edu.jas.root

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

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.

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

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	isRootOfUnity() Is ComplexAlgebraicNumber a root of unity.
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

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

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()

isRootOfUnity

public boolean isRootOfUnity()

Is ComplexAlgebraicNumber a root of unity.

Returns:

true if |this**i| == 1, for some 0 < i ≤ deg(modul), 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<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.

Specified by:

quotientRemainder in interface MonoidElem<ComplexAlgebraicNumber<C extends GcdRingElem<C> & Rational>>

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.