jhypercomplex.numbers.cayley_dickson_algebras
Class Quaternion

java.lang.Object
  jhypercomplex.numbers.Hypernumber
      jhypercomplex.numbers.cayley_dickson_algebras.CayleyDicksonAlgebra
          jhypercomplex.numbers.cayley_dickson_algebras.Quaternion

All Implemented Interfaces:

CommonMethods

Direct Known Subclasses:

BiQuaternion

public class Quaternion
extends CayleyDicksonAlgebra

Field Summary

Fields inherited from class jhypercomplex.numbers.cayley_dickson_algebras.CayleyDicksonAlgebra

_2_N_ON, CLASSICAL, COMPLEX, OCTONION, QUATERNION, SEDENION, TRIGINTADUONION, TWISTED

Fields inherited from class jhypercomplex.numbers.Hypernumber

ARG_NUM, CIRCULAR, COMP_NUM, components, HYPERBOLIC, ZERO_PRECISSION

Constructor Summary

Quaternion()

Quaternion(int type)

Quaternion(Quaternion q)

Quaternion(java.lang.String components)

Method Summary

Quaternion	add(Quaternion q)
Quaternion	conjugate()
static void	doCayleyDicksonProcess(java.lang.String[] signatures, java.lang.String[] vector_basis, int type)
Quaternion	getAntiCommutatorWith(Quaternion q)
java.lang.String[]	getBasis()
Quaternion	getClone()
static Quaternion	getCommutator(Quaternion q1, Quaternion q2)
static Quaternion	getCommutatorJacobian(Quaternion q1, Quaternion q2, Quaternion q3)
Quaternion	getCommutatorWith(Quaternion q)
Quaternion	getGrade(int grade)
static java.util.TreeMap<java.lang.Integer,java.lang.Integer>	getGrades()
java.lang.String	getGradesOccuring()
static Quaternion	getJacobian(Quaternion q1, Quaternion q2, Quaternion q3)
static MultiplicationTable	getMultiplicationTable()
static java.lang.String	getMultTableAsHtml()
Hypernumber	getNewInstance()
static java.lang.String[][]	getNormedMultiplicationTable()
static java.lang.String	getNormedMultiplicationtableAsHtml()
int	getNumberOfComponents()
int	getNumberOfGrades()
static Quaternion	getProduct(Quaternion q1, Quaternion q2)
static java.lang.String	getType() The normed multiplication table is compared with a multiplication table of i) a right handed non-split quaternion ii a left handed non-split quaternion iii) a right handed split quaternion iv) a left handed split quaternion
java.lang.String[]	getVectorComponents()
Quaternion	multiplyWithScalar(java.lang.String constant) Multiplication with a scalar.
Quaternion	negate() Negates the hypernumber: h --> -h.
Quaternion	rightMultiplyWith(Quaternion q)
void	setBiVectorComponents(java.lang.String bivector)
static void	setDefaultTable()
static void	setMultiplicationTable(java.lang.String[][] mult_table)
void	setVectorComponents(java.lang.String vector)

Methods inherited from class jhypercomplex.numbers.cayley_dickson_algebras.CayleyDicksonAlgebra

doCayleyDicksonDoubling, doCayleyDicksonDoubling, getLoopMultiplicationTable, isCayleyDicksonAlgebra, isLoop

Methods inherited from class jhypercomplex.numbers.Hypernumber

add, add, applyLeibnizRule, asString, asString, calculateBCHWith, collectTerms, compressComponents, dual, getAlternator1, getAlternator2, getAntiAssociator, getAntiCommutator, getAntiCommutatorWith, getAssociationType, getAssociationType, getAssociationTypeAsString, getAssociationTypeAsString, getAssociationTypeCommutator, getAssociationTypeCommutator, getAssociationTypeCommutatorAsString, getAssociationTypeCommutatorAsString, getAssociator, getBasisElementsAsString, getCommuAssociator, getCommutator, getCommutator, getCommutatorJacobian, getCommutatorSaglian, getCommutatorWith, getCommutatorWith, getComponent, getComponents, getComponentsAsString, getComponentsAsString, getComponentsOfGrade, getConjugate, getDiagonalProducts, getDifference, getDual, getExpressionAsList, getFirstHetztelPeresian, getFormattedMultTable, getGradedInnerProduct, getHermitianConjugate, getImaginaryPart, getInstance, getIntersection, getJacobian, getJordanAssociator, getLeftCovariantDerivative, getMultiplicativeOrder, getMultiplicativeOrder, getMultTableDiagonal, getNegated, getNextBitmap, getNormedMultiplicationTable, getNormSquared, getNormSquaredAsValue, getNumberOfClosedElements, getNumberOfClosedPairs, getNumberOfComponents, getNumberOfNonzeroComponents, getNumericalInverse, getOuterProduct, getProduct, getProductWithScalar, getPseudoScalarComponent, getRandomClosedPair, getRandomNonClosedPair, getScalarComponent, getScalarProduct, getSecondHetztelPeresian, getSignature, getSubalgebras, getSubalgebrasAsString, getSubalgebrasSignatures, getSum, getTrace, getTraceRespDeterminant, getVectorDerivative, getVectorProduct, isAutomorphism, isClosedAlgebra, isCommutative, isComponentZero, isEqual, isLinearlyDependent, isNumerical, isNumericalityDetected, isOrthogonal, isOrthogonalTo, isZero, resetComponents, rightMultiplyWith, rightMultiplyWith, setBasis, setComponent, setComponents, setComponents, setNumerical, setNumerical, setPseudoScalarComponent, setRandomComponents, setRandomComponents, setRandomComponents, setRandomComponentsAll, setScalarComponent, simplifyNumericalFactors, simplifyNumericalSummands, simplifyPlusMinus, square, subtract

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

Quaternion

public Quaternion()

Quaternion

public Quaternion(int type)

Quaternion

public Quaternion(java.lang.String components)
           throws java.lang.Exception

Throws:

java.lang.Exception

Quaternion

public Quaternion(Quaternion q)

Method Detail

getType

public static java.lang.String getType()

The normed multiplication table is compared with a multiplication table of i) a right handed non-split quaternion ii a left handed non-split quaternion iii) a right handed split quaternion iv) a left handed split quaternion

Returns:

"right-handed-nonsplit" or "left-handed-nonsplit" or "right-handed-split" or "left-handed-nonsplit" or "unknown"

setVectorComponents

public void setVectorComponents(java.lang.String vector)
                         throws java.lang.Exception

Throws:

java.lang.Exception

setBiVectorComponents

public void setBiVectorComponents(java.lang.String bivector)
                           throws java.lang.Exception

Throws:

java.lang.Exception

rightMultiplyWith

public Quaternion rightMultiplyWith(Quaternion q)
                             throws java.lang.Exception

Throws:

java.lang.Exception

conjugate

public Quaternion conjugate()
                     throws java.lang.Exception

Overrides:

conjugate in class Hypernumber

Returns:

The conjugate of the hypernumber, i.e. reverses the signs of the imaginary hypercomplex components.

Throws:

java.lang.Exception

getProduct

public static Quaternion getProduct(Quaternion q1,
                                    Quaternion q2)
                             throws java.lang.Exception

Throws:

java.lang.Exception

add

public Quaternion add(Quaternion q)

multiplyWithScalar

public Quaternion multiplyWithScalar(java.lang.String constant)
                              throws java.lang.Exception

Description copied from class: Hypernumber

Multiplication with a scalar.

Overrides:

multiplyWithScalar in class Hypernumber

Parameters:

constant - Scalar.

Returns:

Hypernumber multiplied with a scalar.

Throws:

java.lang.Exception

negate

public Quaternion negate()
                  throws java.lang.Exception

Description copied from class: Hypernumber

Negates the hypernumber: h --> -h.

Overrides:

negate in class Hypernumber

Returns:

Negated hypernumber h.

Throws:

java.lang.Exception

getAntiCommutatorWith

public Quaternion getAntiCommutatorWith(Quaternion q)
                                 throws java.lang.Exception

Throws:

java.lang.Exception

getCommutatorWith

public Quaternion getCommutatorWith(Quaternion q)
                             throws java.lang.Exception

Throws:

java.lang.Exception

getClone

public Quaternion getClone()

getNewInstance

public Hypernumber getNewInstance()

getBasis

public java.lang.String[] getBasis()

Specified by:

getBasis in class Hypernumber

getNumberOfComponents

public int getNumberOfComponents()

doCayleyDicksonProcess

public static void doCayleyDicksonProcess(java.lang.String[] signatures,
                                          java.lang.String[] vector_basis,
                                          int type)
                                   throws java.lang.Exception

Throws:

java.lang.Exception

getMultiplicationTable

public static MultiplicationTable getMultiplicationTable()

setMultiplicationTable

public static void setMultiplicationTable(java.lang.String[][] mult_table)

setDefaultTable

public static void setDefaultTable()

getMultTableAsHtml

public static java.lang.String getMultTableAsHtml()

getNormedMultiplicationTable

public static java.lang.String[][] getNormedMultiplicationTable()

getNormedMultiplicationtableAsHtml

public static java.lang.String getNormedMultiplicationtableAsHtml()

getNumberOfGrades

public int getNumberOfGrades()

getGrade

public Quaternion getGrade(int grade)
                    throws java.lang.Exception

Throws:

java.lang.Exception

getGradesOccuring

public java.lang.String getGradesOccuring()
                                   throws java.lang.Exception

Throws:

java.lang.Exception

getVectorComponents

public java.lang.String[] getVectorComponents()
                                       throws java.lang.Exception

Throws:

java.lang.Exception

getCommutator

public static Quaternion getCommutator(Quaternion q1,
                                       Quaternion q2)
                                throws java.lang.Exception

Throws:

java.lang.Exception

getJacobian

public static Quaternion getJacobian(Quaternion q1,
                                     Quaternion q2,
                                     Quaternion q3)
                              throws java.lang.Exception

Throws:

java.lang.Exception

getCommutatorJacobian

public static Quaternion getCommutatorJacobian(Quaternion q1,
                                               Quaternion q2,
                                               Quaternion q3)
                                        throws java.lang.Exception

Throws:

java.lang.Exception

getGrades

public static java.util.TreeMap<java.lang.Integer,java.lang.Integer> getGrades()
                                                                        throws java.lang.Exception

Returns:

Array with the grades.

Throws:

java.lang.Exception