java.lang.Object
- java.lang.Number
- - gnu.math.Numeric
  - - gnu.math.Quantity
    - - gnu.math.Quaternion

All Implemented Interfaces:

java.io.Serializable

Direct Known Subclasses:

Complex, CQuaternion, DQuaternion
```
public abstract class Quaternion
extends Quantity
```
A quaternion is a hypercomplex number of the form w + xi + yj + zk where w, x, y, and k are real, and i, j, and k are imaginary units which satisfy i^2 = j^2 = k^2 = ijk = -1.

See Also:

Serialized Form

Field Summary
- Fields inherited from class gnu.math.Numeric
  CEILING, FLOOR, NONNEG_MOD, ROUND, TRUNCATE

Constructor Summary

Constructors
Constructor Description

Quaternion()

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`Numeric`	`abs()`
`static Quaternion`	`add(Quaternion x, Quaternion y, int k)`
`Numeric`	`add(java.lang.Object y, int k)`	Return this + k * obj.
`Numeric`	`addReversed(Numeric x, int k)`	Calculate `x+k&this`.
`RealNum`	`angle()`
`int`	`classifyFinite()`	Check if value is finite, infinite, or NaN.
`RealNum`	`colatitude()`
`static int`	`compare(Quaternion x, Quaternion y)`
`int`	`compare(java.lang.Object obj)`	Return an integer for which of `this` or `obj` is larger.
`Complex`	`complexPart()`
`Quaternion`	`conjugate()`
`Quaternion`	`cos()`
`Numeric`	`div(java.lang.Object y)`
`static Quaternion`	`divide(Quaternion x, Quaternion y)`
`Numeric`	`divReversed(Numeric x)`
`double`	`doubleImagValue()`	The value of the imaginary component, as a double.
`double`	`doubleJmagValue()`	The value of the "j" component, as a double.
`double`	`doubleKmagValue()`	The value of the "k" component, as a double.
`double`	`doubleRealValue()`
`double`	`doubleValue()`	The value of the real component, as a double.
`static boolean`	`equals(Quaternion x, Quaternion y)`
`boolean`	`equals(java.lang.Object obj)`
`Quaternion`	`exp()`
`boolean`	`isExact()`
`boolean`	`isZero()`
`static CQuaternion`	`jmMinusOne()`
`static CQuaternion`	`jmOne()`
`static CQuaternion`	`kmMinusOne()`
`static CQuaternion`	`kmOne()`
`Quaternion`	`log()`
`RealNum`	`longitude()`
`long`	`longValue()`
`static Quaternion`	`make(double re, double im, double jm, double km)`
`static Quaternion`	`make(RealNum re, RealNum im, RealNum jm, RealNum km)`
`Numeric`	`mul(java.lang.Object y)`
`Numeric`	`mulReversed(Numeric x)`
`Numeric`	`neg()`
`static Quaternion`	`neg(Quaternion x)`
`Quaternion`	`number()`
`static Quaternion`	`polar(double r, double t, double u, double v)`
`static Quaternion`	`polar(RealNum r, RealNum t, RealNum u, RealNum v)`
`static Quaternion`	`power(Quaternion x, Quaternion y)`
`Quaternion`	`sin()`
`Quaternion`	`sqrt()`
`Quaternion`	`tan()`
`static Quaternion`	`times(Quaternion x, Quaternion y)`
`Quaternion`	`toExact()`
`Quaternion`	`toInexact()`
`java.lang.String`	`toString(int radix)`
`Quaternion`	`unitQuaternion()`
`Quaternion`	`unitVector()`
`Quaternion`	`vectorPart()`

Methods inherited from class gnu.math.Quantity
add, compare, compareReversed, dimensions, divide, im, imValue, jm, jmValue, km, kmValue, make, make, make, re, reValue, times, unit

Methods inherited from class gnu.math.Numeric
add, asNumericOrNull, div_inv, floatValue, geq, grt, intValue, mul_ident, power, sub, toString

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

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

Constructor Detail
- Quaternion
```
public Quaternion()
```

Method Detail

number
```
public Quaternion number()
```
Specified by:

number in class Quantity

isExact
```
public boolean isExact()
```
Specified by:

isExact in class Numeric

classifyFinite
```
public int classifyFinite()
```
Check if value is finite, infinite, or NaN.

Returns:

1 if finite; 0 if infinite; -1 if NaN.

toExact
```
public Quaternion toExact()
```
Overrides:

toExact in class Numeric

toInexact
```
public Quaternion toInexact()
```
Overrides:

toInexact in class Numeric

jmOne
```
public static CQuaternion jmOne()
```

jmMinusOne

public static CQuaternion jmMinusOne()

kmOne
```
public static CQuaternion kmOne()
```

kmMinusOne

public static CQuaternion kmMinusOne()

doubleValue
```
public double doubleValue()
```
Description copied from class: Quantity

The value of the real component, as a double. This is relative to the unit().dims - i.e. unit()/doubleValue() is factored in.

Overrides:

doubleValue in class Quantity

doubleImagValue
```
public double doubleImagValue()
```
Description copied from class: Quantity

The value of the imaginary component, as a double. This is relative to the unit().dims - i.e. unit()/doubleValue() is factored in.

Overrides:

doubleImagValue in class Quantity

doubleJmagValue
```
public double doubleJmagValue()
```
Description copied from class: Quantity

The value of the "j" component, as a double. This is relative to the unit().dims - i.e. unit()/doubleValue() is factored in.

Overrides:

doubleJmagValue in class Quantity

doubleKmagValue
```
public double doubleKmagValue()
```
Description copied from class: Quantity

The value of the "k" component, as a double. This is relative to the unit().dims - i.e. unit()/doubleValue() is factored in.

Overrides:

doubleKmagValue in class Quantity

doubleRealValue
```
public final double doubleRealValue()
```

longValue
```
public long longValue()
```
Overrides:

longValue in class Numeric

complexPart
```
public Complex complexPart()
```

vectorPart
```
public Quaternion vectorPart()
```

unitVector
```
public Quaternion unitVector()
```

unitQuaternion
```
public Quaternion unitQuaternion()
```

make

public static Quaternion make(RealNum re,
                              RealNum im,
                              RealNum jm,
                              RealNum km)

make

public static Quaternion make(double re,
                              double im,
                              double jm,
                              double km)

polar

public static Quaternion polar(double r,
                               double t,
                               double u,
                               double v)

polar

public static Quaternion polar(RealNum r,
                               RealNum t,
                               RealNum u,
                               RealNum v)

power

public static Quaternion power(Quaternion x,
                               Quaternion y)

abs
```
public Numeric abs()
```
Overrides:

abs in class Quantity

angle
```
public RealNum angle()
```

colatitude
```
public RealNum colatitude()
```

longitude
```
public RealNum longitude()
```

conjugate
```
public Quaternion conjugate()
```

equals

public static boolean equals(Quaternion x,
                             Quaternion y)

equals

public boolean equals(java.lang.Object obj)

Overrides:: equals in class Numeric

compare

public static int compare(Quaternion x,
                          Quaternion y)

compare
```
public int compare(java.lang.Object obj)
```
Description copied from class: Numeric

Return an integer for which of this or obj is larger. Return 1 if this>obj; 0 if this==obj; -1 if this<obj; -2 if this!=obj otherwise (for example if either is NaN); -3 if not comparable (incompatible types).

Overrides:

compare in class Quantity

isZero
```
public boolean isZero()
```
Specified by:

isZero in class Numeric

toString

public java.lang.String toString(int radix)

Overrides:: toString in class Quantity

neg

public static Quaternion neg(Quaternion x)

neg
```
public Numeric neg()
```
Overrides:

neg in class Quantity

add

public static Quaternion add(Quaternion x,
                             Quaternion y,
                             int k)

add
```
public Numeric add(java.lang.Object y,
                   int k)
```
Description copied from class: Numeric

Return this + k * obj.

Overrides:

add in class Quantity

addReversed
```
public Numeric addReversed(Numeric x,
                           int k)
```
Description copied from class: Numeric

Calculate x+k&this.

Overrides:

addReversed in class Quantity

times

public static Quaternion times(Quaternion x,
                               Quaternion y)

mul

public Numeric mul(java.lang.Object y)

Overrides:: mul in class Quantity

mulReversed

public Numeric mulReversed(Numeric x)

Overrides:: mulReversed in class Quantity

divide

public static Quaternion divide(Quaternion x,
                                Quaternion y)

div

public Numeric div(java.lang.Object y)

Overrides:: div in class Quantity

divReversed

public Numeric divReversed(Numeric x)

Overrides:: divReversed in class Quantity

exp
```
public Quaternion exp()
```

log
```
public Quaternion log()
```

sqrt
```
public Quaternion sqrt()
```

sin
```
public Quaternion sin()
```

cos
```
public Quaternion cos()
```

tan
```
public Quaternion tan()
```

Class Quaternion

Field Summary

Fields inherited from class gnu.math.Numeric

Constructor Summary

Method Summary

Methods inherited from class gnu.math.Quantity

Methods inherited from class gnu.math.Numeric

Methods inherited from class java.lang.Number

Methods inherited from class java.lang.Object

Constructor Detail

Quaternion

Method Detail

number

isExact

classifyFinite

toExact

toInexact

jmOne

jmMinusOne

kmOne

kmMinusOne

doubleValue

doubleImagValue

doubleJmagValue

doubleKmagValue

doubleRealValue

longValue

complexPart

vectorPart

unitVector

unitQuaternion

make

make

polar

polar

power

abs

angle

colatitude

longitude

conjugate

equals

equals

compare

compare

isZero

toString

neg

neg

add

add

addReversed

times

mul

mulReversed

divide

div

divReversed

exp

log

sqrt

sin

cos

tan