Package edu.jas.arith

Class BigComplex

java.lang.Object

edu.jas.arith.BigComplex

All Implemented Interfaces:

AbelianGroupElem<BigComplex>, AbelianGroupFactory<BigComplex>, Element<BigComplex>, ElemFactory<BigComplex>, GcdRingElem<BigComplex>, MonoidElem<BigComplex>, MonoidFactory<BigComplex>, RingElem<BigComplex>, RingFactory<BigComplex>, StarRingElem<BigComplex>, java.io.Serializable, java.lang.Comparable<BigComplex>

public final class BigComplex
extends java.lang.Object
implements StarRingElem<BigComplex>, GcdRingElem<BigComplex>, RingFactory<BigComplex>

BigComplex class based on BigRational implementing the RingElem respectively the StarRingElem interface. Objects of this class are immutable. The SAC2 static methods are also provided.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static BigComplex	I	The constant i.
BigRational	im	Imaginary part of the data structure.
static BigComplex	ONE	The constant 1.
BigRational	re	Real part of the data structure.
static BigComplex	ZERO	The constant 0.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	Description
BigComplex	abs()	Complex number absolute value.
long	bitLength()	Returns the number of bits in the representation of this BigComplex, including a sign bit.
static BigRational	CABS(BigComplex A)	Complex number absolute value.
static BigComplex	CCON(BigComplex A)	Complex number conjugate.
static BigComplex	CDIF(BigComplex A, BigComplex B)	Complex number difference.
java.math.BigInteger	characteristic()	Characteristic of this ring.
static BigComplex	CINV(BigComplex A)	Complex number inverse.
static BigComplex	CNEG(BigComplex A)	Complex number negative.
int	compareTo(BigComplex b)	Since complex numbers are unordered, we use lexicographical order of re and im.
BigComplex	conjugate()	Complex number conjugate.
BigComplex	copy()	Clone this.
BigComplex	copy(BigComplex c)	Copy BigComplex element c.
static BigComplex	CPROD(BigComplex A, BigComplex B)	Complex number product.
static BigComplex	CQ(BigComplex A, BigComplex B)	Complex number quotient.
static BigComplex	CRAND(int n)	Complex number, random.
static BigComplex	CSUM(BigComplex A, BigComplex B)	Complex number sum.
BigComplex	divide(BigComplex B)	Complex number divide.
BigComplex[]	egcd(BigComplex S)	BigComplex extended greatest common divisor.
boolean	equals(java.lang.Object b)	Comparison with any other object.
BigComplex	factory()	Get the corresponding element factory.
BigComplex	fromInteger(long a)	Get a BigComplex element from a long.
BigComplex	fromInteger(java.math.BigInteger a)	Get a BigComplex element from a BigInteger.
BigComplex	gcd(BigComplex S)	Complex number greatest common divisor.
java.util.List<BigComplex>	generators()	Get a list of the generating elements.
BigRational	getIm()	Get the imaginary part.
BigComplex	getIMAG()	Get the i element.
BigComplex	getONE()	Get the one element.
BigRational	getRe()	Get the real part.
BigComplex	getZERO()	Get the zero element.
int	hashCode()	Hash code for this BigComplex.
BigComplex	inverse()	Complex number inverse.
boolean	isAssociative()	Query if this ring is associative.
boolean	isCommutative()	Query if this ring is commutative.
static boolean	isCONE(BigComplex A)	Complex number one.
static boolean	isCZERO(BigComplex A)	Complex number zero.
boolean	isField()	Query if this ring is a field.
boolean	isFinite()	Is this structure finite or infinite.
boolean	isIMAG()	Is Complex imaginary one.
boolean	isONE()	Is Complex number one.
boolean	isUnit()	Is Complex unit element.
boolean	isZERO()	Is Complex number zero.
BigComplex	multiply(BigComplex B)	Complex number product.
BigComplex	negate()	Complex number negative.
BigComplex	norm()	Complex number norm.
BigComplex	parse(java.io.Reader r)	Parse complex number from Reader.
BigComplex	parse(java.lang.String s)	Parse complex number from string.
BigComplex[]	quotientRemainder(BigComplex S)	Quotient and remainder by division of this by S.
BigComplex	random(int n)	Complex number, random.
BigComplex	random(int n, java.util.Random rnd)	Complex number, random.
BigComplex	remainder(BigComplex S)	Complex number inverse.
int	signum()	Since complex numbers are unordered, we use lexicographical order of re and im.
BigComplex	subtract(BigComplex B)	Complex number subtract.
BigComplex	sum(BigComplex 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

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface edu.jas.structure.ElemFactory

valueOf

Methods inherited from interface edu.jas.structure.MonoidElem

leftDivide, leftRemainder, power, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

Methods inherited from interface edu.jas.structure.RingElem

leftGcd, rightGcd

Field Detail

re

public final BigRational re

Real part of the data structure.

im

public final BigRational im

Imaginary part of the data structure.

ZERO

public static final BigComplex ZERO

The constant 0.

ONE

public static final BigComplex ONE

The constant 1.

I

public static final BigComplex I

The constant i.

Constructor Detail

BigComplex

public BigComplex(BigRational r,
                  BigRational i)

The constructor creates a BigComplex object from two BigRational objects real and imaginary part.

Parameters:

r - real part.

i - imaginary part.

BigComplex

public BigComplex(BigRational r)

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

Parameters:

r - real part.

BigComplex

public BigComplex(long r)

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

Parameters:

r - real part.

BigComplex

public BigComplex()

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

BigComplex

public BigComplex(java.lang.String s)
           throws java.lang.NumberFormatException

The constructor creates a BigComplex object from a String representation.

Parameters:

s - string of a BigComplex.

Throws:

java.lang.NumberFormatException

Method Detail

factory

public BigComplex factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<BigComplex>

Returns:

factory for this Element.

See Also:

Element.factory()

generators

public java.util.List<BigComplex> generators()

Get a list of the generating elements.

Specified by:

generators in interface ElemFactory<BigComplex>

Returns:

list of generators for the algebraic structure.

See Also:

ElemFactory.generators()

isFinite

public boolean isFinite()

Is this structure finite or infinite.

Specified by:

isFinite in interface ElemFactory<BigComplex>

Returns:

true if this structure is finite, else false.

See Also:

ElemFactory.isFinite()

copy

public BigComplex copy()

Clone this.

Specified by:

copy in interface Element<BigComplex>

Returns:

Creates and returns a copy of this Element.

See Also:

Object.clone()

copy

public BigComplex copy(BigComplex c)

Copy BigComplex element c.

Specified by:

copy in interface ElemFactory<BigComplex>

Parameters:

c - BigComplex.

Returns:

a copy of c.

getZERO

public BigComplex getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<BigComplex>

Returns:

0 as BigComplex.

getONE

public BigComplex getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<BigComplex>

Returns:

1 as BigComplex.

getIMAG

public BigComplex getIMAG()

Get the i element.

Returns:

i as BigComplex.

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

isCommutative in interface MonoidFactory<BigComplex>

Returns:

true.

isAssociative

public boolean isAssociative()

Query if this ring is associative.

Specified by:

isAssociative in interface MonoidFactory<BigComplex>

Returns:

true.

isField

public boolean isField()

Query if this ring is a field.

Specified by:

isField in interface RingFactory<BigComplex>

Returns:

true.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<BigComplex>

Returns:

characteristic of this ring.

fromInteger

public BigComplex fromInteger(java.math.BigInteger a)

Get a BigComplex element from a BigInteger.

Specified by:

fromInteger in interface ElemFactory<BigComplex>

Parameters:

a - BigInteger.

Returns:

a BigComplex.

fromInteger

public BigComplex fromInteger(long a)

Get a BigComplex element from a long.

Specified by:

fromInteger in interface ElemFactory<BigComplex>

Parameters:

a - long.

Returns:

a BigComplex.

getRe

public BigRational getRe()

Get the real part.

Returns:

re.

getIm

public BigRational getIm()

Get the imaginary part.

Returns:

im.

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<BigComplex>

Specified by:

toScript in interface ElemFactory<BigComplex>

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<BigComplex>

Returns:

script compatible representation for this ElemFactory.

See Also:

Element.toScriptFactory()

isCZERO

public static boolean isCZERO(BigComplex A)

Complex number zero.

Parameters:

A - is a complex number.

Returns:

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

isZERO

public boolean isZERO()

Is Complex number zero.

Specified by:

isZERO in interface AbelianGroupElem<BigComplex>

Returns:

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

See Also:

AbelianGroupElem.isZERO()

isCONE

public static boolean isCONE(BigComplex A)

Complex number one.

Parameters:

A - is a complex number.

Returns:

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

isONE

public boolean isONE()

Is Complex number one.

Specified by:

isONE in interface MonoidElem<BigComplex>

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<BigComplex>

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<BigComplex>

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 BigComplex.

Specified by:

hashCode in interface Element<BigComplex>

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

compareTo

public int compareTo(BigComplex b)

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

Specified by:

compareTo in interface java.lang.Comparable<BigComplex>

Specified by:

compareTo in interface Element<BigComplex>

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<BigComplex>

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 BigComplex sum(BigComplex B)

Complex number summation.

Specified by:

sum in interface AbelianGroupElem<BigComplex>

Parameters:

B - a BigComplex number.

Returns:

this+B.

CSUM

public static BigComplex CSUM(BigComplex A,
                              BigComplex B)

Complex number sum.

Parameters:

A - and B are complex numbers.

Returns:

A+B.

CDIF

public static BigComplex CDIF(BigComplex A,
                              BigComplex B)

Complex number difference.

Parameters:

A - and B are complex numbers.

Returns:

A-B.

subtract

public BigComplex subtract(BigComplex B)

Complex number subtract.

Specified by:

subtract in interface AbelianGroupElem<BigComplex>

Parameters:

B - a BigComplex number.

Returns:

this-B.

CNEG

public static BigComplex CNEG(BigComplex A)

Complex number negative.

Parameters:

A - is a complex number.

Returns:

-A

negate

public BigComplex negate()

Complex number negative.

Specified by:

negate in interface AbelianGroupElem<BigComplex>

Returns:

-this.

See Also:

AbelianGroupElem.negate()

CCON

public static BigComplex CCON(BigComplex A)

Complex number conjugate.

Parameters:

A - is a complex number.

Returns:

the complex conjugate of A.

conjugate

public BigComplex conjugate()

Complex number conjugate.

Specified by:

conjugate in interface StarRingElem<BigComplex>

Returns:

the complex conjugate of this.

norm

public BigComplex norm()

Complex number norm.

Specified by:

norm in interface StarRingElem<BigComplex>

Returns:

||this||.

See Also:

StarRingElem.norm()

abs

public BigComplex abs()

Complex number absolute value.

Specified by:

abs in interface AbelianGroupElem<BigComplex>

Returns:

|this|.

See Also:

AbelianGroupElem.abs()

CABS

public static BigRational CABS(BigComplex A)

Complex number absolute value.

Parameters:

A - is a complex number.

Returns:

the absolute value of A, a rational number. Note: The square root is not jet implemented.

CPROD

public static BigComplex CPROD(BigComplex A,
                               BigComplex B)

Complex number product.

Parameters:

A - and B are complex numbers.

Returns:

A*B.

multiply

public BigComplex multiply(BigComplex B)

Complex number product.

Specified by:

multiply in interface MonoidElem<BigComplex>

Parameters:

B - is a complex number.

Returns:

this*B.

CINV

public static BigComplex CINV(BigComplex A)

Complex number inverse.

Parameters:

A - is a non-zero complex number.

Returns:

S with S*A = 1.

inverse

public BigComplex inverse()

Complex number inverse.

Specified by:

inverse in interface MonoidElem<BigComplex>

Returns:

S with S*this = 1.

See Also:

MonoidElem.inverse()

remainder

public BigComplex remainder(BigComplex S)

Complex number inverse.

Specified by:

remainder in interface MonoidElem<BigComplex>

Parameters:

S - is a complex number.

Returns:

0.

CQ

public static BigComplex CQ(BigComplex A,
                            BigComplex B)

Complex number quotient.

Parameters:

A - and B are complex numbers, B non-zero.

Returns:

A/B.

divide

public BigComplex divide(BigComplex B)

Complex number divide.

Specified by:

divide in interface MonoidElem<BigComplex>

Parameters:

B - is a complex number, non-zero.

Returns:

this/B.

quotientRemainder

public BigComplex[] quotientRemainder(BigComplex S)

Quotient and remainder by division of this by S.

Specified by:

quotientRemainder in interface MonoidElem<BigComplex>

Parameters:

S - a complex number

Returns:

[this/S, this - (this/S)*S].

random

public BigComplex random(int n)

Complex number, random. Random rational numbers A and B are generated using random(n). Then R is the complex number with real part A and imaginary part B.

Specified by:

random in interface ElemFactory<BigComplex>

Parameters:

n - such that 0 ≤ A, B ≤ (2ⁿ-1).

Returns:

R.

random

public BigComplex random(int n,
                         java.util.Random rnd)

Complex number, random. Random rational numbers A and B are generated using random(n). Then R is the complex number with real part A and imaginary part B.

Specified by:

random in interface ElemFactory<BigComplex>

Parameters:

n - such that 0 ≤ A, B ≤ (2ⁿ-1).

rnd - is a source for random bits.

Returns:

R.

CRAND

public static BigComplex CRAND(int n)

Complex number, random. Random rational numbers A and B are generated using random(n). Then R is the complex number with real part A and imaginary part B.

Parameters:

n - such that 0 ≤ A, B ≤ (2ⁿ-1).

Returns:

R.

parse

public BigComplex parse(java.lang.String s)

Parse complex number from string.

Specified by:

parse in interface ElemFactory<BigComplex>

Parameters:

s - String.

Returns:

BigComplex from s.

parse

public BigComplex parse(java.io.Reader r)

Parse complex number from Reader.

Specified by:

parse in interface ElemFactory<BigComplex>

Parameters:

r - Reader.

Returns:

next BigComplex from r.

gcd

public BigComplex gcd(BigComplex S)

Complex number greatest common divisor.

Specified by:

gcd in interface RingElem<BigComplex>

Parameters:

S - BigComplex.

Returns:

gcd(this,S).

egcd

public BigComplex[] egcd(BigComplex S)

BigComplex extended greatest common divisor.

Specified by:

egcd in interface RingElem<BigComplex>

Parameters:

S - BigComplex.

Returns:

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

bitLength

public long bitLength()

Returns the number of bits in the representation of this BigComplex, including a sign bit. It is equivalent to re.bitLength() + im.bitLength().)

Returns:

number of bits in the representation of this BigComplex, including a sign bit.