com.numericalmethod.suanshu.number
Class Real

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>

This class represents an arbitrary precision real number.

This 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

static Real	ONE a number representing 1
static Real	ZERO a number representing 0

Constructor Summary

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 representation of a number.

Method Summary

Real	add(Real that) + : G × G → G
java.math.BigDecimal	bigDecimal() Construct a BigDecimal from this Real number.
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 a Real 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 That is, it is the object such as this.multiply(this.inverse()) == this.ONE
long	longValue()
Real	minus(Real that) - : G × G → G - 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 That is, it is the object such as this.add(this.opposite()) == this.ZERO
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. To ensure accuracy, value is first converted to String and then to BigDecimal.

Parameters:

value - a double value

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 representation of a number.

Parameters:

value - a String representation of a number

Method Detail

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

bigDecimal

public java.math.BigDecimal bigDecimal()

Construct a BigDecimal from this Real number.

Returns:

the same value in BigDecimal

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

- 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

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 a Real number by another one. Rounding is performed with the specific scale.

Parameters:

that - another non-zero Real number

scale - 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

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>

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

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object