AlgebraicNumber

Documentation of 'edu.jas.poly.AlgebraicNumber' Java class AlgebraicNumber

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java.lang.Object
- edu.jas.poly.AlgebraicNumber<C>

All Implemented Interfaces:

AbelianGroupElem<AlgebraicNumber<C>>, Element<AlgebraicNumber<C>>, GcdRingElem<AlgebraicNumber<C>>, MonoidElem<AlgebraicNumber<C>>, RingElem<AlgebraicNumber<C>>, java.io.Serializable, java.lang.Comparable<AlgebraicNumber<C>>
```
public class AlgebraicNumber<C extends RingElem<C>>
extends java.lang.Object
implements GcdRingElem<AlgebraicNumber<C>>
```
Algebraic number class based on GenPolynomial with RingElem interface. Objects of this class are immutable.

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

AlgebraicNumberRing<C> ring
Ring part of the data structure.

GenPolynomial<C> val
Value part of the element data structure.

Fields
Modifier and Type	Field and Description
`AlgebraicNumberRing<C>`	`ring` Ring part of the data structure.
`GenPolynomial<C>`	`val` Value part of the element data structure.

Constructor Summary

Constructors
Constructor and Description
`AlgebraicNumber(AlgebraicNumberRing<C> r)` The constructor creates a AlgebraicNumber object from a GenPolynomial object module.
`AlgebraicNumber(AlgebraicNumberRing<C> r, GenPolynomial<C> a)` The constructor creates a AlgebraicNumber object from AlgebraicNumberRing modul and a GenPolynomial value.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`AlgebraicNumber<C>`	`abs()` AlgebraicNumber absolute value.
`int`	`compareTo(AlgebraicNumber<C> b)` AlgebraicNumber comparison.
`AlgebraicNumber<C>`	`copy()` Clone this.
`AlgebraicNumber<C>`	`divide(AlgebraicNumber<C> S)` AlgebraicNumber division.
`AlgebraicNumber<C>[]`	`egcd(AlgebraicNumber<C> S)` AlgebraicNumber extended greatest common divisor.
`boolean`	`equals(java.lang.Object b)` Comparison with any other object.
`AlgebraicNumberRing<C>`	`factory()` Get the corresponding element factory.
`AlgebraicNumber<C>`	`gcd(AlgebraicNumber<C> S)` AlgebraicNumber greatest common divisor.
`GenPolynomial<C>`	`getVal()` Get the value part.
`int`	`hashCode()` Hash code for this AlgebraicNumber.
`AlgebraicNumber<C>`	`inverse()` AlgebraicNumber inverse.
`boolean`	`isONE()` Is AlgebraicNumber one.
`boolean`	`isUnit()` Is AlgebraicNumber unit.
`boolean`	`isZERO()` Is AlgebraicNumber zero.
`AlgebraicNumber<C>`	`monic()` AlgebraicNumber monic.
`AlgebraicNumber<C>`	`multiply(AlgebraicNumber<C> S)` AlgebraicNumber multiplication.
`AlgebraicNumber<C>`	`multiply(C c)` AlgebraicNumber multiplication.
`AlgebraicNumber<C>`	`multiply(GenPolynomial<C> c)` AlgebraicNumber multiplication.
`AlgebraicNumber<C>`	`negate()` AlgebraicNumber negate.
`AlgebraicNumber<C>[]`	`quotientRemainder(AlgebraicNumber<C> S)` Quotient and remainder by division of this by S.
`AlgebraicNumber<C>`	`remainder(AlgebraicNumber<C> S)` AlgebraicNumber remainder.
`int`	`signum()` AlgebraicNumber signum.
`AlgebraicNumber<C>`	`subtract(AlgebraicNumber<C> S)` AlgebraicNumber subtraction.
`AlgebraicNumber<C>`	`sum(AlgebraicNumber<C> S)` AlgebraicNumber summation.
`AlgebraicNumber<C>`	`sum(C c)` AlgebraicNumber summation.
`AlgebraicNumber<C>`	`sum(GenPolynomial<C> c)` AlgebraicNumber 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
getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - ring
```
public final AlgebraicNumberRing<C extends RingElem<C>> ring
```
    Ring part of the data structure.
  - val
```
public final GenPolynomial<C extends RingElem<C>> val
```
    Value part of the element data structure.
- Constructor Detail
  - AlgebraicNumber
```
public AlgebraicNumber(AlgebraicNumberRing<C> r,
                       GenPolynomial<C> a)
```
    The constructor creates a AlgebraicNumber object from AlgebraicNumberRing modul and a GenPolynomial value.
    
    Parameters:
    
    r - ring AlgebraicNumberRing.
    
    a - value GenPolynomial.
  - AlgebraicNumber
```
public AlgebraicNumber(AlgebraicNumberRing<C> r)
```
    The constructor creates a AlgebraicNumber object from a GenPolynomial object module.
    
    Parameters:
    
    r - ring AlgebraicNumberRing.
- Method Detail
  - getVal
```
public GenPolynomial<C> getVal()
```
    Get the value part.
    
    Returns:
    
    val.
  - factory
```
public AlgebraicNumberRing<C> factory()
```
    Get the corresponding element factory.
    
    Specified by:
    
    factory in interface Element<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    
    factory for this Element.
    
    See Also:
    
    Element.factory()
  - copy
```
public AlgebraicNumber<C> copy()
```
    Clone this.
    
    Specified by:
    
    copy in interface Element<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    
    Creates and returns a copy of this Element.
    
    See Also:
    
    Object.clone()
  - isZERO
```
public boolean isZERO()
```
    Is AlgebraicNumber zero.
    
    Specified by:
    
    isZERO in interface AbelianGroupElem<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    
    If this is 0 then true is returned, else false.
    
    See Also:
    
    AbelianGroupElem.isZERO()
  - isONE
```
public boolean isONE()
```
    Is AlgebraicNumber one.
    
    Specified by:
    
    isONE in interface MonoidElem<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    
    If this is 1 then true is returned, else false.
    
    See Also:
    
    MonoidElem.isONE()
  - isUnit
```
public boolean isUnit()
```
    Is AlgebraicNumber unit.
    
    Specified by:
    
    isUnit in interface MonoidElem<AlgebraicNumber<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<AlgebraicNumber<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<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    
    script compatible representation for this ElemFactory.
    
    See Also:
    
    Element.toScriptFactory()
  - compareTo
```
public int compareTo(AlgebraicNumber<C> b)
```
    AlgebraicNumber comparison.
    
    Specified by:
    
    compareTo in interface Element<AlgebraicNumber<C extends RingElem<C>>>
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    
    b - AlgebraicNumber.
    
    Returns:
    
    sign(this-b).
  - equals
```
public boolean equals(java.lang.Object b)
```
    Comparison with any other object.
    
    Specified by:
    
    equals in interface Element<AlgebraicNumber<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 AlgebraicNumber.
    
    Specified by:
    
    hashCode in interface Element<AlgebraicNumber<C extends RingElem<C>>>
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    the hashCode.
    
    See Also:
    
    Object.hashCode()
  - abs
```
public AlgebraicNumber<C> abs()
```
    AlgebraicNumber absolute value.
    
    Specified by:
    
    abs in interface AbelianGroupElem<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    
    the absolute value of this.
    
    See Also:
    
    AbelianGroupElem.abs()
  - sum
```
public AlgebraicNumber<C> sum(AlgebraicNumber<C> S)
```
    AlgebraicNumber summation.
    
    Specified by:
    
    sum in interface AbelianGroupElem<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    
    S - AlgebraicNumber.
    
    Returns:
    
    this+S.
  - sum
```
public AlgebraicNumber<C> sum(GenPolynomial<C> c)
```
    AlgebraicNumber summation.
    
    Parameters:
    
    c - coefficient.
    
    Returns:
    
    this+c.
  - sum
```
public AlgebraicNumber<C> sum(C c)
```
    AlgebraicNumber summation.
    
    Parameters:
    
    c - polynomial.
    
    Returns:
    
    this+c.
  - negate
```
public AlgebraicNumber<C> negate()
```
    AlgebraicNumber negate.
    
    Specified by:
    
    negate in interface AbelianGroupElem<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    
    -this.
    
    See Also:
    
    AbelianGroupElem.negate()
  - signum
```
public int signum()
```
    AlgebraicNumber signum.
    
    Specified by:
    
    signum in interface AbelianGroupElem<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    
    signum(this).
    
    See Also:
    
    AbelianGroupElem.signum()
  - subtract
```
public AlgebraicNumber<C> subtract(AlgebraicNumber<C> S)
```
    AlgebraicNumber subtraction.
    
    Specified by:
    
    subtract in interface AbelianGroupElem<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    
    S - AlgebraicNumber.
    
    Returns:
    
    this-S.
  - divide
```
public AlgebraicNumber<C> divide(AlgebraicNumber<C> S)
```
    AlgebraicNumber division.
    
    Specified by:
    
    divide in interface MonoidElem<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    
    S - AlgebraicNumber.
    
    Returns:
    
    this/S.
  - inverse
```
public AlgebraicNumber<C> inverse()
```
    AlgebraicNumber inverse.
    
    Specified by:
    
    inverse in interface MonoidElem<AlgebraicNumber<C extends RingElem<C>>>
    
    Returns:
    
    S with S = 1/this if defined.
    
    Throws:
    
    NotInvertibleException - if the element is not invertible.
    
    See Also:
    
    MonoidElem.inverse()
  - remainder
```
public AlgebraicNumber<C> remainder(AlgebraicNumber<C> S)
```
    AlgebraicNumber remainder.
    
    Specified by:
    
    remainder in interface MonoidElem<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    
    S - AlgebraicNumber.
    
    Returns:
    
    this - (this/S)*S.
  - quotientRemainder
```
public AlgebraicNumber<C>[] quotientRemainder(AlgebraicNumber<C> S)
```
    Quotient and remainder by division of this by S.
    
    Parameters:
    
    S - a AlgebraicNumber
    
    Returns:
    
    [this/S, this - (this/S)*S].
  - multiply
```
public AlgebraicNumber<C> multiply(AlgebraicNumber<C> S)
```
    AlgebraicNumber multiplication.
    
    Specified by:
    
    multiply in interface MonoidElem<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    
    S - AlgebraicNumber.
    
    Returns:
    
    this*S.
  - multiply
```
public AlgebraicNumber<C> multiply(C c)
```
    AlgebraicNumber multiplication.
    
    Parameters:
    
    c - coefficient.
    
    Returns:
    
    this*c.
  - multiply
```
public AlgebraicNumber<C> multiply(GenPolynomial<C> c)
```
    AlgebraicNumber multiplication.
    
    Parameters:
    
    c - polynomial.
    
    Returns:
    
    this*c.
  - monic
```
public AlgebraicNumber<C> monic()
```
    AlgebraicNumber monic.
    
    Returns:
    
    this with monic value part.
  - gcd
```
public AlgebraicNumber<C> gcd(AlgebraicNumber<C> S)
```
    AlgebraicNumber greatest common divisor.
    
    Specified by:
    
    gcd in interface RingElem<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    
    S - AlgebraicNumber.
    
    Returns:
    
    gcd(this,S).
  - egcd
```
public AlgebraicNumber<C>[] egcd(AlgebraicNumber<C> S)
```
    AlgebraicNumber extended greatest common divisor.
    
    Specified by:
    
    egcd in interface RingElem<AlgebraicNumber<C extends RingElem<C>>>
    
    Parameters:
    
    S - AlgebraicNumber.
    
    Returns:
    
    [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).

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Field |
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Constr |
Method

Class AlgebraicNumber<C extends RingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ring

val

Constructor Detail

AlgebraicNumber

AlgebraicNumber

Method Detail

getVal

factory

copy

isZERO

isONE

isUnit

toString

toScript

toScriptFactory

compareTo

equals

hashCode

abs

sum

sum

sum

negate

signum

subtract

divide

inverse

remainder

quotientRemainder

multiply

multiply

multiply

monic

gcd

egcd