edu.jas.arith

Class BigDecimalComplex

java.lang.Object

edu.jas.arith.BigDecimalComplex

All Implemented Interfaces:

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

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

BigComplex class based on BigDecimal implementing the RingElem respectively the StarRingElem interface. Objects of this class are immutable.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

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

Constructor Summary

Constructors

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

Method Summary

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

leftGcd, rightGcd

Methods inherited from interface edu.jas.structure.MonoidElem

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

Field Detail

re

public final BigDecimal re

Real part of the data structure.

im

public final BigDecimal im

Imaginary part of the data structure.

ZERO

public static final BigDecimalComplex ZERO

The constant 0.

ONE

public static final BigDecimalComplex ONE

The constant 1.

I

public static final BigDecimalComplex I

The constant i.

Constructor Detail

BigDecimalComplex

public BigDecimalComplex(BigDecimal r,
                         BigDecimal i)

The constructor creates a BigDecimalComplex object from two BigDecimal objects real and imaginary part.

Parameters:

r - real part.

i - imaginary part.

BigDecimalComplex

public BigDecimalComplex(BigDecimal r)

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

Parameters:

r - real part.

BigDecimalComplex

public BigDecimalComplex(long r)

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

Parameters:

r - real part.

BigDecimalComplex

public BigDecimalComplex()

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

BigDecimalComplex

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

The constructor creates a BigDecimalComplex object from a String representation.

Parameters:

s - string of a BigDecimalComplex.

Throws:

java.lang.NumberFormatException

BigDecimalComplex

public BigDecimalComplex(BigComplex a)

The constructor creates a BigDecimalComplex object from a BigComplex object.

Parameters:

a - rational BigComplex.

Method Detail

factory

public BigDecimalComplex factory()

Get the corresponding element factory.

Specified by:

factory in interface Element<BigDecimalComplex>

Returns:

factory for this Element.

See Also:

Element.factory()

generators

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

Get a list of the generating elements.

Specified by:

generators in interface ElemFactory<BigDecimalComplex>

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<BigDecimalComplex>

Returns:

true if this structure is finite, else false.

See Also:

ElemFactory.isFinite()

copy

public BigDecimalComplex copy()

Clone this.

Specified by:

copy in interface Element<BigDecimalComplex>

Returns:

Creates and returns a copy of this Element.

See Also:

Object.clone()

copy

public BigDecimalComplex copy(BigDecimalComplex c)

Copy BigDecimalComplex element c.

Specified by:

copy in interface ElemFactory<BigDecimalComplex>

Parameters:

c - BigDecimalComplex.

Returns:

a copy of c.

getZERO

public BigDecimalComplex getZERO()

Get the zero element.

Specified by:

getZERO in interface AbelianGroupFactory<BigDecimalComplex>

Returns:

0 as BigDecimalComplex.

getONE

public BigDecimalComplex getONE()

Get the one element.

Specified by:

getONE in interface MonoidFactory<BigDecimalComplex>

Returns:

1 as BigDecimalComplex.

getIMAG

public BigDecimalComplex getIMAG()

Get the i element.

Returns:

i as BigDecimalComplex.

isCommutative

public boolean isCommutative()

Query if this ring is commutative.

Specified by:

isCommutative in interface MonoidFactory<BigDecimalComplex>

Returns:

true.

isAssociative

public boolean isAssociative()

Query if this ring is associative.

Specified by:

isAssociative in interface MonoidFactory<BigDecimalComplex>

Returns:

true.

isField

public boolean isField()

Query if this ring is a field.

Specified by:

isField in interface RingFactory<BigDecimalComplex>

Returns:

true.

characteristic

public java.math.BigInteger characteristic()

Characteristic of this ring.

Specified by:

characteristic in interface RingFactory<BigDecimalComplex>

Returns:

characteristic of this ring.

fromInteger

public BigDecimalComplex fromInteger(java.math.BigInteger a)

Get a BigDecimalComplex element from a BigInteger.

Specified by:

fromInteger in interface ElemFactory<BigDecimalComplex>

Parameters:

a - BigInteger.

Returns:

a BigDecimalComplex.

fromInteger

public BigDecimalComplex fromInteger(long a)

Get a BigDecimalComplex element from a long.

Specified by:

fromInteger in interface ElemFactory<BigDecimalComplex>

Parameters:

a - long.

Returns:

a BigDecimalComplex.

getRe

public BigDecimal getRe()

Get the real part.

Returns:

re.

getIm

public BigDecimal 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<BigDecimalComplex>

Specified by:

toScript in interface ElemFactory<BigDecimalComplex>

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<BigDecimalComplex>

Returns:

script compatible representation for this ElemFactory.

See Also:

Element.toScriptFactory()

isCZERO

public static boolean isCZERO(BigDecimalComplex 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<BigDecimalComplex>

Returns:

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

See Also:

AbelianGroupElem.isZERO()

isCONE

public static boolean isCONE(BigDecimalComplex 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<BigDecimalComplex>

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<BigDecimalComplex>

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<BigDecimalComplex>

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 BigDecimalComplex.

Specified by:

hashCode in interface Element<BigDecimalComplex>

Overrides:

hashCode in class java.lang.Object

Returns:

the hashCode.

See Also:

Object.hashCode()

compareTo

public int compareTo(BigDecimalComplex b)

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

Specified by:

compareTo in interface Element<BigDecimalComplex>

Specified by:

compareTo in interface java.lang.Comparable<BigDecimalComplex>

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<BigDecimalComplex>

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 BigDecimalComplex sum(BigDecimalComplex B)

Complex number summation.

Specified by:

sum in interface AbelianGroupElem<BigDecimalComplex>

Parameters:

B - a BigDecimalComplex number.

Returns:

this+B.

CSUM

public static BigDecimalComplex CSUM(BigDecimalComplex A,
                                     BigDecimalComplex B)

Complex number sum.

Parameters:

A - and B are complex numbers.

Returns:

A+B.

CDIF

public static BigDecimalComplex CDIF(BigDecimalComplex A,
                                     BigDecimalComplex B)

Complex number difference.

Parameters:

A - and B are complex numbers.

Returns:

A-B.

subtract

public BigDecimalComplex subtract(BigDecimalComplex B)

Complex number subtract.

Specified by:

subtract in interface AbelianGroupElem<BigDecimalComplex>

Parameters:

B - a BigDecimalComplex number.

Returns:

this-B.

CNEG

public static BigDecimalComplex CNEG(BigDecimalComplex A)

Complex number negative.

Parameters:

A - is a complex number.

Returns:

-A

negate

public BigDecimalComplex negate()

Complex number negative.

Specified by:

negate in interface AbelianGroupElem<BigDecimalComplex>

Returns:

-this.

See Also:

AbelianGroupElem.negate()

CCON

public static BigDecimalComplex CCON(BigDecimalComplex A)

Complex number conjugate.

Parameters:

A - is a complex number.

Returns:

the complex conjugate of A.

conjugate

public BigDecimalComplex conjugate()

Complex number conjugate.

Specified by:

conjugate in interface StarRingElem<BigDecimalComplex>

Returns:

the complex conjugate of this.

norm

public BigDecimalComplex norm()

Complex number norm.

Specified by:

norm in interface StarRingElem<BigDecimalComplex>

Returns:

||this||.

See Also:

StarRingElem.norm()

abs

public BigDecimalComplex abs()

Complex number absolute value.

Specified by:

abs in interface AbelianGroupElem<BigDecimalComplex>

Returns:

|this|.

See Also:

AbelianGroupElem.abs()

CABS

public static BigDecimal CABS(BigDecimalComplex 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 BigDecimalComplex CPROD(BigDecimalComplex A,
                                      BigDecimalComplex B)

Complex number product.

Parameters:

A - and B are complex numbers.

Returns:

A*B.

multiply

public BigDecimalComplex multiply(BigDecimalComplex B)

Complex number product.

Specified by:

multiply in interface MonoidElem<BigDecimalComplex>

Parameters:

B - is a complex number.

Returns:

this*B.

CINV

public static BigDecimalComplex CINV(BigDecimalComplex A)

Complex number inverse.

Parameters:

A - is a non-zero complex number.

Returns:

S with S*A = 1.

inverse

public BigDecimalComplex inverse()

Complex number inverse.

Specified by:

inverse in interface MonoidElem<BigDecimalComplex>

Returns:

S with S*this = 1.

See Also:

MonoidElem.inverse()

remainder

public BigDecimalComplex remainder(BigDecimalComplex S)

Complex number inverse.

Specified by:

remainder in interface MonoidElem<BigDecimalComplex>

Parameters:

S - is a complex number.

Returns:

0.

CQ

public static BigDecimalComplex CQ(BigDecimalComplex A,
                                   BigDecimalComplex B)

Complex number quotient.

Parameters:

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

Returns:

A/B.

divide

public BigDecimalComplex divide(BigDecimalComplex B)

Complex number divide.

Specified by:

divide in interface MonoidElem<BigDecimalComplex>

Parameters:

B - is a complex number, non-zero.

Returns:

this/B.

quotientRemainder

public BigDecimalComplex[] quotientRemainder(BigDecimalComplex S)

Quotient and remainder by division of this by S.

Specified by:

quotientRemainder in interface MonoidElem<BigDecimalComplex>

Parameters:

S - a complex number

Returns:

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

random

public BigDecimalComplex 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<BigDecimalComplex>

Parameters:

n - such that 0 ≤ A, B ≤ (2ⁿ-1).

Returns:

R.

random

public BigDecimalComplex 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<BigDecimalComplex>

Parameters:

n - such that 0 ≤ A, B ≤ (2ⁿ-1).

rnd - is a source for random bits.

Returns:

R.

CRAND

public static BigDecimalComplex 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 BigDecimalComplex parse(java.lang.String s)

Parse complex number from string.

Specified by:

parse in interface ElemFactory<BigDecimalComplex>

Parameters:

s - String.

Returns:

BigDecimalComplex from s.

parse

public BigDecimalComplex parse(java.io.Reader r)

Parse complex number from Reader.

Specified by:

parse in interface ElemFactory<BigDecimalComplex>

Parameters:

r - Reader.

Returns:

next BigDecimalComplex from r.

gcd

public BigDecimalComplex gcd(BigDecimalComplex S)

Complex number greatest common divisor.

Specified by:

gcd in interface RingElem<BigDecimalComplex>

Parameters:

S - BigDecimalComplex.

Returns:

gcd(this,S).

egcd

public BigDecimalComplex[] egcd(BigDecimalComplex S)

BigDecimalComplex extended greatest common divisor.

Specified by:

egcd in interface RingElem<BigDecimalComplex>

Parameters:

S - BigDecimalComplex.

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 BigDecimalComplex, including a sign bit. It is equivalent to re.bitLength() + im.bitLength().)

Returns:

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