Residue

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>>, java.io.Serializable, java.lang.Comparable<Residue<C>>
```
public class Residue<C extends GcdRingElem<C>>
extends java.lang.Object
implements GcdRingElem<Residue<C>>
```
Residue ring element based on GenPolynomial with RingElem interface. Objects of this class are (nearly) immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`protected int`	`isunit` Flag to remember if this residue element is a unit. -1 is unknown, 1 is unit, 0 not a unit.
`ResidueRing<C>`	`ring` Residue class factory data structure.
`GenPolynomial<C>`	`val` Value part of the element data structure.

Constructor Summary

Constructors
Constructor and 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

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and 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(java.lang.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.
`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

- Field Detail
  - 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 Detail
  - 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 Detail
  - factory
```
public ResidueRing<C> factory()
```
    Get the corresponding element factory.
    
    Specified by:
    
    factory in interface Element<Residue<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<Residue<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<Residue<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<Residue<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<Residue<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 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<Residue<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<Residue<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 Element<Residue<C extends GcdRingElem<C>>>
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<Residue<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(java.lang.Object b)
```
    Comparison with any other object.
    
    Specified by:
    
    equals in interface Element<Residue<C extends GcdRingElem<C>>>
    
    Overrides:
    
    equals in class java.lang.Object
    
    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<Residue<C extends GcdRingElem<C>>>
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    the hashCode.
    
    See Also:
    
    Object.hashCode()
  - abs
```
public Residue<C> abs()
```
    Residue absolute value.
    
    Specified by:
    
    abs in interface AbelianGroupElem<Residue<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<Residue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    S - Residue.
    
    Returns:
    
    this+S.
  - negate
```
public Residue<C> negate()
```
    Residue negate.
    
    Specified by:
    
    negate in interface AbelianGroupElem<Residue<C extends GcdRingElem<C>>>
    
    Returns:
    
    -this.
    
    See Also:
    
    AbelianGroupElem.negate()
  - signum
```
public int signum()
```
    Residue signum.
    
    Specified by:
    
    signum in interface AbelianGroupElem<Residue<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<Residue<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<Residue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    S - Residue.
    
    Returns:
    
    this/S.
  - inverse
```
public Residue<C> inverse()
```
    Residue inverse.
    
    Specified by:
    
    inverse in interface MonoidElem<Residue<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<Residue<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<Residue<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<Residue<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<Residue<C extends GcdRingElem<C>>>
    
    Parameters:
    
    b - other element.
    
    Returns:
    
    [ gcd(this,b), c1, c2 ] with c1*this + c2*b = gcd(this,b).

Class Residue<C extends GcdRingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ring

val

isunit

Constructor Detail

Residue

Residue

Residue

Method Detail

factory

copy

isZERO

isONE

isUnit

isConstant

toString

toScript

toScriptFactory

compareTo

equals

hashCode

abs

sum

negate

signum

subtract

divide

inverse

remainder

multiply

monic

gcd

egcd