier and Type	Method	Description
Residue<C>	abs()	Residue absolute value.
int	compareTo(Residue<C> b)	Residue comparison.
Residue<C>	copy()	Clone 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 residue.
Residue<C>	inverse()	Residue inverse.
boolean	isConstant()	Is Residue a constant.
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.
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, quotientRemainder, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Methods inherited from interface RingElem

leftGcd, rightGcd

Field Details

ring

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

Residue class factory data structure.

val

public final GenPolynomial<C extends GcdRingElem<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 - residue 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 - residue ring factory.

a - polynomial.

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 - residue ring factory.

a - polynomial.

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 GcdRingElem<C>>

Returns:

factory for this Element.

See Also:

• Element.factory()

copy

public Residue<C> copy()

Clone this.

Specified by:

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

Returns:

Creates and returns a copy of this Element.

See Also:

• Object.clone()

isZERO

public boolean isZERO()

Is Residue zero.

Specified by:

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

Returns:

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

See Also:

• MonoidElem.isUnit()

isConstant

public boolean isConstant()

Is Residue a constant.

Returns:

true if this.val is a constant polynomial, else false.

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 GcdRingElem<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 GcdRingElem<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 GcdRingElem<C>>

Specified by:

compareTo in interface Element<C extends GcdRingElem<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 GcdRingElem<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 residue.

Specified by:

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

Parameters:

S - Residue.

Returns:

this+S.

negate

public Residue<C> negate()

Residue negate.

Specified by:

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

Returns:

-this.

See Also:

• AbelianGroupElem.negate()

signum

public int signum()

Residue signum.

Specified by:

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

Parameters:

S - Residue.

Returns:

this/S.

inverse

public Residue<C> inverse()

Residue inverse.

Specified by:

inverse in interface MonoidElem<C extends GcdRingElem<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 GcdRingElem<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<C extends GcdRingElem<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.

Specified by:

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

Parameters:

b - other element.

Returns:

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