edu.jas.ufd
Class Quotient<C extends GcdRingElem<C>>

java.lang.Object
  edu.jas.ufd.Quotient<C>

All Implemented Interfaces:

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

public class Quotient<C extends GcdRingElem<C>>
extends java.lang.Object
implements GcdRingElem<Quotient<C>>

Quotient, i.e. rational function, based on GenPolynomial with RingElem interface. Objects of this class are immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

GenPolynomial<C>	den Denominator part of the element data structure.
GenPolynomial<C>	num Numerator part of the element data structure.
QuotientRing<C>	ring Quotient class factory data structure.

Constructor Summary

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

Method Summary

Quotient<C>	abs() Quotient absolute value.
Quotient<C>	clone() Clone this.
int	compareTo(Quotient<C> b) Quotient comparison.
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 Qoutient a constant.
boolean	isONE() Is Quotient one.
boolean	isUnit() Is Quotient a unit.
boolean	isZERO() Is Quotient zero.
Quotient<C>	monic() Quotient monic.
Quotient<C>	multiply(C b) Quotient multiplication by coefficient.
Quotient<C>	multiply(GenPolynomial<C> b) Quotient multiplication by GenPolynomial.
Quotient<C>	multiply(Quotient<C> S) Quotient multiplication.
Quotient<C>	negate() Quotient negate.
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

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

Field Detail

ring

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

Quotient class factory data structure.

num

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

Numerator part of the element data structure.

den

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

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

Parameters:

r - ring factory.

n - numerator polynomial.

Quotient

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

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

Parameters:

r - ring factory.

n - numerator polynomial.

d - denominator polynomial.

Quotient

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

The constructor creates a Quotient 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 QuotientRing<C> factory()

Get the corresponding element factory.

Specified by:

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

Returns:

factory for this Element.

See Also:

Element.factory()

clone

public Quotient<C> clone()

Clone this.

Overrides:

clone in class java.lang.Object

See Also:

Object.clone()

isZERO

public boolean isZERO()

Is Quotient zero.

Specified by:

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

Returns:

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

See Also:

MonoidElem.isONE()

isUnit

public boolean isUnit()

Is Quotient a unit.

Specified by:

isUnit in interface MonoidElem<Quotient<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.

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<Quotient<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<Quotient<C extends GcdRingElem<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 GcdRingElem<C>>>

Specified by:

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

Parameters:

S - Quotient.

Returns:

this+S.

negate

public Quotient<C> negate()

Quotient negate.

Specified by:

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

Returns:

-this.

See Also:

AbelianGroupElem.negate()

signum

public int signum()

Quotient signum.

Specified by:

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

Parameters:

S - Quotient.

Returns:

this/S.

inverse

public Quotient<C> inverse()

Quotient inverse.

Specified by:

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

Parameters:

S - Quotient.

Returns:

this - (this/S)*S.

multiply

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

Quotient multiplication.

Specified by:

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

Parameters:

S - Quotient.

Returns:

this*S.

multiply

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

Quotient multiplication by GenPolynomial.

Parameters:

b - GenPolynomial.

Returns:

this*b.

multiply

public Quotient<C> multiply(C b)

Quotient multiplication by coefficient.

Parameters:

b - coefficient.

Returns:

this*b.

monic

public Quotient<C> monic()

Quotient monic.

Returns:

this with monic value part.

gcd

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

Greatest common divisor.

Specified by:

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

Parameters:

b - other element.

Returns:

gcd(this,b).

egcd

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

Extended greatest common divisor.

Specified by:

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

Parameters:

b - other element.

Returns:

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