- SEDENION - Static variable in class jhypercomplex.algebras.cayley_dickson_algebras.CayleyDicksonAlgebra
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- Sedenion - Class in jhypercomplex.algebras.cayley_dickson_algebras
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Copyright © 2005-2015 by Markus Maute.
- Sedenion() - Constructor for class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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Constructors and the like *
- Sedenion(Sedenion) - Constructor for class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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- Sedenion(String) - Constructor for class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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- SedenionLattice - Class in jhypercomplex.algebras.cayley_dickson_algebras.discrete
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Copyright © 2005-2015 by Markus Maute.
- SedenionLattice() - Constructor for class jhypercomplex.algebras.cayley_dickson_algebras.discrete.SedenionLattice
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- SedenionLoop - Class in jhypercomplex.loops
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Copyright © 2005-2015 by Markus Maute.
- SedenionLoop() - Constructor for class jhypercomplex.loops.SedenionLoop
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- set128And112BasisHardCoded() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
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public void setDiadBasis () throws Exception
{
b[0] = new Octonion ("1,0,0,0,0,0,0,0");
b[1] = new Octonion ("0,1,0,0,0,0,0,0");
b[2] = new Octonion ("0,0,1,0,0,0,0,0");
b[3] = new Octonion ("0,0,0,1,0,0,0,0");
b[4] = new Octonion ("0,0,0,0,1,0,0,0");
b[5] = new Octonion ("0,0,0,0,0,1,0,0");
b[6] = new Octonion ("0,0,0,0,0,0,1,0");
b[7] = new Octonion ("0,0,0,0,0,0,0,1");
}
// TODO don't understand that any more !
- set128And112BasisHardCoded() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionicLeechLattice
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- setBasis(String) - Method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
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In case of the Clifford algebras we use a model and a view for the basis.
- setBasis(String[]) - Method in class jhypercomplex.BinaryProductStructure
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Sets the components of the hypercomplex number.
- setBiVectorComponents(String) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
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- setBiVectorComponents(String) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
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- setBiVectorComponents(String) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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Sets the 6 bivector components.
- setBiVectorComponents(String) - Method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
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- setBiVectorComponents(String) - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
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- setBivectorComponents(String) - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
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- setBiVectorComponentsExclusively(String) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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Sets the 6 bivector components.
- setBiVectorComponentsExclusively(String) - Method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
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- setCanoniclalBasis() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionicLeechLattice
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- setCanoniclalBasis() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.QuaternionLattice
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We take the 24 Hurwitz integers as basis:
+-e, +-i, +-j, +-k, +0.5(+-e +-i +-j +-k)
- setCliffordComponentsOfGrade(int, String) - Method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
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- setComponent(int, String) - Method in class jhypercomplex.BinaryProductStructure
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Sets the value of a single component.
- setComponentAsBasisNames() - Method in class jhypercomplex.BinaryProductStructure
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The designation of the basis elements is copied to the respective components.
- setComponentExclusively(int, String) - Method in class jhypercomplex.BinaryProductStructure
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Sets the value of a single component.
- setComponents(String) - Method in class jhypercomplex.BinaryProductStructure
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Sets the components of the hypercomplex number.
- setComponents(String[]) - Method in class jhypercomplex.BinaryProductStructure
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- setComponents(String[][]) - Method in class jhypercomplex.matrices.Matrix
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- setComponents(String[][]) - Method in class jhypercomplex.matrices.SquareMatrix
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- setCycle1(String, int) - Method in class jhypercomplex.multiplication_tables.OctonionMultiplicationTable
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Sets the first octonion cycle.
- setCycle2(String, int) - Method in class jhypercomplex.multiplication_tables.OctonionMultiplicationTable
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Sets the second octonion cycle.
- setCycle3(String, int) - Method in class jhypercomplex.multiplication_tables.OctonionMultiplicationTable
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Sets the third octonion cycle.
- setCycle4(String) - Method in class jhypercomplex.multiplication_tables.OctonionMultiplicationTable
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Sets the fourth octonion cycle.
- setCycles(String, int, String, int, String, int, String) - Method in class jhypercomplex.multiplication_tables.OctonionMultiplicationTable
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Creates the 7 quaternion cycles with the data specified.
- setDefaultTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
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- setDefaultTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
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- setDefaultTable() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
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- setDefaultTable() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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- setDefaultTable() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
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- setEvenGradeComponents(String) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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Sets the 8 even grade components.
- setEvenGradeComponents(String) - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
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- setEvenGradeComponentsExclusively(String) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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Sets the 8 even grade components.
- setFanoPlane(int) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
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Sets a multiplication table based on one of the 30 Fano planes according to
the definition in the octonion multiplication table class.
- setFanoPlane(int, int, int) - Method in class jhypercomplex.multiplication_tables.OctonionMultiplicationTable
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- setIndexedComponents(String, int, boolean) - Method in class jhypercomplex.BinaryProductStructure
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REQUIRES: Only non-numerical mode allowed.
- setIsNumerical(boolean) - Static method in class jhypercomplex.matrices.Matrix
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- setIsNumerical() - Static method in class jhypercomplex.matrices.Matrix
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- setLeftHanded() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
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- setMultiplicationTable(String[][]) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.ComplexNumber
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- setMultiplicationTable(String[][]) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.OctonarySubAlgebra
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- setMultiplicationTable(String[][]) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
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- setMultiplicationTable(MultiplicationTable) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
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- setMultiplicationTable(String[][]) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
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- setMultiplicationTable(MultiplicationTable) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
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- setMultiplicationTable(String[][]) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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- setMultiplicationTable(String[][]) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
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- setMultiplicationTable(String[][]) - Static method in class jhypercomplex.BinaryProductStructure
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- setMultiplicationTable(MultiplicationTable) - Static method in class jhypercomplex.BinaryProductStructure
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- setNaturalBasis() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.SedenionLattice
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This basis is generated by extracting the octads from the 15 octonion like subalgebras
of the sedenions.
- setNumberOfIterations(int) - Static method in class jhypercomplex.MonteCarlo
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Any Monte Carlo simulation is carried out in a loop.
- setNumerical() - Static method in class jhypercomplex.BinaryProductStructure
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- setNumerical(boolean) - Static method in class jhypercomplex.BinaryProductStructure
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- setNumericalMode(boolean) - Static method in class jhypercomplex.algebras.identities.AlgebraicProperties
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- setOctavianUnits_Canonical() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
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This construction of the unit integral octonions serves as a reference.
- setOctavianUnits_Canonical() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionicLeechLattice
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This construction of the unit integral octonions servers as a reference.
- setOctavianUnits_D8Representation() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
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Set 128 elements +/-l0+/-l1+/-l2+/-l3+/-l4+/-l5+/-l6+/-l7 with an odd number of "-"-signs
- setOctavianUnits_D8Representation() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionicLeechLattice
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Set 128 elements +/-l0+/-l1+/-l2+/-l3+/-l4+/-l5+/-l6+/-l7 with an odd number of "-"-signs
- setOctavianUnits_FanoPlaneRepresentation(int, int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
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Representation based on one of the 30 different Fano planes (= STS(7)).
112 basis vectors are constructed from the seven lines of the Fano plane considering all 16
sign combinations.
112 basis vectors are constructed from the dual vectors.
16 basis vectors are +/- one element base vectors.
- setOctavianUnits_FanoPlaneRepresentation(int, int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionicLeechLattice
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Representation based on one of the 30 different Fano planes (= STS(7)).
112 basis vectors are constructed from the seven lines of the Fano plane considering all 16
sign combinations.
112 basis vectors are constructed from the dual vectors.
16 basis vectors are +/- one element base vectors.
- setOctavianUnits_SubalgebrasRepresentation() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionE8Lattice
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The basis is constructed from a STS(7) defined by the 7 (quaternionic) subalgebras of order 4.
- setOctavianUnits_SubalgebrasRepresentation() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.OctonionicLeechLattice
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The basis is constructed from a STS(7) defined by the 7 (quaternionic) subalgebras of order 4.
- setPseudoScalarComponent(String) - Method in class jhypercomplex.BinaryProductStructure
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- setRandomComponents(int) - Method in class jhypercomplex.BinaryProductStructure
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- setRandomComponents(int, boolean) - Method in class jhypercomplex.BinaryProductStructure
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- setRandomComponents(int, boolean, boolean) - Method in class jhypercomplex.BinaryProductStructure
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Assigns random components to the hypernumber.
- setRandomComponentsAll() - Method in class jhypercomplex.BinaryProductStructure
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Sets all components randomly.
- setRandomSignTable(int) - Method in class jhypercomplex.multiplication_tables.SignTable
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TODO at the moment only implemented for a non-split algebra.
- setRepresentation(int) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.SedenionLattice
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- setRepresentation(String) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
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- setRepresentation(String) - Static method in class jhypercomplex.BinaryProductStructure
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Specifies the labeling of the basis elements.
- setRepresentation(int, int) - Method in class jhypercomplex.combinatorics.SevenPointsSTS
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For STS(7) there exist 30 inequivalent labelings.
- setRepresentation(String) - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
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The base elements are "relabeled", the multiplicative structure stays intact.
- setRepresentation(String[]) - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
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The base elements are "relabeled", the multiplicative structure stays intact.
- setRightHanded() - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
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- setScalarComponent(String) - Method in class jhypercomplex.BinaryProductStructure
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- setSedenionUnits_D16Representation() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.SedenionLattice
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- setSignature(String) - Method in class jhypercomplex.multiplication_tables.SignTable
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The diagonal elements of the sign table are set which represent the signature.
- setSignTable(SignTable) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
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- setSignTable(SignTable) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
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- setSignTable(SignTable) - Static method in class jhypercomplex.BinaryProductStructure
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The signs of the multiplication table (i.e. the structure constants) are set.
- setSignTable(SignTable) - Method in class jhypercomplex.multiplication_tables.MultiplicationTable
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- setTriple(int, String[]) - Method in class jhypercomplex.combinatorics.SevenPointsSTS
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Sets one of the 7 triples of a STS(7).
- setTriVectorComponents(String) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
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- setTriVectorComponents(String) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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Sets the 4 trivector components.
- setTriVectorComponents(String) - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
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- setTriVectorComponentsExclusively(String) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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Sets the 4 trivector components.
- setType(int) - Static method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
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Sets the n-th multiplication table, according to the definition in the
octonion multiplication table class.
- setType(int) - Method in class jhypercomplex.multiplication_tables.OctonionMultiplicationTable
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Sets the n-th multiplication table.
- setUnits_PG_3_2_Representation() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.discrete.SedenionLattice
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A fixed 2-(15,7,3) design is taken.
- setVectorComponents(String) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
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Components *
- setVectorComponents(String) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Quaternion
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- setVectorComponents(String) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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Sets the 4 vector components.
- setVectorComponents(String[]) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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- setVectorComponents(String) - Method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
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- setVectorComponents(String) - Method in class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
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- setVectorComponentsExclusively(String) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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Sets the 4 vector components.
- setVectorComponentsExclusively(String) - Method in class jhypercomplex.algebras.clifford_algebras.CliffordAlgebra
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- SevenPointsSTS - Class in jhypercomplex.combinatorics
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Copyright © 2005-2015 by Markus Maute.
- SevenPointsSTS() - Constructor for class jhypercomplex.combinatorics.SevenPointsSTS
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- SignTable - Class in jhypercomplex.multiplication_tables
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Copyright © 2005-2015 by Markus Maute.
- SignTable() - Constructor for class jhypercomplex.multiplication_tables.SignTable
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- SignTable(String[][]) - Constructor for class jhypercomplex.multiplication_tables.SignTable
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- simplifyNumericalFactors() - Method in class jhypercomplex.BinaryProductStructure
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For the components the factors of all terms separated by "+" or "-"
are moved to the front and are multiplied with one another.
- simplifyNumericalSummands() - Method in class jhypercomplex.BinaryProductStructure
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Numerical summands are simplified, i.e. added or subtracted.
- simplifyPlusMinus() - Method in class jhypercomplex.BinaryProductStructure
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Simplifies the components, replacing any adjacent "+"'s and "-"'s
according to:
"++" --> "+"
"+-" --> "-"
"-+" --> "-"
"--" --> "+"
- SpacetimeAlgebra - Class in jhypercomplex.algebras.clifford_algebras
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Copyright © 2005-2015 by Markus Maute.
- SpacetimeAlgebra() - Constructor for class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
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- SpacetimeAlgebra(SpacetimeAlgebra) - Constructor for class jhypercomplex.algebras.clifford_algebras.SpacetimeAlgebra
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- SQRT_2 - Static variable in interface jhypercomplex.CONST
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- square() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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- square() - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
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- square() - Method in class jhypercomplex.BinaryProductStructure
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- SquareMatrix - Class in jhypercomplex.matrices
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Copyright © 2005-2015 by Markus Maute.
- SquareMatrix(int) - Constructor for class jhypercomplex.matrices.SquareMatrix
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- SquareMatrix(String[][]) - Constructor for class jhypercomplex.matrices.SquareMatrix
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- SteinerTripleSystem - Class in jhypercomplex.combinatorics
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Copyright © 2005-2015 by Markus Maute.
- SteinerTripleSystem(int) - Constructor for class jhypercomplex.combinatorics.SteinerTripleSystem
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Constructor
- subtract(BinaryAlgebra) - Method in class jhypercomplex.algebras.BinaryAlgebra
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Subtracts an element from an algebra.
- subtract(BinaryAlgebra) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Octonion
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- subtract(Sedenion) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Sedenion
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- subtract(Trigintaduonion) - Method in class jhypercomplex.algebras.cayley_dickson_algebras.Trigintaduonion
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- swapColumns(String[][], int, int) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
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Swaps two colums of the multiplication table.
- swapRows(String[][], int, int) - Static method in class jhypercomplex.multiplication_tables.MultiplicationTable
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Swaps two rows of the multiplication table.
- SymbolicAlgebra - Class in jhypercomplex.algebras.identities
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Copyright © 2005-2015 by Markus Maute.
- SymbolicAlgebra() - Constructor for class jhypercomplex.algebras.identities.SymbolicAlgebra
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- SymbolicFunctions - Class in jhypercomplex.algebras.identities
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Copyright © 2005-2015 by Markus Maute.
- SymbolicFunctions() - Constructor for class jhypercomplex.algebras.identities.SymbolicFunctions
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