Real (SuanShuExtension API)

java.lang.Object
- java.lang.Number
- - com.numericalmethod.suanshu.number.Real

All Implemented Interfaces:

AbelianGroup<Real>, Field<Real>, Monoid<Real>, Ring<Real>, java.io.Serializable, java.lang.Comparable<Real>
```
public class Real
extends java.lang.Number
implements Field<Real>, java.lang.Comparable<Real>
```
A real number is an arbitrary precision number. This implementation is simply a wrapper around BigDecimal and implements the Field interface.
This class is immutable.

See Also:

Serialized Form

Nested Class Summary
- Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.mathstructure.Field
  Field.InverseNonExistent

Field Summary

Fields
Modifier and Type Field and Description

static Real ONE
a number representing 1

static Real ZERO
a number representing 0

Fields
Modifier and Type	Field and Description
`static Real`	`ONE` a number representing 1
`static Real`	`ZERO` a number representing 0

Constructor Summary

Constructors
Constructor and Description
`Real(java.math.BigDecimal value)` Construct a `Real` from a `BigDecimal`.
`Real(java.math.BigInteger value)` Construct a `Real` from a `BigInteger`.
`Real(double value)` Construct a `Real` from a `double`.
`Real(long value)` Construct a `Real` from an integer.
`Real(java.lang.String value)` Construct a `Real` from a `String`.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`Real`	`add(Real that)` + : G × G → G
`int`	`compareTo(Real that)`
`Real`	`divide(Real that)` / : F × F → F That is the same as `this.multiply(that.inverse())`
`Real`	`divide(Real that, int scale)` / : R × R → R Divide this number by another one.
`double`	`doubleValue()`
`boolean`	`equals(java.lang.Object obj)`
`float`	`floatValue()`
`int`	`hashCode()`
`int`	`intValue()`
`Real`	`inverse()` For each a in F, there exists an element b in F such that a × b = b × a = 1.
`long`	`longValue()`
`Real`	`minus(Real that)` - : G × G → G The operation "-" is not in the definition of of an additive group but can be deduced.
`Real`	`multiply(Real that)` × : G × G → G
`Real`	`ONE()` The multiplicative element 1 in the group such that for any elements a in the group, the equation 1 × a = a × 1 = a holds.
`Real`	`opposite()` For each a in G, there exists an element b in G such that a + b = b + a = 0.
`java.math.BigDecimal`	`toBigDecimal()` Convert this number to a `BigDecimal`.
`java.lang.String`	`toString()`
`Real`	`ZERO()` The additive element 0 in the group, such that for all elements a in the group, the equation 0 + a = a + 0 = a holds.

Methods inherited from class java.lang.Number
byteValue, shortValue

Methods inherited from class java.lang.Object
clone, finalize, getClass, notify, notifyAll, wait, wait, wait

- Field Detail
  - ZERO
```
public static final Real ZERO
```
    a number representing 0
  - ONE
```
public static final Real ONE
```
    a number representing 1
- Constructor Detail
  - Real
```
public Real(double value)
```
    Construct a Real from a double.
    
    Parameters:
    
    value - a double
  - Real
```
public Real(long value)
```
    Construct a Real from an integer.
    
    Parameters:
    
    value - an integer
  - Real
```
public Real(java.math.BigDecimal value)
```
    Construct a Real from a BigDecimal.
    
    Parameters:
    
    value - a BigDecimal
  - Real
```
public Real(java.math.BigInteger value)
```
    Construct a Real from a BigInteger.
    
    Parameters:
    
    value - a BigInteger
  - Real
```
public Real(java.lang.String value)
```
    Construct a Real from a String.
    
    Parameters:
    
    value - a String representation of a number
- Method Detail
  - toBigDecimal
```
public java.math.BigDecimal toBigDecimal()
```
    Convert this number to a BigDecimal.
    
    Returns:
    
    the value in BigDecimal
  - intValue
```
public int intValue()
```
    Specified by:
    
    intValue in class java.lang.Number
  - longValue
```
public long longValue()
```
    Specified by:
    
    longValue in class java.lang.Number
  - floatValue
```
public float floatValue()
```
    Specified by:
    
    floatValue in class java.lang.Number
  - doubleValue
```
public double doubleValue()
```
    Specified by:
    
    doubleValue in class java.lang.Number
  - add
```
public Real add(Real that)
```
    Description copied from interface: AbelianGroup
    
    + : G × G → G
    
    Specified by:
    
    add in interface AbelianGroup<Real>
    
    Parameters:
    
    that - the object to be added
    
    Returns:
    
    this + that
  - minus
```
public Real minus(Real that)
```
    Description copied from interface: AbelianGroup
    
    - : G × G → G
    The operation "-" is not in the definition of of an additive group but can be deduced. This function is provided for convenience purpose. It is equivalent to
    this.add(that.opposite())
    .
    
    Specified by:
    
    minus in interface AbelianGroup<Real>
    
    Parameters:
    
    that - the object to be subtracted (subtrahend)
    
    Returns:
    
    this - that
  - opposite
```
public Real opposite()
```
    Description copied from interface: AbelianGroup
    
    For each a in G, there exists an element b in G such that a + b = b + a = 0. That is, it is the object such as
    this.add(this.opposite()) == this.ZERO
    
    Specified by:
    
    opposite in interface AbelianGroup<Real>
    
    Returns:
    
    -this, the additive opposite
    
    See Also:
    
    Wikipedia: Additive inverse
  - multiply
```
public Real multiply(Real that)
```
    Description copied from interface: Monoid
    
    × : G × G → G
    
    Specified by:
    
    multiply in interface Monoid<Real>
    
    Parameters:
    
    that - the multiplicand
    
    Returns:
    
    this × that
  - divide
```
public Real divide(Real that)
```
    Description copied from interface: Field
    
    / : F × F → F
    That is the same as
    this.multiply(that.inverse())
    
    Specified by:
    
    divide in interface Field<Real>
    
    Parameters:
    
    that - the denominator
    
    Returns:
    
    this / that
  - divide
```
public Real divide(Real that,
                   int scale)
```
    / : R × R → R
    Divide this number by another one. Rounding is performed with the specified scale.
    
    Parameters:
    
    that - another non-zero real number
    
    scale - rounding scale as in BigDecimal
    
    Returns:
    
    this/that
  - inverse
```
public Real inverse()
             throws Field.InverseNonExistent
```
    Description copied from interface: Field
    
    For each a in F, there exists an element b in F such that a × b = b × a = 1. That is, it is the object such as
    this.multiply(this.inverse()) == this.ONE
    
    Specified by:
    
    inverse in interface Field<Real>
    
    Returns:
    
    1 / this if it exists
    
    Throws:
    
    Field.InverseNonExistent - if the inverse does not exist
    
    See Also:
    
    Wikipedia: Multiplicative inverse
  - ZERO
```
public Real ZERO()
```
    Description copied from interface: AbelianGroup
    
    The additive element 0 in the group, such that for all elements a in the group, the equation 0 + a = a + 0 = a holds.
    
    Specified by:
    
    ZERO in interface AbelianGroup<Real>
    
    Returns:
    
    0, the additive identity
  - ONE
```
public Real ONE()
```
    Description copied from interface: Monoid
    
    The multiplicative element 1 in the group such that for any elements a in the group, the equation 1 × a = a × 1 = a holds.
    
    Specified by:
    
    ONE in interface Monoid<Real>
    
    Returns:
    
    1
  - compareTo
```
public int compareTo(Real that)
```
    Specified by:
    
    compareTo in interface java.lang.Comparable<Real>
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Overrides:
    
    equals in class java.lang.Object
  - hashCode
```
public int hashCode()
```
    Overrides:
    
    hashCode in class java.lang.Object

Class Real

Nested Class Summary

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.mathstructure.Field

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Number

Methods inherited from class java.lang.Object

Field Detail

ZERO

ONE

Constructor Detail

Real

Real

Real

Real

Real

Method Detail

toBigDecimal

intValue

longValue

floatValue

doubleValue

add

minus

opposite

multiply

divide

divide

inverse

ZERO

ONE

compareTo

toString

equals

hashCode