edu.jas.poly

Class Quotient<C extends RingElem<C>>

java.lang.Object

edu.jas.poly.Quotient<C>

All Implemented Interfaces:

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

public class Quotient<C extends RingElem<C>>
extends java.lang.Object
implements RingElem<Quotient<C>>, QuotPair<C>

Quotient element based on RingElem pairs. Objects of this class are immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
C	den Denominator part of the element data structure.
C	num Numerator part of the element data structure.
QuotientRing<C>	ring Quotient class factory data structure.

Constructor Summary

Constructors

Modifier	Constructor and Description
	Quotient(QuotientRing<C> r) The constructor creates a Quotient object from a ring factory.
	Quotient(QuotientRing<C> r, C n) The constructor creates a Quotient object from a ring factory and a numerator element.
	Quotient(QuotientRing<C> r, C n, C d) The constructor creates a Quotient object from a ring factory and a numerator and denominator element.
protected	Quotient(QuotientRing<C> r, C n, C d, boolean isred) The constructor creates a Quotient object from a ring factory and a numerator and denominator element.

Method Summary

Modifier and Type	Method and Description
Quotient<C>	abs() Quotient absolute value.
int	compareTo(Quotient<C> b) Quotient comparison.
Quotient<C>	copy() Clone this.
C	denominator() Denominator.
Quotient<C>	divide(Quotient<C> S) Quotient division.
Quotient<C>[]	egcd(Quotient<C> b) Extended greatest common divisor.
boolean	equals(java.lang.Object b) Comparison with any other object.
QuotientRing<C>	factory() Get the corresponding element factory.
Quotient<C>	gcd(Quotient<C> b) Greatest common divisor.
int	hashCode() Hash code for this local.
Quotient<C>	inverse() Quotient inverse.
boolean	isConstant() Is Quotient a constant.
boolean	isONE() Is Quotient one.
boolean	isUnit() Is Quotient unit.
boolean	isZERO() Is Quotient zero.
Quotient<C>	monic() Quotient monic.
Quotient<C>	multiply(Quotient<C> S) Quotient multiplication.
Quotient<C>	negate() Quotient negate.
C	numerator() Numerator.
Quotient<C>[]	quotientRemainder(Quotient<C> S) Quotient and remainder by division of this by S.
Quotient<C>	remainder(Quotient<C> S) Quotient remainder.
int	signum() Quotient signum.
Quotient<C>	subtract(Quotient<C> S) Quotient subtraction.
Quotient<C>	sum(Quotient<C> S) Quotient 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, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Field Detail

ring

public final QuotientRing<C extends RingElem<C>> ring

Quotient class factory data structure.

num

public final C extends RingElem<C> num

Numerator part of the element data structure.

den

public final C extends RingElem<C> den

Denominator part of the element data structure.

Constructor Detail

Quotient

public Quotient(QuotientRing<C> r)

The constructor creates a Quotient object from a ring factory.

Parameters:

r - ring factory.

Quotient

public Quotient(QuotientRing<C> r,
                C n)

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

Parameters:

r - ring factory.

n - numerator.

Quotient

public Quotient(QuotientRing<C> r,
                C n,
                C d)

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

Parameters:

r - ring factory.

n - numerator.

d - denominator.

Quotient

protected Quotient(QuotientRing<C> r,
                   C n,
                   C d,
                   boolean isred)

The constructor creates a Quotient 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

factory

public QuotientRing<C> factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<Quotient<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 Quotient a constant. Not implemented.

Specified by:

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

Throws:

UnsupportedOperationException.

copy

public Quotient<C> copy()

Clone this.

Specified by:

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

Returns:

Creates and returns a copy of this Element.

See Also:

Object.clone()

isZERO

public boolean isZERO()

Is Quotient zero.

Specified by:

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

Returns:

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

See Also:

AbelianGroupElem.isZERO()

isONE

public boolean isONE()

Is Quotient one.

Specified by:

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

Returns:

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

See Also:

MonoidElem.isONE()

isUnit

public boolean isUnit()

Is Quotient unit.

Specified by:

isUnit in interface MonoidElem<Quotient<C extends RingElem<C>>>

Returns:

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

See Also:

MonoidElem.isUnit()

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<Quotient<C extends RingElem<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<Quotient<C extends RingElem<C>>>

Returns:

script compatible representation for this ElemFactory.

See Also:

Element.toScriptFactory()

compareTo

public int compareTo(Quotient<C> b)

Quotient comparison.

Specified by:

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

Specified by:

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

Parameters:

b - Quotient.

Returns:

sign(this-b).

equals

public boolean equals(java.lang.Object b)

Comparison with any other object.

Specified by:

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

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

abs

public Quotient<C> abs()

Quotient absolute value.

Specified by:

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

Returns:

the absolute value of this.

See Also:

AbelianGroupElem.abs()

sum

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

Quotient summation.

Specified by:

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

Parameters:

S - Quotient.

Returns:

this+S.

negate

public Quotient<C> negate()

Quotient negate.

Specified by:

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

Returns:

-this.

See Also:

AbelianGroupElem.negate()

signum

public int signum()

Quotient signum.

Specified by:

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

Returns:

signum(this).

See Also:

AbelianGroupElem.signum()

subtract

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

Quotient subtraction.

Specified by:

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

Parameters:

S - Quotient.

Returns:

this-S.

divide

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

Quotient division.

Specified by:

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

Parameters:

S - Quotient.

Returns:

this/S.

inverse

public Quotient<C> inverse()

Quotient inverse.

Specified by:

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

Returns:

S with S = 1/this.

See Also:

MonoidElem.inverse()

remainder

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

Quotient remainder.

Specified by:

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

Parameters:

S - Quotient.

Returns:

this - (this/S)*S.

quotientRemainder

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

Quotient and remainder by division of this by S.

Specified by:

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

Parameters:

S - a Quotient

Returns:

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

multiply

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

Quotient multiplication.

Specified by:

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

Parameters:

S - Quotient.

Returns:

this*S.

monic

public Quotient<C> monic()

Quotient monic.

Returns:

this with monic value part.

gcd

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

Greatest common divisor. Note: If not defined, throws UnsupportedOperationException.

Specified by:

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

Parameters:

b - other element.

Returns:

gcd(this,b).

egcd

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

Extended greatest common divisor. Note: If not defined, throws UnsupportedOperationException.

Specified by:

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

Parameters:

b - other element.

Returns:

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