- get16UnaryElements() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
-
- getAlgebraicAssociator(ComplexNumber, ComplexNumber, ComplexNumber) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
Although the complex numbers are associative, it turns out that they are useful for
checking the triviality of (nonassociative) identities.
- getAlgebraicCommutator(ComplexNumber, ComplexNumber) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getAlgebraicProduct(ComplexNumber, ComplexNumber) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getAlgebraType() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
Checking for the 480 variants of multiplication tables is omitted.
- getAlgebraType(boolean) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
The normed multiplication table is compared with the normed multiplication tables
obtained by the different Cayley-Dickson doubling formulas for all 8 possible
signature combinations.
- getAllCyclesUnsigned() - Method in class jhypercomplex.multiplication_tables.OctonionMultiplicationTable
-
- getAllUnitElements() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.HypercomplexLattice
-
- getAllUnitElements() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
-
- getAllUnitElements() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionicLeechLattice
-
- getAllUnitElements() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.QuaternionLattice
-
- getAllUnitElements() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.SedenionLattice
-
- getAllUnitsAsString() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.HypercomplexLattice
-
- getAntiAssociator(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getAntiAssociator(Sedenion, Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getAntiAssociator(Trigintaduonion, Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getAntiAssociator(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getAntiCommutator(Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getAntiCommutator(Quaternion, Quaternion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getAntiCommutator(Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getAntiCommutator(Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getAntiCommutator(DeSitterAlgebra, DeSitterAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
- getAntiCommutator(PauliAlgebra, PauliAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getAntiCommutator(PlaneAlgebra, PlaneAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getAntiCommutator(SpacetimeAlgebra, SpacetimeAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getAntiCommutator(BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getAntiCommutatorWith(BinaryAlgebra) - Method in class jhypercomplex.algebras.BinaryAlgebra
-
Calculates the anti-commutator of the element a1 of the algebra with another one a2
which is defined as:
{a1, a2} = a1*a2 + a2*a1
- getAntiCommutatorWith(ComplexNumber) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getAntiCommutatorWith(BinaryAlgebra) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getAntiCommutatorWith(Quaternion) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getAssociationType(int, Octonion, Octonion, Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getAssociationType(int, Sedenion, Sedenion, Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getAssociationType(int, Sedenion, Sedenion, Sedenion, Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getAssociationType(int, Trigintaduonion, Trigintaduonion, Trigintaduonion, Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getAssociationType(int, Trigintaduonion, Trigintaduonion, Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getAssociationType(int, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, boolean) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
"Switch"-method, that allows for an invocation of the association type method or alternatively the commutator
association type method.
- getAssociationType(int, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
There are 5 ways to put the brackets in a product of 4 Algebras.
- getAssociationType(int, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, boolean) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
"Switch"-method, that allows for an invocation of the association type method or alternatively the commutator
association type method.
- getAssociationType(int, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
There are 14 ways to put the brackets in a product of 5 Algebras.
- getAssociationTypeAsString(int, String, String, String, String) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getAssociationTypeAsString(int, String, String, String, String, String) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getAssociationTypeCommutator(int, Octonion, Octonion, Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getAssociationTypeCommutator(int, Sedenion, Sedenion, Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getAssociationTypeCommutator(int, Sedenion, Sedenion, Sedenion, Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getAssociationTypeCommutator(int, Trigintaduonion, Trigintaduonion, Trigintaduonion, Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getAssociationTypeCommutator(int, Trigintaduonion, Trigintaduonion, Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getAssociationTypeCommutator(int, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
There are 5 ways to nest 3 commutators of 4 Algebras, namely
nr
1 [[[a,b],c],d]
2 [a,[b,[c,d]]]
3 [[a,[b,c]],d]
4 [a,[[b,c],d]]
5 [[a,b],[c,d]]
- getAssociationTypeCommutator(int, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
There are 14 ways to nest 4 commutators of 5 Algebras, namely
nr
1 [a,[b,[c,[d,e]]]]
3 [a,[b,[[c,d],e]]]
8 [a,[[b,c],[d,e]]]
5 [a,[[b,[c,d]],e]]
9 [a,[[[b,c],d],e]]
2 [[a,b],[c,[d,e]]]
4 [[a,b],[[c,d],e]]
11 [[a,[b,c]],[d,e]]
6 [[a,[b,[c,d]]],e]
10 [[a,[[b,c],d]],e]
13 [[[a,b],c],[d,e]]
7 [[[a,b],[c,d]],e]
12 [[[a,[b,c]],d],e]
14 [[[[a,b],c],d],e]
- getAssociationTypeCommutatorAsString(int, String, String, String, String) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getAssociationTypeCommutatorAsString(int, String, String, String, String, String) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getAssociationTypeIdentitiesCheckList(int, int, int, boolean) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getAssociationTypeIdentitiesCheckList(Class, int, int, int, boolean) - Static method in class jhypercomplex.algebras.identities.AlgebraicProperties
-
Method that wraps (bunches) the checking of association type identities.
- getAssociator(ComplexNumber, ComplexNumber, ComplexNumber) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getAssociator(Octonion, Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
Calculates the associator of 3 octonions o1, o2, o3 which is defined as
{o1, o2, o3} = (o1*o2)*o3 - o1*(o2*o3)
The associator is non-trivial as the octonion algebra is non-associative.
- getAssociator(Sedenion, Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getAssociator(Trigintaduonion, Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getAssociator(DeSitterAlgebra, DeSitterAlgebra, DeSitterAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
- getAssociator(PauliAlgebra, PauliAlgebra, PauliAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getAssociator(PlaneAlgebra, PlaneAlgebra, PlaneAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getAssociator(SpacetimeAlgebra, SpacetimeAlgebra, SpacetimeAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getAssociator(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getBasis() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getBasis() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.HypercomplexLattice
-
- getBasis() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.OctonarySubAlgebra
-
- getBasis() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getBasis() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getBasis() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
Multiplication table and basis *
- getBasis() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
Multiplication table and basis *
- getBasis() - Method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
- getBasis() - Method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getBasis() - Method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getBasis() - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getBasis() - Method in class jhypercomplex.algebras.TensoredAlgebra
-
- getBasis() - Method in class jhypercomplex.BinaryProductStructure
-
- getBasis() - Method in class jhypercomplex.matrices.Vector
-
- getBasis() - Method in class jhypercomplex.multiplication_tables.OctonionMultiplicationTable
-
- getBasisElementAsString(int) - Method in class jhypercomplex.BinaryProductStructure
-
- getBasisElementsAsString() - Method in class jhypercomplex.BinaryProductStructure
-
- getBinarySignMask() - Method in class jhypercomplex.multiplication_tables.SignTable
-
The signs of the upper triangle are mapped according to:
"-" --> 0
"+" --> 1
and the result is concatenated.
- getBiVectorComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getBivectorComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getBiVectorComponents() - Method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
-
- getBivectorPartAsString(boolean) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getBivectorPartAsString() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getBladeNumbers() - Method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
-
- getBladeNumbers() - Method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
- getBlades(String) - Method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
-
Projects out a given set of blades.
- getBlades(String) - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getBMQuaternator1(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
First quaternator as defined by Murray R.
- getBMQuaternator2(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
Second quaternator as defined by Murray R.
- getBMQuaternatorIdentity1(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getBMQuaternatorIdentity2(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getBMQuaternatorIdentity3(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getBMQuaternatorIdentity4(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getBrandtTransformer(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
-
// TODO explain //
- getBrandtTransformer(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionicLeechLattice
-
// TODO explain //
- getCayleyDicksonTable(String[], String[], int) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getCayleyDicksonTable(String[], int) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getCayleyDicksonTable(String[], String[], int) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getCDTypeAsString(int) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.CayleyDicksonAlgebra
-
- getClone() - Method in class jhypercomplex.algebras.BinaryAlgebra
-
- getClone() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras.ComplexOctonion
-
- getClone() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras.ComplexQuaternion
-
Simplifies the components of a bi-hypercomplex number, given a complex unit.
- getClone() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras.ComplexSedenion
-
- getClone() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getClone() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.OctonarySubAlgebra
-
- getClone() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getClone() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getClone() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getClone(BinaryProductStructure) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getClone() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getClone(BinaryAlgebra) - Method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
-
- getClone(BinaryProductStructure) - Method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
- getClone(BinaryAlgebra) - Method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
- getClone() - Method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
- getClone(BinaryAlgebra) - Method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getClone() - Method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getClone(PlaneAlgebra) - Method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getClone(BinaryAlgebra) - Method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getClone() - Method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getClone() - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getClone(BinaryAlgebra) - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getClone() - Method in class jhypercomplex.BinaryProductStructure
-
- getClone() - Method in class jhypercomplex.matrices.Vector
-
- getClosedPairsAsString(BinaryProductStructure[]) - Static method in class jhypercomplex.BinaryProductStructure
-
- getCommuAssociator(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getCommutator(ComplexNumber, ComplexNumber) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getCommutator(ComplexNumber, ComplexNumber, boolean) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getCommutator(Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getCommutator(Quaternion, Quaternion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getCommutator(Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getCommutator(Sedenion, Sedenion, boolean) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getCommutator(Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getCommutator(Trigintaduonion, Trigintaduonion, boolean) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getCommutator(DeSitterAlgebra, DeSitterAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
- getCommutator(PauliAlgebra, PauliAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getCommutator(PlaneAlgebra, PlaneAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getCommutator(SpacetimeAlgebra, SpacetimeAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getCommutator(BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getCommutator(BinaryAlgebra, BinaryAlgebra, boolean) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getCommutatorBMQuaternator1(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
First quaternator as defined by Murray R.
- getCommutatorJacobian(Octonion, Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getCommutatorJacobian(Quaternion, Quaternion, Quaternion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getCommutatorJacobian(Sedenion, Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getCommutatorJacobian(Trigintaduonion, Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getCommutatorJacobian(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getCommutatorSaglian(Octonion, Octonion, Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getCommutatorSaglian(Sedenion, Sedenion, Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getCommutatorSaglian(Trigintaduonion, Trigintaduonion, Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getCommutatorSaglian(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getCommutatorWith(BinaryAlgebra, boolean) - Method in class jhypercomplex.algebras.BinaryAlgebra
-
Calculates the commutator of an element a1 of the algebra with another one a2.
- getCommutatorWith(BinaryAlgebra) - Method in class jhypercomplex.algebras.BinaryAlgebra
-
- getCommutatorWith(ComplexNumber) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getCommutatorWith(BinaryAlgebra) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getCommutatorWith(Quaternion) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getComparisonTable(String[][], String[][]) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
Compares the entries of two multiplication tables.
- getComponent(int) - Method in class jhypercomplex.BinaryProductStructure
-
- getComponents() - Method in class jhypercomplex.BinaryProductStructure
-
- getComponentsAsString() - Method in class jhypercomplex.BinaryProductStructure
-
- getComponentsAsString(boolean) - Method in class jhypercomplex.BinaryProductStructure
-
- getComponentsOfGrade(int, TreeMap<Integer, Integer>) - Method in class jhypercomplex.algebras.BinaryAlgebra
-
- getConjugate(ComplexNumber) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getConjugate(Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getConjugate(Quaternion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getConjugate(Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getConjugate(Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getConjugate(BinaryProductStructure) - Static method in class jhypercomplex.BinaryProductStructure
-
- getCopy(String[][]) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getCycle(int) - Method in class jhypercomplex.multiplication_tables.OctonionMultiplicationTable
-
- getDeepestBracketPosition(String) - Static method in class jhypercomplex.algebras.identities.SymbolicAlgebra
-
The depth of the deepest nesting of bracket(s) is determined.
- getDeterminant() - Method in class jhypercomplex.matrices.SquareMatrix
-
The determinant is computed.
- getDeterminant(double[][]) - Static method in class jhypercomplex.matrices.SquareMatrix
-
- getDeterminant(String[][], boolean) - Static method in class jhypercomplex.matrices.SquareMatrix
-
- getDeterminant2(double[][]) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getDiagonalProducts() - Method in class jhypercomplex.BinaryProductStructure
-
- getDiagonalVectorProducts() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getDifference(BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.BinaryAlgebra
-
- getDifference(ComplexNumber, ComplexNumber) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getDifference(Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getDifference(Quaternion, Quaternion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getDifference(Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getDifference(Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getDoubledMultiplicationTable(int, BinaryAlgebra, String[], int) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTableDoubling
-
- getDual(BinaryProductStructure) - Static method in class jhypercomplex.BinaryProductStructure
-
- getE7Roots() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
-
- getE7Roots() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionicLeechLattice
-
- getElements(int, int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.HypercomplexLattice
-
- getEvenGrade(DeSitterAlgebra) - Method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
- getEvenGrade(PauliAlgebra) - Method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getEvenGrade(PlaneAlgebra) - Method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getEvenGrade(SpacetimeAlgebra) - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getEvenGradeComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getEvenGradePartAsString(boolean) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getEvenGradePartAsString() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getExpressionAsList(String) - Static method in class jhypercomplex.BinaryProductStructure
-
An expression is split up in respect to the summands.
- getFanoPlane() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getFirstHetztelPeresian(Sedenion, Sedenion, Sedenion, Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getFirstHetztelPeresian(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getFormattedMultTable() - Method in class jhypercomplex.BinaryProductStructure
-
- getGrade(int) - Method in class jhypercomplex.algebras.BinaryAlgebra
-
- getGrade(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras.ComplexOctonion
-
- getGrade(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras.ComplexQuaternion
-
- getGrade(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras.ComplexSedenion
-
- getGrade(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getGrade(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.OctonarySubAlgebra
-
- getGrade(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getGrade(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getGrade(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getGrade(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getGrade(int) - Method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
-
- getGrade(int) - Method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
Projects out a given grade.
- getGrade(int) - Method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
Projects out a given grade.
- getGrade(int) - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
Projects out a given grade.
- getGrade(int) - Method in class jhypercomplex.matrices.Vector
-
- getGradedInnerProduct(BinaryAlgebra, BinaryAlgebra, boolean) - Static method in class jhypercomplex.algebras.BinaryAlgebra
-
- getGrades() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getGrades() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getGrades() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getGrades() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getGrades() - Static method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
-
- getGradesOccuring() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getGradesOccuring() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getGradesOccuring() - Method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
-
- getGrading() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getHermitianConjugate() - Method in class jhypercomplex.BinaryProductStructure
-
The hermitian conjugate of a hypernumber H is defined as:
*H = *(S,S) = (*S,S) where S is the subalgebra from which the hypernumber is constructed
via a (Cayley-Dickson) doubling procedure.
- getIdemotents(Class, int) - Static method in class jhypercomplex.MonteCarlo
-
Idempotents (modulo '-1') are determined.
- getImaginaryPart(Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getImaginaryPart(BinaryProductStructure) - Static method in class jhypercomplex.BinaryProductStructure
-
- getInstance(Class) - Static method in class jhypercomplex.BinaryProductStructure
-
- getIntersection(BinaryProductStructure[], BinaryProductStructure[]) - Static method in class jhypercomplex.algebras.BinaryAlgebra
-
Two sets of hypernumbers are compared.
- getInverse(Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getInverse(Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getIsNumerical() - Static method in class jhypercomplex.matrices.Matrix
-
- getJacobian(Octonion, Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getJacobian(Quaternion, Quaternion, Quaternion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getJacobian(Sedenion, Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getJacobian(Trigintaduonion, Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getJacobian(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getJordanAssociator(Sedenion, Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getJordanAssociator(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getKleinfeldFunction(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getLeftCovariantDerivative(BinaryAlgebra, BinaryAlgebra) - Method in class jhypercomplex.algebras.BinaryAlgebra
-
The covariant derivative of the hypernumber is calculated.
- getMatrix() - Method in class jhypercomplex.matrices.Matrix
-
- getMatrixAsHtml(Matrix, boolean) - Static method in class jhypercomplex.matrices.Matrix
-
- getMatrixAsHtml() - Method in class jhypercomplex.matrices.Matrix
-
- getMTab() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getMTab() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.OctonarySubAlgebra
-
- getMTab() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getMTab() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getMTab() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getMTab() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getMTab() - Method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
- getMTab() - Method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getMTab() - Method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getMTab() - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getMTab() - Method in class jhypercomplex.algebras.TensoredAlgebra
-
- getMTab() - Method in class jhypercomplex.BinaryProductStructure
-
Multiplication table and basis *
- getMTab() - Method in class jhypercomplex.matrices.Vector
-
- getMultiplicationTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getMultiplicationTable() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.OctonarySubAlgebra
-
- getMultiplicationTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getMultiplicationTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getMultiplicationTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getMultiplicationTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getMultiplicationTable() - Static method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
-
- getMultiplicationTable() - Static method in class jhypercomplex.algebras.TensoredAlgebra
-
- getMultiplicationTableAsArray() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getMultiplicationTableAsArray() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getMultiplicationTableAsArray() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getMultiplicationTableAsArray() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getMultiplicationTableAsArray() - Static method in class jhypercomplex.BinaryProductStructure
-
To be implemented in the classes that inherit from class 'Hypernumber'.
- getMultiplicativeOrder(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getMultiplicativeOrder(BinaryProductStructure, int) - Method in class jhypercomplex.BinaryProductStructure
-
- getMultiplicativeOrder(BinaryProductStructure, int, double) - Method in class jhypercomplex.BinaryProductStructure
-
Multiplicative order n, defined by: {min n: h1*(h2^n) = l*h1} with l a scalar factor.
- getMultTable() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getMultTableAsArray() - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getMultTableAsHtml() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getMultTableAsHtml() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getMultTableAsHtml() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getMultTableAsHtml() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getMultTableAsHtml() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getMultTableAsHtml() - Method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
-
- getMultTableAsHtml() - Static method in class jhypercomplex.algebras.TensoredAlgebra
-
- getMultTableAsHtml(String[], String[][]) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getMultTableAsHtml(String[], String[][], boolean) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getMultTableAsHtml() - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getMultTableAsHtml(boolean) - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getMultTableDiagonal() - Method in class jhypercomplex.BinaryProductStructure
-
- getMultTableListAsHtml(LinkedList<MultiplicationTable>) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getMultTableStringDelimited(String) - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getMultTableStringDelimited(String[][], String) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getMutliplicativeOrderDistribution() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.HypercomplexLattice
-
- getMutliplicativeOrderDistribution() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionicLeechLattice
-
- getNCycleGrades(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
Intended for usage in context with multiplication tables generated by Cayley Dickson
doubling.
- getNegated(Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getNegated(Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getNegated(BinaryProductStructure) - Static method in class jhypercomplex.BinaryProductStructure
-
- getNewInstance() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras.ComplexOctonion
-
- getNewInstance() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras.ComplexQuaternion
-
- getNewInstance() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras.ComplexSedenion
-
- getNewInstance() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getNewInstance() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.OctonarySubAlgebra
-
- getNewInstance() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getNewInstance() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getNewInstance() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getNewInstance() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getNewInstance() - Method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
-
- getNewInstance() - Method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
- getNewInstance() - Method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getNewInstance() - Method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getNewInstance() - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getNewInstance() - Method in class jhypercomplex.BinaryProductStructure
-
- getNewInstance() - Method in class jhypercomplex.matrices.Vector
-
- getNextBitmap(String) - Static method in class jhypercomplex.BinaryProductStructure
-
Used for permuting a bitmap with n 1's.
- getNonassociativeSpacetimeQuadruples() - Static method in class jhypercomplex.MonteCarlo
-
- getNonassociativeSpacetimeTriples() - Static method in class jhypercomplex.MonteCarlo
-
- getNonQuaternionGroupSubbasisis() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.QuaternionLattice
-
- getNonzeroComponentsNumbered(boolean) - Method in class jhypercomplex.BinaryProductStructure
-
If the n-th component (numbering starting from 0) is non-zero, "n" is added to a list.
- getNonzeroComponentsNumbered() - Method in class jhypercomplex.BinaryProductStructure
-
- getNormedHTMLTable() - Method in class jhypercomplex.multiplication_tables.OctonionMultiplicationTable
-
- getNormedMultiplicationTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getNormedMultiplicationTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getNormedMultiplicationTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getNormedMultiplicationTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getNormedMultiplicationTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getNormedMultiplicationTable(String[][], String[], String[]) - Static method in class jhypercomplex.BinaryProductStructure
-
A normed multiplication table is per definition a table where the base
elements are numbered according to the order of their occurrence
in the basis vector (integers running from 1 upwards).
- getNormedMultiplicationTable() - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getNormedMultiplicationTable(String[][], String[]) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
A normed multiplication table is per definition a table where the base
elements are numbered according to the order of their occurrence
in the basis vector (integers running from 1 upwards).
- getNormedMultiplicationtableAsHtml() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getNormedMultiplicationtableAsHtml() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getNormedMultiplicationtableAsHtml() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getNormedMultiplicationtableAsHtml() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getNormedMultiplicationtableAsHtml() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getNormedMultTableStringDelimited(String) - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getNormSquared(BinaryProductStructure) - Static method in class jhypercomplex.BinaryProductStructure
-
- getNormSquaredAsValue() - Method in class jhypercomplex.BinaryProductStructure
-
REQUIRES: Invocation in numerical mode.
- getNucleus() - Method in class jhypercomplex.MonteCarlo
-
Every component is randomly set to -1,0 or 1.
- getNumberedBasis() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.OctonarySubAlgebra
-
The n basis elements of the algebra for which this algebra is a subalgebra
are numbered (0,...n-1).
- getNumberOfBlocks() - Method in class jhypercomplex.combinatorics.SteinerTripleSystem
-
- getNumberOfClosedElements(BinaryProductStructure[]) - Static method in class jhypercomplex.BinaryProductStructure
-
In case that the full set of elements is not closed under multiplication, it might be of interest
for how many of its elements this property is still given.
- getNumberOfClosedPairs(BinaryProductStructure[]) - Static method in class jhypercomplex.BinaryProductStructure
-
For every posssible pair of the given set of hypernumbers it is checked if the prodeuct is again
contained in the set.
- getNumberOfComponents(int, TreeMap<Integer, Integer>) - Method in class jhypercomplex.algebras.BinaryAlgebra
-
- getNumberOfComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras.ComplexOctonion
-
- getNumberOfComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras.ComplexQuaternion
-
- getNumberOfComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras.ComplexSedenion
-
- getNumberOfComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getNumberOfComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.OctonarySubAlgebra
-
- getNumberOfComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getNumberOfComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getNumberOfComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
Components *
- getNumberOfComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getNumberOfComponents() - Method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
- getNumberOfComponents() - Method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getNumberOfComponents() - Method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getNumberOfComponents() - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getNumberOfComponents() - Method in class jhypercomplex.BinaryProductStructure
-
- getNumberOfComponents() - Method in class jhypercomplex.matrices.Vector
-
- getNumberOfGrades() - Method in class jhypercomplex.algebras.BinaryAlgebra
-
- getNumberOfGrades() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getNumberOfGrades() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.OctonarySubAlgebra
-
- getNumberOfGrades() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getNumberOfGrades() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getNumberOfGrades() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getNumberOfGrades() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getNumberOfGrades() - Method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
- getNumberOfGrades() - Method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getNumberOfGrades() - Method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getNumberOfGrades() - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getNumberOfGrades() - Method in class jhypercomplex.algebras.TensoredAlgebra
-
- getNumberOfGrades() - Method in class jhypercomplex.matrices.Vector
-
- getNumberOfHadamardMatrices(int) - Static method in class jhypercomplex.matrices.HadamardMatrix
-
- getNumberOfNonzeroComponents() - Method in class jhypercomplex.BinaryProductStructure
-
- getNumberOfPoints() - Method in class jhypercomplex.combinatorics.SteinerTripleSystem
-
- getNumberOfUnitElement(BinaryAlgebra) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.HypercomplexLattice
-
- getNumericalDifference(Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getNumericalInverse(BinaryAlgebra) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getNumericalInverse(BinaryProductStructure) - Static method in class jhypercomplex.BinaryProductStructure
-
The inverse of a hypernumber h is calculated.
- getNumericalProduct(Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
Multiplies two sedenions numerically.
- getNumericalSum(Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getOctavianUnits(int, int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
-
- getOctavianUnits(int, int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionicLeechLattice
-
- getOctonarySubalgebras() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getOctonionicGenerators() - Method in class jhypercomplex.groups.OctonionicG2
-
- getOrder4Subalgebras() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getOrder8Subalgebras() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getOuterProduct(BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.BinaryAlgebra
-
- getOuterProduct(Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getOuterProduct(PauliAlgebra, PauliAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getPrimeNumbers(int) - Static method in class jhypercomplex.PrimeNumbers
-
- getProduct(BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.BinaryAlgebra
-
- getProduct(ComplexNumber, ComplexNumber) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getProduct(Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getProduct(Quaternion, Quaternion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getProduct(Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getProduct(Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getProduct(DeSitterAlgebra, DeSitterAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
- getProduct(PauliAlgebra, PauliAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getProduct(PlaneAlgebra, PlaneAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getProduct(SpacetimeAlgebra, SpacetimeAlgebra) - Static method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getProduct(BinaryProductStructure, BinaryProductStructure) - Static method in class jhypercomplex.BinaryProductStructure
-
Multiplies two hypernummers according to the order of the arguments of the method.
- getProduct(Matrix, Matrix) - Static method in class jhypercomplex.matrices.Matrix
-
Right-multiplies matrix m1 with matrix m2.
- getProduct(Vector, Vector) - Static method in class jhypercomplex.matrices.Vector
-
- getProductWithScalar(BinaryAlgebra, String) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getProductWithScalar(BinaryProductStructure, String) - Static method in class jhypercomplex.BinaryProductStructure
-
- getPseudoScalarComponent() - Method in class jhypercomplex.BinaryProductStructure
-
- getQuaternator(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getQuaternator1(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getQuaternator2(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getQuaternionGroupSubbasisis() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.QuaternionLattice
-
- getRandomClosedPair(BinaryProductStructure[]) - Static method in class jhypercomplex.BinaryProductStructure
-
From the given set of hypernumbers a random pair is chosen (non trivial, i.a. the two elements
are supposed to be different).
- getRandomInteger(int, int, HashSet<String>) - Static method in class jhypercomplex.MonteCarlo
-
- getRandomInteger(int, int) - Static method in class jhypercomplex.MonteCarlo
-
- getRandomNonClosedPair(BinaryProductStructure[]) - Static method in class jhypercomplex.BinaryProductStructure
-
From the given set of hypernumbers a random pair is chosen (non trivial, i.a. the two elements
are supposed to be different).
- getRepresentation() - Method in class jhypercomplex.combinatorics.SevenPointsSTS
-
- getReverted() - Method in class jhypercomplex.algebras.clifford_algebras.DeSitterAlgebra
-
Reverts a vector.
- getReverted() - Method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
Reverts a vector.
- getReverted() - Method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
Reverts a vector.
- getReverted() - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
Reverts a vector.
- getSabininator(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getSabininQuaternator(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getScalarComponent() - Method in class jhypercomplex.BinaryProductStructure
-
- getScalarProduct(BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.BinaryAlgebra
-
The scalar product (= real inner product) <.|.> of two algebra a1 and a2 is defined as
= 1/2(a1a2*+a2a1*)
- getScalarProduct(Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getScalarProduct(Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getScalarProduct(Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getSecondHetztelPeresian(Sedenion, Sedenion, Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getSecondHetztelPeresian(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.identities.AlgebraicFunctions
-
- getSignature() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getSignature() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getSignTable(String, String) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getSignTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getSignTable(String, String) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getSignTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getSignTable(String[][], String, String) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getSignTable(String, String) - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getSignTable() - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getSignTableAsArray(String[][]) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getSignTableAsArray(String[][], String, String) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getSignTableAsHtml(String[][], String, String) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getSignTableAsHtml(String, String) - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getSignTableStringDelimited(String) - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getSignTableStringDelimited(String, String, String) - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getSixthRootsOfUnity() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
-
- getSize() - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
Dimension of the square matrix defining the multiplication table.
- getSO16Roots() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
-
The 112 roots of SO(16), a maximal subgroup of E8 are generated.
- getSO16Roots() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionicLeechLattice
-
- getSO32Roots() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.SedenionLattice
-
- getSO8Roots() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
-
The 24 roots of SO(8) correspond with the 24 Hurwitz numbers of a given
quaternionic subalgebra.
- getSTS7() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
-
- getSTS7() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionicLeechLattice
-
- getSubalgebras(int) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getSubalgebras(int) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getSubalgebras(int) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getSubalgebras(Class, int) - Static method in class jhypercomplex.BinaryProductStructure
-
Determines all subalgebras of order n.
- getSubalgebrasAsString(Class<?>, int) - Static method in class jhypercomplex.BinaryProductStructure
-
- getSubalgebrasSignatures(Class<?>, int) - Method in class jhypercomplex.BinaryProductStructure
-
- getSubalgebrasUnsigned(int) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getSubalgebrasUnsigned(int) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getSubBasis() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getSubMatrix(int, int, int, int) - Method in class jhypercomplex.matrices.Matrix
-
- getSum(BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.BinaryAlgebra
-
- getSum(ComplexNumber, ComplexNumber) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getSum(Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getSum(Quaternion, Quaternion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getSum(Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getSum(Trigintaduonion, Trigintaduonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
-
- getTableAsHTML() - Method in class jhypercomplex.multiplication_tables.OctonionMultiplicationTable
-
- getTableView(String[][], String) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getTernaryInnerProduct(BinaryAlgebra, BinaryAlgebra, BinaryAlgebra) - Static method in class jhypercomplex.algebras.BinaryAlgebra
-
The scalar product (= real inner product) <.|.|.> of three algebras a1 and a2 and a3 is defined as
= 1/12((ab)^*c + a(bc^*) + 5 permutations)
- getTernaryInnerProduct(Octonion, Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getTernaryInnerProduct(Sedenion, Sedenion, Sedenion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getTetrads(int) - Static method in class jhypercomplex.MonteCarlo
-
For a given number of elements all possible tetrads (4-sets) are generated.
- getTrace(BinaryProductStructure) - Static method in class jhypercomplex.BinaryProductStructure
-
The trace of a hypernumber is defined as
tr(h) = h + conjugate(h) = 2*real part (h).
- getTraceRespDeterminant(BinaryProductStructure) - Method in class jhypercomplex.BinaryProductStructure
-
- getTranspose() - Method in class jhypercomplex.matrices.Matrix
-
- getTriads(int) - Static method in class jhypercomplex.MonteCarlo
-
For a given number of elements all possible triads are generated.
- getTriadSet(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getTripledMultiplicationTable(BinaryProductStructure, String[], int, int) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTableTripling
-
Given three sets of basis elements a, b, c of the original algebra, the (Cayley-Dickson) tripling formula used
(due to "Alternative twisted tensor products and Cayley algebras" by H.
- getTriples() - Method in class jhypercomplex.combinatorics.SteinerTripleSystem
-
- getTriVectorComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getTrivectorComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getTrivectorComponents() - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getTrivectorPartAsString(boolean) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getTrivectorPartAsString() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getType() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
-
- getType() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
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.
- getType() - Method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getType() - Method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getType() - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getType() - Method in class jhypercomplex.matrices.Vector
-
- getUnitElement(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.HypercomplexLattice
-
- getUnitElement(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
-
- getUnitElement(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionicLeechLattice
-
- getUnitElement(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.QuaternionLattice
-
- getUnsignedMultTableStringDelimited(String) - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getUnsignedTable(String[][]) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getUnsignedTable() - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
-
- getVectorComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getVectorComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
-
- getVectorComponents() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getVectorComponents() - Method in class jhypercomplex.algebras.clifford_algebras.PauliAlgebra
-
- getVectorComponents() - Method in class jhypercomplex.algebras.clifford_algebras.PlaneAlgebra
-
- getVectorComponents() - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
-
- getVectorDerivative(BinaryProductStructure, BinaryProductStructure) - Static method in class jhypercomplex.BinaryProductStructure
-
Derivative in direction of a vector 'a' for a hypernumber-valued function F:
(a*d)F with '*' being the inner product and 'd' a
- getVectorPartAsString(boolean) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getVectorPartAsString() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getVectorProduct(Octonion, Octonion) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
-
- getVectorProduct(BinaryProductStructure, BinaryProductStructure) - Static method in class jhypercomplex.BinaryProductStructure
-
The vector product "x" of two hypernumbers h1 and h2 is defined as
h1 x h2 = Im(Im(h1)*Im(h2)) = 0.5 [h1,h2]
It coincides with the conventional vector product in 3 dimensions for the
quaternions and the vector product in 7-dimensions for the
octonions.
- getVectorSignature() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
-
- getZeroDivisors(int) - Static method in class jhypercomplex.MonteCarlo
-
- grade_nr - Static variable in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
-