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(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

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`BigDecimalComplex`	`abs()` Complex number absolute value.
`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

- 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
- 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.
    
    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).

Class BigDecimalComplex

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

re

im

ZERO

ONE

I

Constructor Detail

BigDecimalComplex

BigDecimalComplex

BigDecimalComplex

BigDecimalComplex

BigDecimalComplex

Method Detail

factory

generators

isFinite

copy

copy

getZERO

getONE

getIMAG

isCommutative

isAssociative

isField

characteristic

fromInteger

fromInteger

getRe

getIm

toString

toScript

toScriptFactory

isCZERO

isZERO

isCONE

isONE

isIMAG

isUnit

equals

hashCode

compareTo

signum

sum

CSUM

CDIF

subtract

CNEG

negate

CCON

conjugate

norm

abs

CABS

CPROD

multiply

CINV

inverse

remainder

CQ

divide

quotientRemainder

random

random

CRAND

parse

parse

gcd

egcd