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

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

All Implemented Interfaces:

AbelianGroupElem<Quotient<C>>, Element<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 RingElem<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.
Quotient<C>	gcd(Quotient<C> b) Greatest common divisor.
int	hashCode() Hash code for this local.
Quotient<C>	inverse() Quotient inverse.
boolean	isONE() Is Quotient one.
boolean	isUnit() Is Quotient unit.
boolean	isZERO() Is Quotient zero.
Quotient<C>	monic() Quotient monic.
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	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

clone

public Quotient<C> clone()

Clone this.

Specified by:

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

Overrides:

clone in class java.lang.Object

See Also:

Object.clone()

Returns:

Creates and returns a copy of this Elemnt.

isZERO

public boolean isZERO()

Is Quotient zero.

Specified by:

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

See Also:

AbelianGroupElem.isZERO()

Returns:

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

isONE

public boolean isONE()

Is Quotient one.

Specified by:

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

See Also:

MonoidElem.isONE()

Returns:

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

isUnit

public boolean isUnit()

Is Quotient unit.

Specified by:

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

See Also:

MonoidElem.isUnit()

Returns:

If this is a unit then true is returned, 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()

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

See Also:

Object.equals(java.lang.Object)

Returns:

true if this is equal to b, else false.

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

See Also:

Object.hashCode()

Returns:

the hashCode.

abs

public Quotient<C> abs()

Quotient absolute value.

Specified by:

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

See Also:

AbelianGroupElem.abs()

Returns:

the absolute value of this.

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>>>

See Also:

AbelianGroupElem.negate()

Returns:

-this.

signum

public int signum()

Quotient signum.

Specified by:

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

See Also:

AbelianGroupElem.signum()

Returns:

signum(this).

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>>>

See Also:

MonoidElem.inverse()

Returns:

S with S = 1/this.

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.

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: Not implemented, throws RuntimeException.

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. Note: Not implemented, throws RuntimeException.

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).