jhypercomplex.numbers.cayley_dickson_algebras
Class Sedenion

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

All Implemented Interfaces:

CommonMethods

public class Sedenion
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

Sedenion()
Constructors and the like *

Sedenion(Sedenion s)

Sedenion(java.lang.String components)

Method Summary

Sedenion	add(Sedenion sedenion)
Sedenion	conjugate() Arithmetics *
static void	doCayleyDicksonDoubling(java.lang.String signature)
static void	doCayleyDicksonDoubling(java.lang.String signatures, java.lang.String vector_basis)
static void	doCayleyDicksonDoubling(java.lang.String signatures, java.lang.String vector_basis, int type) A sequence of 4 Cayley-Dickson doublings is carried out starting from the real numbers and resulting in the sedenion algebra.
static Sedenion	getAntiAssociator(Sedenion sta1, Sedenion sta2, Sedenion sta3)
static Sedenion	getAntiCommutator(Sedenion s1, Sedenion s2)
static Sedenion	getAssociationType(int nr, Sedenion s1, Sedenion s2, Sedenion s3, Sedenion s4)
static Sedenion	getAssociationType(int nr, Sedenion s1, Sedenion s2, Sedenion s3, Sedenion s4, Sedenion s5)
static Sedenion	getAssociationTypeCommutator(int nr, Sedenion s1, Sedenion s2, Sedenion s3, Sedenion s4)
static Sedenion	getAssociationTypeCommutator(int nr, Sedenion s1, Sedenion s2, Sedenion s3, Sedenion s4, Sedenion s5)
static Sedenion	getAssociator(Sedenion sta1, Sedenion sta2, Sedenion sta3)
java.lang.String[]	getBasis() Multiplication table and basis *
java.lang.String[]	getBivectorComponents()
java.lang.String	getBivectorPartAsString()
java.lang.String	getBivectorPartAsString(boolean with_blanks)
Sedenion	getClone()
static Sedenion	getCommutator(Sedenion s1, Sedenion s2)
static Sedenion	getCommutator(Sedenion s1, Sedenion s2, boolean collect_terms)
static Sedenion	getCommutatorJacobian(Sedenion s1, Sedenion s2, Sedenion s3)
static Sedenion	getCommutatorSaglian(Sedenion s1, Sedenion s2, Sedenion s3, Sedenion s4)
static Sedenion	getConjugate(Sedenion s)
java.lang.String	getDiagonalVectorProducts()
static Sedenion	getDifference(Sedenion s1, Sedenion s2)
java.lang.String[]	getEvenGradeComponents()
java.lang.String	getEvenGradePartAsString()
java.lang.String	getEvenGradePartAsString(boolean with_blanks)
static Sedenion	getFirstHetztelPeresian(Sedenion s1, Sedenion s2, Sedenion s3, Sedenion s4, Sedenion s5)
Sedenion	getGrade(int grade)
static java.util.TreeMap<java.lang.Integer,java.lang.Integer>	getGrades()
java.lang.String	getGrading()
static Sedenion	getImaginaryPart(Sedenion s)
static Sedenion	getInverse(Sedenion s)
static Sedenion	getJacobian(Sedenion s1, Sedenion s2, Sedenion s3)
static Sedenion	getJordanAssociator(Sedenion sta1, Sedenion sta2, Sedenion sta3)
static MultiplicationTable	getMultiplicationTable()
static java.lang.String[][]	getMultiplicationTableAsArray()
static java.lang.String	getMultTableAsHtml()
java.util.Collection<java.lang.String>	getNCycleGrades(int ncycle) Intended for usage in context with multiplication tables generated by Cayley Dickson doubling.
static Sedenion	getNegated(Sedenion s)
Sedenion	getNewInstance()
static java.lang.String[][]	getNormedMultiplicationTable()
static java.lang.String	getNormedMultiplicationtableAsHtml()
int	getNumberOfComponents() Components *
int	getNumberOfGrades()
static Sedenion	getNumericalDifference(Sedenion s, Sedenion t)
static Sedenion	getNumericalProduct(Sedenion s, Sedenion t) Multiplies two sedenions numerically.
static Sedenion	getNumericalSum(Sedenion s, Sedenion t)
java.util.LinkedList<MultiplicationTable>	getOrder4Subalgebras()
java.util.LinkedList<MultiplicationTable>	getOrder8Subalgebras()
static Sedenion	getProduct(Sedenion s1, Sedenion s2)
static Sedenion	getScalarProduct(Sedenion s1, Sedenion s2)
static Sedenion	getSecondHetztelPeresian(Sedenion s1, Sedenion s2, Sedenion s3, Sedenion s4)
static java.util.HashSet<java.lang.String>	getSubalgebras(int order)
static java.util.HashSet<int[]>	getSubalgebrasUnsigned(int order)
static Sedenion	getSum(Sedenion s1, Sedenion s2)
java.lang.String[]	getTrivectorComponents()
java.lang.String	getTrivectorPartAsString()
java.lang.String	getTrivectorPartAsString(boolean with_blanks)
java.lang.String[]	getVectorComponents()
java.lang.String	getVectorPartAsString()
java.lang.String	getVectorPartAsString(boolean with_blanks)
java.lang.String	getVectorSignature()
Sedenion	multiplyWithScalar(java.lang.String scalar) Multiplication with a scalar.
Sedenion	negate() Negates the hypernumber: h --> -h.
Sedenion	rightMultiplyWith(Hypernumber s)
void	setBiVectorComponents(java.lang.String bivector) Sets the 6 bivector components.
void	setBiVectorComponentsExclusively(java.lang.String bivector) Sets the 6 bivector components.
void	setDefaultTable()
void	setEvenGradeComponents(java.lang.String comps) Sets the 8 even grade components.
void	setEvenGradeComponentsExclusively(java.lang.String comps) Sets the 8 even grade components.
static void	setMultiplicationTable(java.lang.String[][] mult_table)
void	setTriVectorComponents(java.lang.String trivector) Sets the 4 trivector components.
void	setTriVectorComponentsExclusively(java.lang.String trivector) Sets the 4 trivector components.
void	setVectorComponents(java.lang.String vector) Sets the 4 vector components.
void	setVectorComponents(java.lang.String[] vector_comps)
void	setVectorComponentsExclusively(java.lang.String vector) Sets the 4 vector components.
Sedenion	square()
Sedenion	subtract(Sedenion sedenion)

Methods inherited from class jhypercomplex.numbers.cayley_dickson_algebras.CayleyDicksonAlgebra

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, setBasis, setComponent, setComponents, setComponents, setNumerical, setNumerical, setPseudoScalarComponent, setRandomComponents, setRandomComponents, setRandomComponents, setRandomComponentsAll, setScalarComponent, simplifyNumericalFactors, simplifyNumericalSummands, simplifyPlusMinus, subtract

Methods inherited from class java.lang.Object

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

Constructor Detail

Sedenion

public Sedenion()

Constructors and the like *

Sedenion

public Sedenion(Sedenion s)

Sedenion

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

Throws:

java.lang.Exception

Method Detail

getNewInstance

public Sedenion getNewInstance()

getClone

public Sedenion getClone()

getBasis

public java.lang.String[] getBasis()

Multiplication table and basis *

Specified by:

getBasis in class Hypernumber

getMultiplicationTableAsArray

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

getMultiplicationTable

public static MultiplicationTable getMultiplicationTable()

setMultiplicationTable

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

setDefaultTable

public void setDefaultTable()

getMultTableAsHtml

public static java.lang.String getMultTableAsHtml()

getNormedMultiplicationTable

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

getNormedMultiplicationtableAsHtml

public static java.lang.String getNormedMultiplicationtableAsHtml()

doCayleyDicksonDoubling

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

A sequence of 4 Cayley-Dickson doublings is carried out starting from the real numbers and resulting in the sedenion algebra. The sequence is specified by 4 signatures, determining if the doubling of the real numbers, the complex numbers, the quaternions and the octonions is a split or a non-split one respectively.

Parameters:

signatures - Comma delimited string of 4 signatures with "+" specifying a non-split and "-" a split doubling. (e.g. "+,-,+,+").

vector_basis -

Throws:

java.lang.Exception

doCayleyDicksonDoubling

public static void doCayleyDicksonDoubling(java.lang.String signature)
                                    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

Throws:

java.lang.Exception

getNumberOfComponents

public int getNumberOfComponents()

Components *

getImaginaryPart

public static Sedenion getImaginaryPart(Sedenion s)
                                 throws java.lang.Exception

Throws:

java.lang.Exception

setVectorComponents

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

Sets the 4 vector components. The order is given by the order in the multiplication table. Intended only for usage in context with a multiplication table generated by Cayley Dickson doubling.

Parameters:

vector - 4 vector components, formatting: comma seperated, e.g. "x1,x2,x3,t".

Throws:

java.lang.Exception

setVectorComponents

public void setVectorComponents(java.lang.String[] vector_comps)
                         throws java.lang.Exception

Throws:

java.lang.Exception

setVectorComponentsExclusively

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

Sets the 4 vector components. The other components are reset. The order is given by the order in the multiplication table. Intended only for usage in context with a multiplication table generated by Cayley Dickson doubling.

Parameters:

vector - 4 vector components, formatting: comma seperated, e.g. "x1,x2,x3,t".

Throws:

java.lang.Exception

getVectorComponents

public java.lang.String[] getVectorComponents()

Returns:

Vector components in the order defined by the basis.

getVectorPartAsString

public java.lang.String getVectorPartAsString(boolean with_blanks)

Parameters:

no_blanks - 'true' No blanks between summands. 'false' A blank between summands.

Returns:

Representation of the vector part of the hypernumber with components and base elements. E.g. "x1*e1+x2*e2+x3*e3". Useful in context with a multiplication table generated by Cayley Dickson doubling.

getVectorPartAsString

public java.lang.String getVectorPartAsString()

setBiVectorComponents

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

Sets the 6 bivector components. The other components are retained. The order is given by the order in the multiplication table. Intended only for usage in context with a multiplication table generated by Cayley Dickson doubling.

Parameters:

vector - 6 bivector components, formatting: comma seperated, e.g. "a,b,c,d".

Throws:

java.lang.Exception

setBiVectorComponentsExclusively

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

Sets the 6 bivector components. The other components are reset. The order is given by the order in the multiplication table. Intended only for usage in context with a multiplication table generated by Cayley Dickson doubling.

Parameters:

vector - 4 vector components, formatting: comma seperated, e.g. "a,b,c,d".

Throws:

java.lang.Exception

getBivectorComponents

public java.lang.String[] getBivectorComponents()

Returns:

Bivector components in the order defined by the basis.

getBivectorPartAsString

public java.lang.String getBivectorPartAsString(boolean with_blanks)

Parameters:

no_blanks - 'true' No blanks between summands. 'false' A blank between summands.

Returns:

Representation of the bivector part of the hypernumber with components and base elements. E.g. "x1*e1e2+x2*e2e3. Useful in context with a multiplication table generated by Cayley Dickson doubling.

setTriVectorComponents

public void setTriVectorComponents(java.lang.String trivector)
                            throws java.lang.Exception

Sets the 4 trivector components. The other components are retained. The order is given by the order in the multiplication table. Intended only for usage in context with a multiplication table generated by Cayley Dickson doubling.

Parameters:

vector - 4 trivector components, formatting: comma seperated, e.g. "a,b,c,d".

Throws:

java.lang.Exception

setTriVectorComponentsExclusively

public void setTriVectorComponentsExclusively(java.lang.String trivector)
                                       throws java.lang.Exception

Sets the 4 trivector components. The other components are reset. The order is given by the order in the multiplication table. Intended only for usage in context with a multiplication table generated by Cayley Dickson doubling.

Parameters:

vector - 4 vector components, formatting: comma seperated, e.g. "a,b,c,d".

Throws:

java.lang.Exception

getBivectorPartAsString

public java.lang.String getBivectorPartAsString()

getTrivectorComponents

public java.lang.String[] getTrivectorComponents()

Returns:

Trivector components in the order defined by the basis.

getTrivectorPartAsString

public java.lang.String getTrivectorPartAsString(boolean with_blanks)

Parameters:

no_blanks - 'true' No blanks between summands. 'false' A blank between summands.

Returns:

Representation of the trivector part of the hypernumber with components and base elements. E.g. "x1*e1(e2e3)+x2*e1(e2e4). Useful in context with a multiplication table generated by Cayley Dickson doubling.

getTrivectorPartAsString

public java.lang.String getTrivectorPartAsString()

setEvenGradeComponents

public void setEvenGradeComponents(java.lang.String comps)
                            throws java.lang.Exception

Sets the 8 even grade components. The other components are reset. The order is given by the order in the multiplication table: (scalar, bivector 1, bv 2, bv 3, bv 4, bv 5, bv 6, 4-vector). Intended only for usage in context with a multiplication table generated by Cayley Dickson doubling.

Parameters:

spinor - 8 even grade components, formatting: comma seperated, e.g. "s,p1,p2,p3,p4,p5,p6,w".

Throws:

java.lang.Exception

setEvenGradeComponentsExclusively

public void setEvenGradeComponentsExclusively(java.lang.String comps)
                                       throws java.lang.Exception

Sets the 8 even grade components. The other components are retained. The order is given by the order in the multiplication table: (scalar, bivector 1, bv 2, bv 3, bv 4, bv 5, bv 6, 4-vector). Intended only for usage in context with a multiplication table generated by Cayley Dickson doubling.

Parameters:

spinor - 8 even grade components, formatting: comma seperated, e.g. "s,p1,p2,p3,p4,p5,p6,w".

Throws:

java.lang.Exception

getEvenGradeComponents

public java.lang.String[] getEvenGradeComponents()

Returns:

Even grade components in the order defined by the basis.

getEvenGradePartAsString

public java.lang.String getEvenGradePartAsString(boolean with_blanks)

Parameters:

no_blanks - 'true' No blanks between summands. 'false' A blank between summands.

Returns:

Representation of the even grade part (scalar + bivector + 4-vector) of the hypernumber with components and base elements. E.g. "x1*e+x2*e2e3+x3*e1((e2e3)e4). Useful in context with a multiplication table generated by Cayley Dickson doubling.

getEvenGradePartAsString

public java.lang.String getEvenGradePartAsString()

getOrder4Subalgebras

public java.util.LinkedList<MultiplicationTable> getOrder4Subalgebras()
                                                               throws java.lang.Exception

Returns:

The multiplication tables of all algebras of order 4. (For the Cayley-Dickson sedenions this should be 35 quaternion algebras).

Throws:

java.lang.Exception

getOrder8Subalgebras

public java.util.LinkedList<MultiplicationTable> getOrder8Subalgebras()
                                                               throws java.lang.Exception

Returns:

The multiplication tables of all algebras of order 8. (For the Cayley-Dickson sedenions this should be 15 algebras, not necessarily octonions).

Throws:

java.lang.Exception

conjugate

public Sedenion conjugate()
                   throws java.lang.Exception

Arithmetics *

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

square

public Sedenion square()
                throws java.lang.Exception

Overrides:

square in class Hypernumber

Returns:

The hypernumber multiplied with itself.

Throws:

java.lang.Exception

rightMultiplyWith

public Sedenion rightMultiplyWith(Hypernumber s)
                           throws java.lang.Exception

Overrides:

rightMultiplyWith in class Hypernumber

Throws:

java.lang.Exception

negate

public Sedenion 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

getNegated

public static Sedenion getNegated(Sedenion s)
                           throws java.lang.Exception

Throws:

java.lang.Exception

subtract

public Sedenion subtract(Sedenion sedenion)
                  throws java.lang.Exception

Throws:

java.lang.Exception

multiplyWithScalar

public Sedenion multiplyWithScalar(java.lang.String scalar)
                            throws java.lang.Exception

Description copied from class: Hypernumber

Multiplication with a scalar.

Overrides:

multiplyWithScalar in class Hypernumber

Parameters:

scalar - Scalar.

Returns:

Hypernumber multiplied with a scalar.

Throws:

java.lang.Exception

add

public Sedenion add(Sedenion sedenion)

getInverse

public static Sedenion getInverse(Sedenion s)
                           throws java.lang.Exception

Throws:

java.lang.Exception

getConjugate

public static Sedenion getConjugate(Sedenion s)
                             throws java.lang.Exception

Throws:

java.lang.Exception

getSum

public static Sedenion getSum(Sedenion s1,
                              Sedenion s2)
                       throws java.lang.Exception

Throws:

java.lang.Exception

getDifference

public static Sedenion getDifference(Sedenion s1,
                                     Sedenion s2)
                              throws java.lang.Exception

Throws:

java.lang.Exception

getProduct

public static Sedenion getProduct(Sedenion s1,
                                  Sedenion s2)
                           throws java.lang.Exception

Throws:

java.lang.Exception

getNumericalProduct

public static Sedenion getNumericalProduct(Sedenion s,
                                           Sedenion t)
                                    throws java.lang.Exception

Multiplies two sedenions numerically.

Parameters:

s1 - Sedenion 1 with numerical components.

s2 - Sedenion 2 with numerical components.

Returns:

Numerical product of two sedenions.

Throws:

java.lang.Exception

getNumericalSum

public static Sedenion getNumericalSum(Sedenion s,
                                       Sedenion t)
                                throws java.lang.Exception

Throws:

java.lang.Exception

getNumericalDifference

public static Sedenion getNumericalDifference(Sedenion s,
                                              Sedenion t)
                                       throws java.lang.Exception

Throws:

java.lang.Exception

getCommutator

public static Sedenion getCommutator(Sedenion s1,
                                     Sedenion s2)
                              throws java.lang.Exception

Throws:

java.lang.Exception

getCommutator

public static Sedenion getCommutator(Sedenion s1,
                                     Sedenion s2,
                                     boolean collect_terms)
                              throws java.lang.Exception

Throws:

java.lang.Exception

getAntiCommutator

public static Sedenion getAntiCommutator(Sedenion s1,
                                         Sedenion s2)
                                  throws java.lang.Exception

Throws:

java.lang.Exception

getAssociator

public static Sedenion getAssociator(Sedenion sta1,
                                     Sedenion sta2,
                                     Sedenion sta3)
                              throws java.lang.Exception

Throws:

java.lang.Exception

getJordanAssociator

public static Sedenion getJordanAssociator(Sedenion sta1,
                                           Sedenion sta2,
                                           Sedenion sta3)
                                    throws java.lang.Exception

Throws:

java.lang.Exception

getAntiAssociator

public static Sedenion getAntiAssociator(Sedenion sta1,
                                         Sedenion sta2,
                                         Sedenion sta3)
                                  throws java.lang.Exception

Throws:

java.lang.Exception

getScalarProduct

public static Sedenion getScalarProduct(Sedenion s1,
                                        Sedenion s2)
                                 throws java.lang.Exception

Throws:

java.lang.Exception

getJacobian

public static Sedenion getJacobian(Sedenion s1,
                                   Sedenion s2,
                                   Sedenion s3)
                            throws java.lang.Exception

Throws:

java.lang.Exception

getCommutatorJacobian

public static Sedenion getCommutatorJacobian(Sedenion s1,
                                             Sedenion s2,
                                             Sedenion s3)
                                      throws java.lang.Exception

Throws:

java.lang.Exception

getCommutatorSaglian

public static Sedenion getCommutatorSaglian(Sedenion s1,
                                            Sedenion s2,
                                            Sedenion s3,
                                            Sedenion s4)
                                     throws java.lang.Exception

Throws:

java.lang.Exception

getSecondHetztelPeresian

public static Sedenion getSecondHetztelPeresian(Sedenion s1,
                                                Sedenion s2,
                                                Sedenion s3,
                                                Sedenion s4)
                                         throws java.lang.Exception

Throws:

java.lang.Exception

getFirstHetztelPeresian

public static Sedenion getFirstHetztelPeresian(Sedenion s1,
                                               Sedenion s2,
                                               Sedenion s3,
                                               Sedenion s4,
                                               Sedenion s5)
                                        throws java.lang.Exception

Throws:

java.lang.Exception

getAssociationTypeCommutator

public static Sedenion getAssociationTypeCommutator(int nr,
                                                    Sedenion s1,
                                                    Sedenion s2,
                                                    Sedenion s3,
                                                    Sedenion s4,
                                                    Sedenion s5)
                                             throws java.lang.Exception

Throws:

java.lang.Exception

getAssociationType

public static Sedenion getAssociationType(int nr,
                                          Sedenion s1,
                                          Sedenion s2,
                                          Sedenion s3,
                                          Sedenion s4,
                                          Sedenion s5)
                                   throws java.lang.Exception

Throws:

java.lang.Exception

getAssociationType

public static Sedenion getAssociationType(int nr,
                                          Sedenion s1,
                                          Sedenion s2,
                                          Sedenion s3,
                                          Sedenion s4)
                                   throws java.lang.Exception

Throws:

java.lang.Exception

getAssociationTypeCommutator

public static Sedenion getAssociationTypeCommutator(int nr,
                                                    Sedenion s1,
                                                    Sedenion s2,
                                                    Sedenion s3,
                                                    Sedenion s4)
                                             throws java.lang.Exception

Throws:

java.lang.Exception

getNCycleGrades

public java.util.Collection<java.lang.String> getNCycleGrades(int ncycle)
                                                       throws java.lang.Exception

Intended for usage in context with multiplication tables generated by Cayley Dickson doubling. There are 5 grades 0,...4 corresponding to 0-,1-...,4-vectors. The number of elements of each grade in the n-cycle are counted.

Parameters:

ncycle - N cycle.

Returns:

Set with 5-tuples of numbers of occurences of grades. Example: 2 4-cycles: {1,1,1,1,0}, {1,2,1,0,0}, the first one contains each grade once except for grade 4, the second one contains two elements of grade 1.

Throws:

java.lang.Exception

getDiagonalVectorProducts

public java.lang.String getDiagonalVectorProducts()

getVectorSignature

public java.lang.String getVectorSignature()

getNumberOfGrades

public int getNumberOfGrades()
                      throws java.lang.Exception

Throws:

java.lang.Exception

getGrade

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

Throws:

java.lang.Exception

getGrading

public java.lang.String getGrading()
                            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 of a sedenion.

Throws:

java.lang.Exception

getSubalgebras

public static java.util.HashSet<java.lang.String> getSubalgebras(int order)
                                                          throws java.lang.Exception

Throws:

java.lang.Exception

getSubalgebrasUnsigned

public static java.util.HashSet<int[]> getSubalgebrasUnsigned(int order)
                                                       throws java.lang.Exception

Throws:

java.lang.Exception