Quotient

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

All Implemented Interfaces:

AbelianGroupElem<Quotient<C>>, Element<Quotient<C>>, GcdRingElem<Quotient<C>>, MonoidElem<Quotient<C>>, QuotPair<GenPolynomial<C>>, RingElem<Quotient<C>>, java.io.Serializable, java.lang.Comparable<Quotient<C>>
```
public class Quotient<C extends GcdRingElem<C>>
extends java.lang.Object
implements GcdRingElem<Quotient<C>>, QuotPair<GenPolynomial<C>>
```
Quotient, that is a rational function, based on GenPolynomial with RingElem interface. Objects of this class are immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`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

Constructors
Modifier	Constructor and Description
	`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

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Quotient<C>`	`abs()` Quotient absolute value.
`int`	`compareTo(Quotient<C> b)` Quotient comparison.
`Quotient<C>`	`copy()` Clone this.
`GenPolynomial<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 quotient.
`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.
`GenPolynomial<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 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()
  - numerator
```
public GenPolynomial<C> numerator()
```
    Numerator.
    
    Specified by:
    
    numerator in interface QuotPair<GenPolynomial<C extends GcdRingElem<C>>>
    
    See Also:
    
    QuotPair.numerator()
  - denominator
```
public GenPolynomial<C> denominator()
```
    Denominator.
    
    Specified by:
    
    denominator in interface QuotPair<GenPolynomial<C extends GcdRingElem<C>>>
    
    See Also:
    
    QuotPair.denominator()
  - copy
```
public Quotient<C> copy()
```
    Clone this.
    
    Specified by:
    
    copy in interface Element<Quotient<C extends GcdRingElem<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 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.
    
    Specified by:
    
    isConstant in interface QuotPair<GenPolynomial<C extends GcdRingElem<C>>>
    
    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 quotient.
    
    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.
  - 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 GcdRingElem<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 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).

Class Quotient<C extends GcdRingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface edu.jas.structure.RingElem

Methods inherited from interface edu.jas.structure.MonoidElem

Field Detail

ring

num

den

Constructor Detail

Quotient

Quotient

Quotient

Quotient

Method Detail

factory

numerator

denominator

copy

isZERO

isONE

isUnit

isConstant

toString

toScript

toScriptFactory

compareTo

equals

hashCode

abs

sum

negate

signum

subtract

divide

inverse

remainder

quotientRemainder

multiply

multiply

multiply

monic

gcd

egcd