jhypercomplex.numbers.cayley_dickson_algebras
Class BiQuaternion

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

All Implemented Interfaces:

CommonMethods

public class BiQuaternion
extends Quaternion

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

BiQuaternion()

BiQuaternion(BiQuaternion bq)

BiQuaternion(java.lang.String complex_unit)

Method Summary

BiQuaternion	biComplexConjugate() The bicomplex conjugation is carried out which is a combination of a conjugation of the quaternion-part and a conjugation of the complex quaternion components.
BiQuaternion	complexConjugate()
BiQuaternion	getClone(Hypernumber h)
java.util.LinkedList<java.lang.String>	getExpressionAsList(java.lang.String expression) An expression is split up in respect to the summands.
static java.lang.String	getMultTableAsHtml()
Hypernumber	getNewInstance()
BiQuaternion	negate() Negates the hypernumber: h --> -h.
void	setType(int type)

Methods inherited from class jhypercomplex.numbers.cayley_dickson_algebras.Quaternion

add, conjugate, doCayleyDicksonProcess, getAntiCommutatorWith, getBasis, getClone, getCommutator, getCommutatorJacobian, getCommutatorWith, getGrade, getGrades, getGradesOccuring, getJacobian, getMultiplicationTable, getNormedMultiplicationTable, getNormedMultiplicationtableAsHtml, getNumberOfComponents, getNumberOfGrades, getProduct, getType, getVectorComponents, multiplyWithScalar, rightMultiplyWith, setBiVectorComponents, setDefaultTable, setMultiplicationTable, setVectorComponents

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, 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

BiQuaternion

public BiQuaternion()

BiQuaternion

public BiQuaternion(BiQuaternion bq)

BiQuaternion

public BiQuaternion(java.lang.String complex_unit)

Method Detail

biComplexConjugate

public BiQuaternion biComplexConjugate()
                                throws java.lang.Exception

The bicomplex conjugation is carried out which is a combination of a conjugation of the quaternion-part and a conjugation of the complex quaternion components. I.e. (x0+I*y0) + (x1+I*y1)i + (x2+I*y2)j + (x3+I*y3)k --> (x0-I*y0) - (x1-I*y1)i - (x2-I*y2)j - (x3-I*y3)k = (x0-I*y0) + (-x1+I*y1)i + (-x2+I*y2)j + (-x3+I*y3)k (i,j,k) being the quaternion complex units, I the ordinary complex unit.

Parameters:

bq - Biquaternion to be bicomplex conjugated.

Returns:

Bicomplex conjugated Quaternion.

Throws:

java.lang.Exception

complexConjugate

public BiQuaternion complexConjugate()

negate

public BiQuaternion negate()
                    throws java.lang.Exception

Description copied from class: Hypernumber

Negates the hypernumber: h --> -h.

Overrides:

negate in class Quaternion

Returns:

Negated hypernumber h.

Throws:

java.lang.Exception

getExpressionAsList

public java.util.LinkedList<java.lang.String> getExpressionAsList(java.lang.String expression)

Description copied from class: Hypernumber

An expression is split up in respect to the summands. E.g. a1+2*a2-3*a3 |--> (a1,2*a2,-3*a3). REQUIRES: The numerical factors must be in front of the terms.

Overrides:

getExpressionAsList in class Hypernumber

Parameters:

expression - Expression consisting of terms.

Returns:

Array of the terms.

setType

public void setType(int type)

getClone

public BiQuaternion getClone(Hypernumber h)

getNewInstance

public Hypernumber getNewInstance()

Specified by:

getNewInstance in interface CommonMethods

Overrides:

getNewInstance in class Quaternion

getMultTableAsHtml

public static java.lang.String getMultTableAsHtml()