RealAlgebraicNumber

Documentation of 'edu.jas.application.RealAlgebraicNumber' Java class RealAlgebraicNumber

All Classes

Summary:
Nested |
Field |
Constr |
Method

Detail:
Field |
Constr |
Method

java.lang.Object
- edu.jas.application.RealAlgebraicNumber<C>

All Implemented Interfaces:

Rational, AbelianGroupElem<RealAlgebraicNumber<C>>, Element<RealAlgebraicNumber<C>>, GcdRingElem<RealAlgebraicNumber<C>>, MonoidElem<RealAlgebraicNumber<C>>, RingElem<RealAlgebraicNumber<C>>, java.io.Serializable, java.lang.Comparable<RealAlgebraicNumber<C>>
```
public class RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>
extends java.lang.Object
implements GcdRingElem<RealAlgebraicNumber<C>>, Rational
```
Complex algebraic number class based on bi-variate real algebraic numbers. Objects of this class are immutable. Bi-variate ideal implementation is in version 3614 2011-04-28 09:20:34Z.

See Also:

Serialized Form

Field Summary

Fields
Modifier and Type	Field and Description
`RealAlgebraicNumber<RealAlgebraicNumber<C>>`	`number` Representing recursive RealAlgebraicNumber.
`RealAlgebraicRing<C>`	`ring` Ring part of the data structure.

Constructor Summary

Constructors
Constructor and Description
`RealAlgebraicNumber(RealAlgebraicRing<C> r)` The constructor creates a zero RealAlgebraicNumber.
`RealAlgebraicNumber(RealAlgebraicRing<C> r, C a)` The constructor creates a RealAlgebraicNumber object from a GenPolynomial value.
`RealAlgebraicNumber(RealAlgebraicRing<C> r, GenPolynomial<C> a)` The constructor creates a RealAlgebraicNumber object from a GenPolynomial value.
`RealAlgebraicNumber(RealAlgebraicRing<C> r, RealAlgebraicNumber<RealAlgebraicNumber<C>> a)` The constructor creates a RealAlgebraicNumber object from a recursive real algebraic value.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`RealAlgebraicNumber<C>`	`abs()` RealAlgebraicNumber absolute value.
`int`	`compareTo(RealAlgebraicNumber<C> b)` RealAlgebraicNumber comparison.
`int`	`compareTo(RealAlgebraicNumber<RealAlgebraicNumber<C>> b)` RealAlgebraicNumber comparison.
`RealAlgebraicNumber<C>`	`copy()` Clone this.
`BigDecimal`	`decimalMagnitude()` RealAlgebraicNumber decimal magnitude.
`RealAlgebraicNumber<C>`	`divide(RealAlgebraicNumber<C> S)` RealAlgebraicNumber division.
`RealAlgebraicNumber<C>[]`	`egcd(RealAlgebraicNumber<C> S)` RealAlgebraicNumber extended greatest common divisor.
`boolean`	`equals(java.lang.Object b)` Comparison with any other object.
`RealAlgebraicRing<C>`	`factory()` Get the corresponding element factory.
`RealAlgebraicNumber<C>`	`gcd(RealAlgebraicNumber<C> S)` RealAlgebraicNumber greatest common divisor.
`BigRational`	`getRational()` Return a BigRational approximation of this Element.
`int`	`hashCode()` Hash code for this RealAlgebraicNumber.
`RealAlgebraicNumber<C>`	`inverse()` RealAlgebraicNumber inverse.
`boolean`	`isONE()` Is RealAlgebraicNumber one.
`boolean`	`isUnit()` Is RealAlgebraicNumber unit.
`boolean`	`isZERO()` Is RealAlgebraicNumber zero.
`BigRational`	`magnitude()` RealAlgebraicNumber magnitude.
`RealAlgebraicNumber<C>`	`monic()` RealAlgebraicNumber monic.
`RealAlgebraicNumber<C>`	`multiply(RealAlgebraicNumber<C> S)` RealAlgebraicNumber multiplication.
`RealAlgebraicNumber<C>`	`multiply(RealAlgebraicNumber<RealAlgebraicNumber<C>> c)` RealAlgebraicNumber multiplication.
`RealAlgebraicNumber<C>`	`negate()` RealAlgebraicNumber negate.
`RealAlgebraicNumber<C>`	`remainder(RealAlgebraicNumber<C> S)` RealAlgebraicNumber remainder.
`int`	`signum()` RealAlgebraicNumber signum.
`RealAlgebraicNumber<C>`	`subtract(RealAlgebraicNumber<C> S)` RealAlgebraicNumber subtraction.
`RealAlgebraicNumber<C>`	`sum(RealAlgebraicNumber<C> S)` RealAlgebraicNumber summation.
`RealAlgebraicNumber<C>`	`sum(RealAlgebraicNumber<RealAlgebraicNumber<C>> c)` RealAlgebraicNumber 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
  - number
```
public final RealAlgebraicNumber<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>> number
```
    Representing recursive RealAlgebraicNumber.
  - ring
```
public final RealAlgebraicRing<C extends GcdRingElem<C> & Rational> ring
```
    Ring part of the data structure.
- Constructor Detail
  - RealAlgebraicNumber
```
public RealAlgebraicNumber(RealAlgebraicRing<C> r)
```
    The constructor creates a zero RealAlgebraicNumber.
    
    Parameters:
    
    r - ring RealAlgebraicRing.
  - RealAlgebraicNumber
```
public RealAlgebraicNumber(RealAlgebraicRing<C> r,
                           C a)
```
    The constructor creates a RealAlgebraicNumber object from a GenPolynomial value.
    
    Parameters:
    
    r - ring RealAlgebraicRing.
    
    a - value element .
  - RealAlgebraicNumber
```
public RealAlgebraicNumber(RealAlgebraicRing<C> r,
                           GenPolynomial<C> a)
```
    The constructor creates a RealAlgebraicNumber object from a GenPolynomial value.
    
    Parameters:
    
    r - ring RealAlgebraicRing.
    
    a - value GenPolynomial.
  - RealAlgebraicNumber
```
public RealAlgebraicNumber(RealAlgebraicRing<C> r,
                           RealAlgebraicNumber<RealAlgebraicNumber<C>> a)
```
    The constructor creates a RealAlgebraicNumber object from a recursive real algebraic value.
    
    Parameters:
    
    r - ring RealAlgebraicRing.
    
    a - recursive real algebraic number.
- Method Detail
  - factory
```
public RealAlgebraicRing<C> factory()
```
    Get the corresponding element factory.
    
    Specified by:
    
    factory in interface Element<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    factory for this Element.
    
    See Also:
    
    Element.factory()
  - copy
```
public RealAlgebraicNumber<C> copy()
```
    Clone this.
    
    Specified by:
    
    copy in interface Element<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    Creates and returns a copy of this Element.
    
    See Also:
    
    Object.clone()
  - getRational
```
public BigRational getRational()
```
    Return a BigRational approximation of this Element.
    
    Specified by:
    
    getRational in interface Rational
    
    Returns:
    
    a BigRational approximation of this.
    
    See Also:
    
    Rational.getRational()
  - isZERO
```
public boolean isZERO()
```
    Is RealAlgebraicNumber zero.
    
    Specified by:
    
    isZERO in interface AbelianGroupElem<RealAlgebraicNumber<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 RealAlgebraicNumber one.
    
    Specified by:
    
    isONE in interface MonoidElem<RealAlgebraicNumber<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 RealAlgebraicNumber unit.
    
    Specified by:
    
    isUnit in interface MonoidElem<RealAlgebraicNumber<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<RealAlgebraicNumber<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<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    script compatible representation for this ElemFactory.
    
    See Also:
    
    Element.toScriptFactory()
  - compareTo
```
public int compareTo(RealAlgebraicNumber<C> b)
```
    RealAlgebraicNumber comparison.
    
    Specified by:
    
    compareTo in interface Element<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    b - RealAlgebraicNumber.
    
    Returns:
    
    sign(this-b).
  - compareTo
```
public int compareTo(RealAlgebraicNumber<RealAlgebraicNumber<C>> b)
```
    RealAlgebraicNumber 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<RealAlgebraicNumber<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 RealAlgebraicNumber.
    
    Specified by:
    
    hashCode in interface Element<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Overrides:
    
    hashCode in class java.lang.Object
    
    Returns:
    
    the hashCode.
    
    See Also:
    
    Object.hashCode()
  - abs
```
public RealAlgebraicNumber<C> abs()
```
    RealAlgebraicNumber absolute value.
    
    Specified by:
    
    abs in interface AbelianGroupElem<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    the absolute value of this.
    
    See Also:
    
    AbelianGroupElem.abs()
  - sum
```
public RealAlgebraicNumber<C> sum(RealAlgebraicNumber<C> S)
```
    RealAlgebraicNumber summation.
    
    Specified by:
    
    sum in interface AbelianGroupElem<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    S - RealAlgebraicNumber.
    
    Returns:
    
    this+S.
  - sum
```
public RealAlgebraicNumber<C> sum(RealAlgebraicNumber<RealAlgebraicNumber<C>> c)
```
    RealAlgebraicNumber summation.
    
    Parameters:
    
    c - recursive real algebraic number.
    
    Returns:
    
    this+c.
  - negate
```
public RealAlgebraicNumber<C> negate()
```
    RealAlgebraicNumber negate.
    
    Specified by:
    
    negate in interface AbelianGroupElem<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    -this.
    
    See Also:
    
    AbelianGroupElem.negate()
  - subtract
```
public RealAlgebraicNumber<C> subtract(RealAlgebraicNumber<C> S)
```
    RealAlgebraicNumber subtraction.
    
    Specified by:
    
    subtract in interface AbelianGroupElem<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    S - RealAlgebraicNumber.
    
    Returns:
    
    this-S.
  - divide
```
public RealAlgebraicNumber<C> divide(RealAlgebraicNumber<C> S)
```
    RealAlgebraicNumber division.
    
    Specified by:
    
    divide in interface MonoidElem<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    S - RealAlgebraicNumber.
    
    Returns:
    
    this/S.
  - inverse
```
public RealAlgebraicNumber<C> inverse()
```
    RealAlgebraicNumber inverse.
    
    Specified by:
    
    inverse in interface MonoidElem<RealAlgebraicNumber<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 RealAlgebraicNumber<C> remainder(RealAlgebraicNumber<C> S)
```
    RealAlgebraicNumber remainder.
    
    Specified by:
    
    remainder in interface MonoidElem<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    S - RealAlgebraicNumber.
    
    Returns:
    
    this - (this/S)*S.
  - multiply
```
public RealAlgebraicNumber<C> multiply(RealAlgebraicNumber<C> S)
```
    RealAlgebraicNumber multiplication.
    
    Specified by:
    
    multiply in interface MonoidElem<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    S - RealAlgebraicNumber.
    
    Returns:
    
    this*S.
  - multiply
```
public RealAlgebraicNumber<C> multiply(RealAlgebraicNumber<RealAlgebraicNumber<C>> c)
```
    RealAlgebraicNumber multiplication.
    
    Parameters:
    
    c - recursive real algebraic number.
    
    Returns:
    
    this*c.
  - monic
```
public RealAlgebraicNumber<C> monic()
```
    RealAlgebraicNumber monic.
    
    Returns:
    
    this with monic value part.
  - gcd
```
public RealAlgebraicNumber<C> gcd(RealAlgebraicNumber<C> S)
```
    RealAlgebraicNumber greatest common divisor.
    
    Specified by:
    
    gcd in interface RingElem<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    S - RealAlgebraicNumber.
    
    Returns:
    
    gcd(this,S).
  - egcd
```
public RealAlgebraicNumber<C>[] egcd(RealAlgebraicNumber<C> S)
```
    RealAlgebraicNumber extended greatest common divisor.
    
    Specified by:
    
    egcd in interface RingElem<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Parameters:
    
    S - RealAlgebraicNumber.
    
    Returns:
    
    [ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).
  - signum
```
public int signum()
```
    RealAlgebraicNumber signum.
    
    Specified by:
    
    signum in interface AbelianGroupElem<RealAlgebraicNumber<C extends GcdRingElem<C> & Rational>>
    
    Returns:
    
    signum(this).
    
    See Also:
    
    AbelianGroupElem.signum()
  - magnitude
```
public BigRational magnitude()
```
    RealAlgebraicNumber magnitude.
    
    Returns:
    
    |this| as rational number.
  - decimalMagnitude
```
public BigDecimal decimalMagnitude()
```
    RealAlgebraicNumber decimal magnitude.
    
    Returns:
    
    |this| as big decimal.

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All Classes

Summary:
Nested |
Field |
Constr |
Method

Detail:
Field |
Constr |
Method

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

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

number

ring

Constructor Detail

RealAlgebraicNumber

RealAlgebraicNumber

RealAlgebraicNumber

RealAlgebraicNumber

Method Detail

factory

copy

getRational

isZERO

isONE

isUnit

toString

toScript

toScriptFactory

compareTo

compareTo

equals

hashCode

abs

sum

sum

negate

subtract

divide

inverse

remainder

multiply

multiply

monic

gcd

egcd

signum

magnitude

decimalMagnitude