public class Quaternion extends CayleyDicksonAlgebra
CD_LIKE0, CD_LIKE1, CD_LIKE10, CD_LIKE11, CD_LIKE12, CD_LIKE13, CD_LIKE14, CD_LIKE15, CD_LIKE16, CD_LIKE17, CD_LIKE18, CD_LIKE19, CD_LIKE2, CD_LIKE20, CD_LIKE21, CD_LIKE22, CD_LIKE23, CD_LIKE24, CD_LIKE25, CD_LIKE26, CD_LIKE27, CD_LIKE28, CD_LIKE29, CD_LIKE3, CD_LIKE30, CD_LIKE31, CD_LIKE4, CD_LIKE5, CD_LIKE6, CD_LIKE7, CD_LIKE8, CD_LIKE9, CLASSICAL, CLASSICAL2, COMPLEX, MAX_TYPE, MIN_TYPE, OCTONION, QUATERNION, SEDENION, TRIGINTADUONION, TWISTED, TWISTED2
ARG_NUM, CIRCULAR, COMP_NUM, components, HYPERBOLIC, ZERO_PRECISSION
Constructor and Description |
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Quaternion() |
Quaternion(int type) |
Quaternion(Quaternion q) |
Quaternion(java.lang.String components) |
Modifier and Type | Method and Description |
---|---|
Quaternion |
add(Quaternion q) |
Quaternion |
conjugate() |
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 Quaternion |
getAntiCommutator(Quaternion q1,
Quaternion q2) |
Quaternion |
getAntiCommutatorWith(Quaternion q) |
java.lang.String[] |
getBasis() |
static java.lang.String[][] |
getCayleyDicksonTable(java.lang.String[] signature,
java.lang.String[] vector_basis,
int type) |
Quaternion |
getClone() |
static Quaternion |
getCommutator(Quaternion q1,
Quaternion q2) |
static Quaternion |
getCommutatorJacobian(Quaternion q1,
Quaternion q2,
Quaternion q3) |
Quaternion |
getCommutatorWith(Quaternion q) |
static Quaternion |
getConjugate(Quaternion q) |
static Quaternion |
getDifference(Quaternion q1,
Quaternion q2) |
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) |
java.lang.String[][] |
getMTab()
Multiplication table and basis *
|
static MultiplicationTable |
getMultiplicationTable() |
static java.lang.String[][] |
getMultiplicationTableAsArray() |
int |
getMultiplicativeOrder(int max_steps) |
static java.lang.String |
getMultTableAsHtml() |
BinaryProductStructure |
getNewInstance() |
static java.lang.String[][] |
getNormedMultiplicationTable() |
static java.lang.String |
getNormedMultiplicationtableAsHtml() |
int |
getNumberOfComponents() |
int |
getNumberOfGrades() |
static Quaternion |
getProduct(Quaternion q1,
Quaternion q2) |
static SignTable |
getSignTable() |
static SignTable |
getSignTable(java.lang.String plus,
java.lang.String minus) |
static Quaternion |
getSum(Quaternion q1,
Quaternion q2) |
static java.lang.String |
getType()
The normed multiplication table is compared with the 8 normed multiplication tables of
the "left-" and "right-handed" quaternion algebras for the 4 possible signatures.
|
java.lang.String[] |
getVectorComponents() |
boolean |
isCayleyDicksonAlgebra() |
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 |
setLeftHanded() |
static void |
setMultiplicationTable(MultiplicationTable mult_table) |
static void |
setMultiplicationTable(java.lang.String[][] mult_table) |
static void |
setRightHanded() |
static void |
setSignTable(SignTable sign_table) |
void |
setVectorComponents(java.lang.String vector) |
getCDTypeAsString
add, add, applyLeibnizRule, calculateBCHWith, getAntiCommutatorWith, getCommutatorWith, getCommutatorWith, getComponentsOfGrade, getDifference, getGradedInnerProduct, getIntersection, getLeftCovariantDerivative, getNumberOfComponents, getOuterProduct, getProduct, getScalarProduct, getSum, getTernaryInnerProduct, isCommutative, isEqual, isOrthogonal, isOrthogonalTo, isProjectionOperator, rightMultiplyWith, subtract
asString, asString, collectTerms, compressComponents, dual, getBasisElementAsString, getBasisElementsAsString, getClosedPairsAsString, getComponent, getComponents, getComponentsAsString, getComponentsAsString, getConjugate, getDiagonalProducts, getDual, getExpressionAsList, getFormattedMultTable, getHermitianConjugate, getImaginaryPart, getInstance, getMultiplicativeOrder, getMultiplicativeOrder, getMultTableDiagonal, getNegated, getNextBitmap, getNonzeroComponentsNumbered, getNonzeroComponentsNumbered, getNormedMultiplicationTable, getNormSquared, getNormSquaredAsValue, getNumberOfClosedElements, getNumberOfClosedPairs, getNumberOfNonzeroComponents, getNumericalInverse, getProduct, getProductWithScalar, getPseudoScalarComponent, getRandomClosedPair, getRandomNonClosedPair, getScalarComponent, getSubalgebras, getSubalgebrasAsString, getSubalgebrasSignatures, getTrace, getTraceRespDeterminant, getVectorDerivative, getVectorProduct, isAutomorphism, isCayleyDicksonLoop, isComponentZero, isLinearlyDependent, isNumerical, isNumericalityDetected, isProductClosed, isZero, resetComponents, rightMultiplyWith, rightMultiplyWith, setBasis, setComponent, setComponentAsBasisNames, setComponentExclusively, setComponents, setComponents, setIndexedComponents, setNumerical, setNumerical, setPseudoScalarComponent, setRandomComponents, setRandomComponents, setRandomComponents, setRandomComponentsAll, setRepresentation, setScalarComponent, simplifyNumericalFactors, simplifyNumericalSummands, simplifyPlusMinus, square
public Quaternion()
public Quaternion(int type)
public Quaternion(java.lang.String components) throws java.lang.Exception
java.lang.Exception
public Quaternion(Quaternion q)
public static java.lang.String getType() throws java.lang.Exception
java.lang.Exception
public static void setLeftHanded() throws java.lang.Exception
java.lang.Exception
public static void setRightHanded() throws java.lang.Exception
java.lang.Exception
public void setVectorComponents(java.lang.String vector) throws java.lang.Exception
java.lang.Exception
public void setBiVectorComponents(java.lang.String bivector) throws java.lang.Exception
java.lang.Exception
public Quaternion rightMultiplyWith(Quaternion q) throws java.lang.Exception
java.lang.Exception
public Quaternion conjugate() throws java.lang.Exception
conjugate
in class BinaryProductStructure
java.lang.Exception
public static Quaternion getProduct(Quaternion q1, Quaternion q2) throws java.lang.Exception
java.lang.Exception
public Quaternion add(Quaternion q)
public Quaternion multiplyWithScalar(java.lang.String constant) throws java.lang.Exception
BinaryProductStructure
multiplyWithScalar
in class BinaryProductStructure
constant
- Scalar.java.lang.Exception
public Quaternion negate() throws java.lang.Exception
BinaryProductStructure
negate
in class BinaryProductStructure
java.lang.Exception
public static Quaternion getAntiCommutator(Quaternion q1, Quaternion q2) throws java.lang.Exception
java.lang.Exception
public Quaternion getAntiCommutatorWith(Quaternion q) throws java.lang.Exception
java.lang.Exception
public Quaternion getCommutatorWith(Quaternion q) throws java.lang.Exception
java.lang.Exception
public Quaternion getClone()
getClone
in class BinaryAlgebra
public BinaryProductStructure getNewInstance()
getNewInstance
in class BinaryProductStructure
public java.lang.String[] getBasis()
getBasis
in class BinaryProductStructure
public int getNumberOfComponents()
getNumberOfComponents
in class BinaryProductStructure
public static void setSignTable(SignTable sign_table) throws java.lang.Exception
java.lang.Exception
public static SignTable getSignTable(java.lang.String plus, java.lang.String minus) throws java.lang.Exception
java.lang.Exception
public static SignTable getSignTable() throws java.lang.Exception
java.lang.Exception
public static void doCayleyDicksonDoubling(java.lang.String signatures, java.lang.String vector_basis) throws java.lang.Exception
java.lang.Exception
public static void doCayleyDicksonDoubling(java.lang.String signatures, java.lang.String vector_basis, int type) throws java.lang.Exception
signatures
- Comma delimited string of 4 signatures with "+" specifying a non-split and "-" a
split doubling. (e.g. "+,-,+,+").vector_basis
- java.lang.Exception
public static MultiplicationTable getMultiplicationTable()
public static void setMultiplicationTable(java.lang.String[][] mult_table)
public java.lang.String[][] getMTab()
BinaryProductStructure
getMTab
in class BinaryProductStructure
public static void setDefaultTable()
public static java.lang.String getMultTableAsHtml()
public static java.lang.String[][] getNormedMultiplicationTable()
public static java.lang.String getNormedMultiplicationtableAsHtml()
public int getNumberOfGrades()
getNumberOfGrades
in class BinaryAlgebra
public static void setMultiplicationTable(MultiplicationTable mult_table) throws java.lang.Exception
java.lang.Exception
public Quaternion getGrade(int grade) throws java.lang.Exception
getGrade
in class BinaryAlgebra
java.lang.Exception
public java.lang.String getGradesOccuring() throws java.lang.Exception
java.lang.Exception
public java.lang.String[] getVectorComponents() throws java.lang.Exception
java.lang.Exception
public static Quaternion getConjugate(Quaternion q) throws java.lang.Exception
java.lang.Exception
public static Quaternion getSum(Quaternion q1, Quaternion q2) throws java.lang.Exception
java.lang.Exception
public static Quaternion getDifference(Quaternion q1, Quaternion q2) throws java.lang.Exception
java.lang.Exception
public static Quaternion getCommutator(Quaternion q1, Quaternion q2) throws java.lang.Exception
java.lang.Exception
public static Quaternion getJacobian(Quaternion q1, Quaternion q2, Quaternion q3) throws java.lang.Exception
java.lang.Exception
public static Quaternion getCommutatorJacobian(Quaternion q1, Quaternion q2, Quaternion q3) throws java.lang.Exception
java.lang.Exception
public static java.lang.String[][] getMultiplicationTableAsArray()
public int getMultiplicativeOrder(int max_steps) throws java.lang.Exception
java.lang.Exception
public static java.util.TreeMap<java.lang.Integer,java.lang.Integer> getGrades() throws java.lang.Exception
java.lang.Exception
public static java.lang.String[][] getCayleyDicksonTable(java.lang.String[] signature, java.lang.String[] vector_basis, int type) throws java.lang.Exception
java.lang.Exception
public boolean isCayleyDicksonAlgebra() throws java.lang.Exception
isCayleyDicksonAlgebra
in class BinaryAlgebra
java.lang.Exception