ComplexAlgebraicNumber

java.lang.Object
- edu.jas.root.ComplexAlgebraicNumber<C>

All Implemented Interfaces:

AbelianGroupElem<ComplexAlgebraicNumber<C>>, Element<ComplexAlgebraicNumber<C>>, GcdRingElem<ComplexAlgebraicNumber<C>>, MonoidElem<ComplexAlgebraicNumber<C>>, RingElem<ComplexAlgebraicNumber<C>>, java.io.Serializable, java.lang.Comparable<ComplexAlgebraicNumber<C>>
```
public class ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>
extends java.lang.Object
implements GcdRingElem<ComplexAlgebraicNumber<C>>
```
Complex algebraic number class based on AlgebraicNumber. Objects of this class are immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

AlgebraicNumber<Complex<C>> number
Representing AlgebraicNumber.

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

Fields
Modifier and Type	Field and Description
`AlgebraicNumber<Complex<C>>`	`number` Representing AlgebraicNumber.
`ComplexAlgebraicRing<C>`	`ring` Ring part of the data structure.

Constructor Summary

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

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`ComplexAlgebraicNumber<C>`	`abs()` ComplexAlgebraicNumber absolute value.
`int`	`compareTo(AlgebraicNumber<Complex<C>> b)` ComplexAlgebraicNumber comparison.
`int`	`compareTo(ComplexAlgebraicNumber<C> b)` ComplexAlgebraicNumber comparison.
`ComplexAlgebraicNumber<C>`	`copy()` Copy this.
`Complex<BigDecimal>`	`decimalMagnitude()` ComplexAlgebraicNumber magnitude.
`ComplexAlgebraicNumber<C>`	`divide(ComplexAlgebraicNumber<C> S)` ComplexAlgebraicNumber division.
`ComplexAlgebraicNumber<C>[]`	`egcd(ComplexAlgebraicNumber<C> S)` ComplexAlgebraicNumber extended greatest common divisor.
`boolean`	`equals(java.lang.Object b)` Comparison with any other object.
`ComplexAlgebraicRing<C>`	`factory()` Get the corresponding element factory.
`ComplexAlgebraicNumber<C>`	`gcd(ComplexAlgebraicNumber<C> S)` ComplexAlgebraicNumber greatest common divisor.
`int`	`hashCode()` Hash code for this ComplexAlgebraicNumber.
`ComplexAlgebraicNumber<C>`	`inverse()` ComplexAlgebraicNumber inverse.
`boolean`	`isONE()` Is ComplexAlgebraicNumber one.
`boolean`	`isUnit()` Is ComplexAlgebraicNumber unit.
`boolean`	`isZERO()` Is ComplexAlgebraicNumber zero.
`Complex<BigRational>`	`magnitude()` ComplexAlgebraicNumber magnitude.
`ComplexAlgebraicNumber<C>`	`monic()` ComplexAlgebraicNumber monic.
`ComplexAlgebraicNumber<C>`	`multiply(Complex<C> c)` ComplexAlgebraicNumber multiplication.
`ComplexAlgebraicNumber<C>`	`multiply(ComplexAlgebraicNumber<C> S)` ComplexAlgebraicNumber multiplication.
`ComplexAlgebraicNumber<C>`	`multiply(GenPolynomial<Complex<C>> c)` ComplexAlgebraicNumber multiplication.
`ComplexAlgebraicNumber<C>`	`negate()` ComplexAlgebraicNumber negate.
`ComplexAlgebraicNumber<C>[]`	`quotientRemainder(ComplexAlgebraicNumber<C> S)` Quotient and remainder by division of this by S.
`ComplexAlgebraicNumber<C>`	`remainder(ComplexAlgebraicNumber<C> S)` ComplexAlgebraicNumber remainder.
`int`	`signum()` ComplexAlgebraicNumber signum.
`ComplexAlgebraicNumber<C>`	`subtract(ComplexAlgebraicNumber<C> S)` ComplexAlgebraicNumber subtraction.
`ComplexAlgebraicNumber<C>`	`sum(AlgebraicNumber<Complex<C>> c)` ComplexAlgebraicNumber summation.
`ComplexAlgebraicNumber<C>`	`sum(Complex<C> c)` ComplexAlgebraicNumber summation.
`ComplexAlgebraicNumber<C>`	`sum(ComplexAlgebraicNumber<C> S)` ComplexAlgebraicNumber summation.
`ComplexAlgebraicNumber<C>`	`sum(GenPolynomial<Complex<C>> c)` ComplexAlgebraicNumber 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
  - number
```
public final AlgebraicNumber<Complex<C extends GcdRingElem<C> & Rational>> number
```
    Representing AlgebraicNumber.
  - ring
```
public final ComplexAlgebraicRing<C extends GcdRingElem<C> & Rational> ring
```
    Ring part of the data structure.
- Constructor Detail
  - ComplexAlgebraicNumber
```
public ComplexAlgebraicNumber(ComplexAlgebraicRing<C> r,
                              GenPolynomial<Complex<C>> a)
```
    The constructor creates a ComplexAlgebraicNumber object from ComplexAlgebraicRing modul and a GenPolynomial value.
    
    Parameters:
    
    r - ring ComplexAlgebraicRing.
    
    a - value GenPolynomial.
  - ComplexAlgebraicNumber
```
public ComplexAlgebraicNumber(ComplexAlgebraicRing<C> r,
                              AlgebraicNumber<Complex<C>> a)
```
    The constructor creates a ComplexAlgebraicNumber object from ComplexAlgebraicRing modul and a AlgebraicNumber value.
    
    Parameters:
    
    r - ring ComplexAlgebraicRing.
    
    a - value AlgebraicNumber.
  - ComplexAlgebraicNumber
```
public ComplexAlgebraicNumber(ComplexAlgebraicRing<C> r)
```
    The constructor creates a ComplexAlgebraicNumber object from a GenPolynomial object module.
    
    Parameters:
    
    r - ring ComplexAlgebraicRing.
- Method Detail
  - factory
```
public ComplexAlgebraicRing<C> factory()
```
    Get the corresponding element factory.
    
    Specified by:
    
    factory in interface Element<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    factory for this Element.
    
    See Also:
    
    Element.factory()
  - copy
```
public ComplexAlgebraicNumber<C> copy()
```
    Copy this.
    
    Specified by:
    
    copy in interface Element<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    Creates and returns a copy of this Element.
    
    See Also:
    
    Element.copy()
  - isZERO
```
public boolean isZERO()
```
    Is ComplexAlgebraicNumber zero.
    
    Specified by:
    
    isZERO in interface AbelianGroupElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    If this is 0 then true is returned, else false.
    
    See Also:
    
    AbelianGroupElem.isZERO()
  - isONE
```
public boolean isONE()
```
    Is ComplexAlgebraicNumber one.
    
    Specified by:
    
    isONE in interface MonoidElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    If this is 1 then true is returned, else false.
    
    See Also:
    
    MonoidElem.isONE()
  - isUnit
```
public boolean isUnit()
```
    Is ComplexAlgebraicNumber unit.
    
    Specified by:
    
    isUnit in interface MonoidElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    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<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    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<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    script compatible representation for this ElemFactory.
    
    See Also:
    
    Element.toScriptFactory()
  - compareTo
```
public int compareTo(ComplexAlgebraicNumber<C> b)
```
    ComplexAlgebraicNumber comparison.
    
    Specified by:
    
    compareTo in interface Element<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    b - ComplexAlgebraicNumber.
    
    Returns:
    
    sign(this-b).
  - compareTo
```
public int compareTo(AlgebraicNumber<Complex<C>> b)
```
    ComplexAlgebraicNumber comparison.
    
    Parameters:
    
    b - AlgebraicNumber.
    
    Returns:
    
    polynomial sign(this-b).
  - equals
```
public boolean equals(java.lang.Object b)
```
    Comparison with any other object.
    
    Specified by:
    
    equals in interface Element<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    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 ComplexAlgebraicNumber.
    
    Specified by:
    
    hashCode in interface Element<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    the hashCode.
    
    See Also:
    
    Object.hashCode()
  - abs
```
public ComplexAlgebraicNumber<C> abs()
```
    ComplexAlgebraicNumber absolute value.
    
    Specified by:
    
    abs in interface AbelianGroupElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    the absolute value of this.
    
    See Also:
    
    AbelianGroupElem.abs()
  - sum
```
public ComplexAlgebraicNumber<C> sum(ComplexAlgebraicNumber<C> S)
```
    ComplexAlgebraicNumber summation.
    
    Specified by:
    
    sum in interface AbelianGroupElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    S - ComplexAlgebraicNumber.
    
    Returns:
    
    this+S.
  - sum
```
public ComplexAlgebraicNumber<C> sum(GenPolynomial<Complex<C>> c)
```
    ComplexAlgebraicNumber summation.
    
    Parameters:
    
    c - complex polynomial.
    
    Returns:
    
    this+c.
  - sum
```
public ComplexAlgebraicNumber<C> sum(AlgebraicNumber<Complex<C>> c)
```
    ComplexAlgebraicNumber summation.
    
    Parameters:
    
    c - algebraic number.
    
    Returns:
    
    this+c.
  - sum
```
public ComplexAlgebraicNumber<C> sum(Complex<C> c)
```
    ComplexAlgebraicNumber summation.
    
    Parameters:
    
    c - coefficient.
    
    Returns:
    
    this+c.
  - negate
```
public ComplexAlgebraicNumber<C> negate()
```
    ComplexAlgebraicNumber negate.
    
    Specified by:
    
    negate in interface AbelianGroupElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    -this.
    
    See Also:
    
    AbelianGroupElem.negate()
  - subtract
```
public ComplexAlgebraicNumber<C> subtract(ComplexAlgebraicNumber<C> S)
```
    ComplexAlgebraicNumber subtraction.
    
    Specified by:
    
    subtract in interface AbelianGroupElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    S - ComplexAlgebraicNumber.
    
    Returns:
    
    this-S.
  - divide
```
public ComplexAlgebraicNumber<C> divide(ComplexAlgebraicNumber<C> S)
```
    ComplexAlgebraicNumber division.
    
    Specified by:
    
    divide in interface MonoidElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    S - ComplexAlgebraicNumber.
    
    Returns:
    
    this/S.
  - inverse
```
public ComplexAlgebraicNumber<C> inverse()
```
    ComplexAlgebraicNumber inverse.
    
    Specified by:
    
    inverse in interface MonoidElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    S with S = 1/this if defined.
    
    Throws:
    
    NotInvertibleException - if the element is not invertible.
    
    See Also:
    
    MonoidElem.inverse()
  - remainder
```
public ComplexAlgebraicNumber<C> remainder(ComplexAlgebraicNumber<C> S)
```
    ComplexAlgebraicNumber remainder.
    
    Specified by:
    
    remainder in interface MonoidElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    S - ComplexAlgebraicNumber.
    
    Returns:
    
    this - (this/S)*S.
  - quotientRemainder
```
public ComplexAlgebraicNumber<C>[] quotientRemainder(ComplexAlgebraicNumber<C> S)
```
    Quotient and remainder by division of this by S.
    
    Parameters:
    
    S - a ComplexAlgebraicNumber
    
    Returns:
    
    [this/S, this - (this/S)*S].
  - multiply
```
public ComplexAlgebraicNumber<C> multiply(ComplexAlgebraicNumber<C> S)
```
    ComplexAlgebraicNumber multiplication.
    
    Specified by:
    
    multiply in interface MonoidElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    S - ComplexAlgebraicNumber.
    
    Returns:
    
    this*S.
  - multiply
```
public ComplexAlgebraicNumber<C> multiply(Complex<C> c)
```
    ComplexAlgebraicNumber multiplication.
    
    Parameters:
    
    c - coefficient.
    
    Returns:
    
    this*c.
  - multiply
```
public ComplexAlgebraicNumber<C> multiply(GenPolynomial<Complex<C>> c)
```
    ComplexAlgebraicNumber multiplication.
    
    Parameters:
    
    c - polynomial.
    
    Returns:
    
    this*c.
  - monic
```
public ComplexAlgebraicNumber<C> monic()
```
    ComplexAlgebraicNumber monic.
    
    Returns:
    
    this with monic value part.
  - gcd
```
public ComplexAlgebraicNumber<C> gcd(ComplexAlgebraicNumber<C> S)
```
    ComplexAlgebraicNumber greatest common divisor.
    
    Specified by:
    
    gcd in interface RingElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    S - ComplexAlgebraicNumber.
    
    Returns:
    
    gcd(this,S).
  - egcd
```
public ComplexAlgebraicNumber<C>[] egcd(ComplexAlgebraicNumber<C> S)
```
    ComplexAlgebraicNumber extended greatest common divisor.
    
    Specified by:
    
    egcd in interface RingElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    S - ComplexAlgebraicNumber.
    
    Returns:
    
    [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).
  - signum
```
public int signum()
```
    ComplexAlgebraicNumber signum.
    
    Specified by:
    
    signum in interface AbelianGroupElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    signum(this).
    
    See Also:
    
    AbelianGroupElem.signum()
  - magnitude
```
public Complex<BigRational> magnitude()
```
    ComplexAlgebraicNumber magnitude.
    
    Returns:
    
    |this| as complex rational number.
  - decimalMagnitude
```
public Complex<BigDecimal> decimalMagnitude()
```
    ComplexAlgebraicNumber magnitude.
    
    Returns:
    
    |this| as complex big decimal.

Class ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

number

ring

Constructor Detail

ComplexAlgebraicNumber

ComplexAlgebraicNumber

ComplexAlgebraicNumber

Method Detail

factory

copy

isZERO

isONE

isUnit

toString

toScript

toScriptFactory

compareTo

compareTo

equals

hashCode

abs

sum

sum

sum

sum

negate

subtract

divide

inverse

remainder

quotientRemainder

multiply

multiply

multiply

monic

gcd

egcd

signum

magnitude

decimalMagnitude