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

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and 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(java.math.BigInteger a)` Get a BigComplex element from a BigInteger.
`BigComplex`	`fromInteger(long a)` Get a BigComplex element from a long.
`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.RingElem
leftGcd, rightGcd

Methods inherited from interface edu.jas.structure.MonoidElem
leftDivide, leftRemainder, power, rightDivide, rightRemainder, twosidedDivide, twosidedRemainder

- 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 Element<BigComplex>
    
    Specified by:
    
    compareTo in interface java.lang.Comparable<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.

Class BigComplex

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface edu.jas.structure.RingElem

Methods inherited from interface edu.jas.structure.MonoidElem

Field Detail

re

im

ZERO

ONE

I

Constructor Detail

BigComplex

BigComplex

BigComplex

BigComplex

BigComplex

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

bitLength