jhypercomplex.numbers.cayley_dickson_algebras
Class CayleyDicksonAlgebra

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

All Implemented Interfaces:

CommonMethods

Direct Known Subclasses:

Complex, Octonion, Quaternion, Sedenion, Trigintaduonion

public abstract class CayleyDicksonAlgebra
extends Hypernumber

Field Summary

static int	_2_N_ON
static int	CLASSICAL
static java.lang.String	COMPLEX
static java.lang.String	OCTONION
static java.lang.String	QUATERNION
static java.lang.String	SEDENION
static java.lang.String	TRIGINTADUONION
static int	TWISTED

Fields inherited from class jhypercomplex.numbers.Hypernumber

ARG_NUM, CIRCULAR, COMP_NUM, components, HYPERBOLIC, ZERO_PRECISSION

Constructor Summary

CayleyDicksonAlgebra()

Method Summary

static void	doCayleyDicksonDoubling(java.lang.String signatures, java.lang.String vector_basis) The canonical Cayley Dickson doubling procedure.
static void	doCayleyDicksonDoubling(java.lang.String signatures, java.lang.String vector_basis, int type) To be overridden.
MultiplicationTable	getLoopMultiplicationTable() Every CD algebra can be represented as a loop, in that the basis is doubled, adding to the basis the negated basis elements.
boolean	isCayleyDicksonAlgebra()
boolean	isLoop()

Methods inherited from class jhypercomplex.numbers.Hypernumber

add, add, applyLeibnizRule, asString, asString, calculateBCHWith, collectTerms, compressComponents, conjugate, dual, getAlternator1, getAlternator2, getAntiAssociator, getAntiCommutator, getAntiCommutatorWith, getAssociationType, getAssociationType, getAssociationTypeAsString, getAssociationTypeAsString, getAssociationTypeCommutator, getAssociationTypeCommutator, getAssociationTypeCommutatorAsString, getAssociationTypeCommutatorAsString, getAssociator, getBasis, 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, multiplyWithScalar, negate, 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

Methods inherited from interface jhypercomplex.numbers.CommonMethods

getClone, getGrade, getNewInstance, getNumberOfComponents, getNumberOfGrades

Field Detail

COMPLEX

public static final java.lang.String COMPLEX

See Also:

Constant Field Values

QUATERNION

public static final java.lang.String QUATERNION

See Also:

Constant Field Values

OCTONION

public static final java.lang.String OCTONION

See Also:

Constant Field Values

SEDENION

public static final java.lang.String SEDENION

See Also:

Constant Field Values

TRIGINTADUONION

public static final java.lang.String TRIGINTADUONION

See Also:

Constant Field Values

CLASSICAL

public static final int CLASSICAL

See Also:

Constant Field Values

TWISTED

public static final int TWISTED

See Also:

Constant Field Values

_2_N_ON

public static final int _2_N_ON

See Also:

Constant Field Values

Constructor Detail

CayleyDicksonAlgebra

public CayleyDicksonAlgebra()

Method Detail

getLoopMultiplicationTable

public MultiplicationTable getLoopMultiplicationTable()

Every CD algebra can be represented as a loop, in that the basis is doubled, adding to the basis the negated basis elements. Hence the resulting multiplication table has twice the dimension.

Returns:

Multiplication table.

isCayleyDicksonAlgebra

public boolean isCayleyDicksonAlgebra()
                               throws java.lang.Exception

Throws:

java.lang.Exception

doCayleyDicksonDoubling

public static void doCayleyDicksonDoubling(java.lang.String signatures,
                                           java.lang.String vector_basis)
                                    throws java.lang.Exception

The canonical Cayley Dickson doubling procedure.

Parameters:

signatures -

vector_basis -

Throws:

java.lang.Exception

doCayleyDicksonDoubling

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

To be overridden.

Parameters:

signatures -

vector_basis -

type: - CLASSICAL, TWISTED or_2_N_ON;

Throws:

java.lang.Exception

isLoop

public boolean isLoop()

Parameters:

dimension -

Returns:

Set of elements of the algebra ... example Octonion[0] = (1,0,0,1,1,1,0) Octonion[1] = (1,1,0,0,1,0,1) would be two quaternion subalgebras, describe that ...