edu.jas.poly

Class Complex<C extends RingElem<C>>

java.lang.Object

edu.jas.poly.Complex<C>

Type Parameters:

C - base type of RingElem (for complex polynomials).

All Implemented Interfaces:

AbelianGroupElem<Complex<C>>, Element<Complex<C>>, GcdRingElem<Complex<C>>, MonoidElem<Complex<C>>, RingElem<Complex<C>>, StarRingElem<Complex<C>>, java.io.Serializable, java.lang.Comparable<Complex<C>>

public class Complex<C extends RingElem<C>>
extends java.lang.Object
implements StarRingElem<Complex<C>>, GcdRingElem<Complex<C>>

Generic Complex class implementing the RingElem interface. Objects of this class are immutable.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
ComplexRing<C>	ring Complex class factory data structure.

Constructor Summary

Constructors

Constructor and Description
Complex(ComplexRing<C> ring) The constructor creates a Complex object with real part 0 and imaginary part 0.
Complex(ComplexRing<C> ring, C r) The constructor creates a Complex object from a C object as real part, the imaginary part is set to 0.
Complex(ComplexRing<C> ring, C r, C i) The constructor creates a Complex object from two C objects as real and imaginary part.
Complex(ComplexRing<C> ring, long r) The constructor creates a Complex object from a long element as real part, the imaginary part is set to 0.
Complex(ComplexRing<C> ring, java.lang.String s) The constructor creates a Complex object from a String representation.

Method Summary

Modifier and Type	Method and Description
Complex<C>	abs() Complex number absolute value.
int	compareTo(Complex<C> b) Since complex numbers are unordered, we use lexicographical order of re and im.
Complex<C>	conjugate() Complex number conjugate.
Complex<C>	copy() Clone this.
Complex<C>	divide(Complex<C> B) Complex number divide.
Complex<C>[]	divideAndRemainder(Complex<C> S) Deprecated. use quotientRemainder()
Complex<C>[]	egcd(Complex<C> S) Complex extended greatest common divisor.
boolean	equals(java.lang.Object b) Comparison with any other object.
ComplexRing<C>	factory() Get the corresponding element factory.
Complex<C>	gcd(Complex<C> S) Complex number greatest common divisor.
C	getIm() Get the imaginary part.
C	getRe() Get the real part.
int	hashCode() Hash code for this Complex.
Complex<C>	inverse() Complex number inverse.
boolean	isIMAG() Is Complex imaginary one.
boolean	isONE() Is Complex number one.
boolean	isUnit() Is Complex unit element.
boolean	isZERO() Is Complex number zero.
Complex<C>	multiply(Complex<C> B) Complex number product.
Complex<C>	negate() Complex number negative.
Complex<C>	norm() Complex number norm.
Complex<C>[]	quotientRemainder(Complex<C> S) Complex number quotient and remainder.
Complex<C>	remainder(Complex<C> S) Complex number remainder.
int	signum() Since complex numbers are unordered, we use lexicographical order of re and im.
Complex<C>	subtract(Complex<C> B) Complex number subtract.
Complex<C>	sum(Complex<C> B) Complex number 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.

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Field Detail

ring

public final ComplexRing<C extends RingElem<C>> ring

Complex class factory data structure.

Constructor Detail

Complex

public Complex(ComplexRing<C> ring,
               C r,
               C i)

The constructor creates a Complex object from two C objects as real and imaginary part.

Parameters:

ring - factory for Complex objects.

r - real part.

i - imaginary part.

Complex

public Complex(ComplexRing<C> ring,
               C r)

The constructor creates a Complex object from a C object as real part, the imaginary part is set to 0.

Parameters:

r - real part.

Complex

public Complex(ComplexRing<C> ring,
               long r)

The constructor creates a Complex object from a long element as real part, the imaginary part is set to 0.

Parameters:

r - real part.

Complex

public Complex(ComplexRing<C> ring)

The constructor creates a Complex object with real part 0 and imaginary part 0.

Complex

public Complex(ComplexRing<C> ring,
               java.lang.String s)
        throws java.lang.NumberFormatException

The constructor creates a Complex object from a String representation.

Parameters:

s - string of a Complex.

Throws:

java.lang.NumberFormatException

Method Detail

factory

public ComplexRing<C> factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<Complex<C extends RingElem<C>>>

Returns:

factory for this Element.

See Also:

Element.factory()

getRe

public C getRe()

Get the real part.

Returns:

re.

getIm

public C getIm()

Get the imaginary part.

Returns:

im.

copy

public Complex<C> copy()

Clone this.

Specified by:

copy in interface Element<Complex<C extends RingElem<C>>>

Returns:

Creates and returns a copy of this Element.

See Also:

Object.clone()

toString

public java.lang.String toString()

Get the String representation.

Overrides:

toString in class java.lang.Object

toScript

public java.lang.String toScript()

Get a scripting compatible string representation.

Specified by:

toScript in interface Element<Complex<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<Complex<C extends RingElem<C>>>

Returns:

script compatible representation for this ElemFactory.

See Also:

Element.toScriptFactory()

isZERO

public boolean isZERO()

Is Complex number zero.

Specified by:

isZERO in interface AbelianGroupElem<Complex<C extends RingElem<C>>>

Returns:

If this is 0 then true is returned, else false.

See Also:

AbelianGroupElem.isZERO()

isONE

public boolean isONE()

Is Complex number one.

Specified by:

isONE in interface MonoidElem<Complex<C extends RingElem<C>>>

Returns:

If this is 1 then true is returned, else false.

See Also:

MonoidElem.isONE()

isIMAG

public boolean isIMAG()

Is Complex imaginary one.

Returns:

If this is i then true is returned, else false.

isUnit

public boolean isUnit()

Is Complex unit element.

Specified by:

isUnit in interface MonoidElem<Complex<C extends RingElem<C>>>

Returns:

If this is a unit then true is returned, else false.

See Also:

MonoidElem.isUnit()

equals

public boolean equals(java.lang.Object b)

Comparison with any other object.

Specified by:

equals in interface Element<Complex<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 Complex.

Specified by:

hashCode in interface Element<Complex<C extends RingElem<C>>>

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

compareTo

public int compareTo(Complex<C> b)

Since complex numbers are unordered, we use lexicographical order of re and im.

Specified by:

compareTo in interface Element<Complex<C extends RingElem<C>>>

Specified by:

compareTo in interface java.lang.Comparable<Complex<C extends RingElem<C>>>

Returns:

0 if this is equal to b; 1 if re > b.re, or re == b.re and im > b.im; -1 if re < b.re, or re == b.re and im < b.im

signum

public int signum()

Since complex numbers are unordered, we use lexicographical order of re and im.

Specified by:

signum in interface AbelianGroupElem<Complex<C extends RingElem<C>>>

Returns:

0 if this is equal to 0; 1 if re > 0, or re == 0 and im > 0; -1 if re < 0, or re == 0 and im < 0

See Also:

AbelianGroupElem.signum()

sum

public Complex<C> sum(Complex<C> B)

Complex number summation.

Specified by:

sum in interface AbelianGroupElem<Complex<C extends RingElem<C>>>

Parameters:

B - a Complex number.

Returns:

this+B.

subtract

public Complex<C> subtract(Complex<C> B)

Complex number subtract.

Specified by:

subtract in interface AbelianGroupElem<Complex<C extends RingElem<C>>>

Parameters:

B - a Complex number.

Returns:

this-B.

negate

public Complex<C> negate()

Complex number negative.

Specified by:

negate in interface AbelianGroupElem<Complex<C extends RingElem<C>>>

Returns:

-this.

See Also:

AbelianGroupElem.negate()

conjugate

public Complex<C> conjugate()

Complex number conjugate.

Specified by:

conjugate in interface StarRingElem<Complex<C extends RingElem<C>>>

Returns:

the complex conjugate of this.

norm

public Complex<C> norm()

Complex number norm.

Specified by:

norm in interface StarRingElem<Complex<C extends RingElem<C>>>

Returns:

||this||.

See Also:

StarRingElem.norm()

abs

public Complex<C> abs()

Complex number absolute value.

Specified by:

abs in interface AbelianGroupElem<Complex<C extends RingElem<C>>>

Returns:

|this|^2. Note: The square root is not jet implemented.

See Also:

AbelianGroupElem.abs()

multiply

public Complex<C> multiply(Complex<C> B)

Complex number product.

Specified by:

multiply in interface MonoidElem<Complex<C extends RingElem<C>>>

Parameters:

B - is a complex number.

Returns:

this*B.

inverse

public Complex<C> inverse()

Complex number inverse.

Specified by:

inverse in interface MonoidElem<Complex<C extends RingElem<C>>>

Returns:

S with S*this = 1, if it is defined.

See Also:

MonoidElem.inverse()

remainder

public Complex<C> remainder(Complex<C> S)

Complex number remainder.

Specified by:

remainder in interface MonoidElem<Complex<C extends RingElem<C>>>

Parameters:

S - is a complex number.

Returns:

0.

divide

public Complex<C> divide(Complex<C> B)

Complex number divide.

Specified by:

divide in interface MonoidElem<Complex<C extends RingElem<C>>>

Parameters:

B - is a complex number, non-zero.

Returns:

this/B.

quotientRemainder

public Complex<C>[] quotientRemainder(Complex<C> S)

Complex number quotient and remainder.

Parameters:

S - Complex.

Returns:

Complex[] { q, r } with q = this/S and r = rem(this,S).

divideAndRemainder

@Deprecated
public Complex<C>[] divideAndRemainder(Complex<C> S)

Deprecated. use quotientRemainder()

Complex number quotient and remainder.

Parameters:

S - Complex.

Returns:

Complex[] { q, r } with q = this/S and r = rem(this,S).

gcd

public Complex<C> gcd(Complex<C> S)

Complex number greatest common divisor.

Specified by:

gcd in interface RingElem<Complex<C extends RingElem<C>>>

Parameters:

S - Complex.

Returns:

gcd(this,S).

egcd

public Complex<C>[] egcd(Complex<C> S)

Complex extended greatest common divisor.

Specified by:

egcd in interface RingElem<Complex<C extends RingElem<C>>>

Parameters:

S - Complex.

Returns:

[ gcd(this,S), a, b ] with a*this + b*S = gcd(this,S).