Uses of Class
jhypercomplex.algebras.BinaryAlgebra

Packages that use BinaryAlgebra

Package	Description
jhypercomplex.algebras
jhypercomplex.algebras.cayley_dickson_algebras
jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras
jhypercomplex.algebras.cayley_dickson_algebras.discrete
jhypercomplex.algebras.clifford_algebras
jhypercomplex.algebras.identities
jhypercomplex.multiplication_tables

Uses of BinaryAlgebra in jhypercomplex.algebras

Subclasses of BinaryAlgebra in jhypercomplex.algebras

Modifier and Type	Class and Description
class	TensoredAlgebra Tensor product of two algebras.

Methods in jhypercomplex.algebras that return BinaryAlgebra

Modifier and Type	Method and Description
BinaryAlgebra	BinaryAlgebra.add(BinaryProductStructure a)
BinaryAlgebra	BinaryAlgebra.add(BinaryProductStructure a, boolean collect_terms) Add an element from the algebra.
static BinaryAlgebra	BinaryAlgebra.applyLeibnizRule(BinaryAlgebra h) TODO: meanwhile see 'getLeftCovariantDerivative ()'
BinaryAlgebra	BinaryAlgebra.calculateBCHWith(BinaryAlgebra a, int from_order, int to_order) The Baker Campbell Hausdorff formula (BCH) is calculated for a specified range of orders.
BinaryAlgebra	BinaryAlgebra.getAntiCommutatorWith(BinaryAlgebra a) 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
abstract BinaryAlgebra	BinaryAlgebra.getClone()
BinaryAlgebra	BinaryAlgebra.getCommutatorWith(BinaryAlgebra a)
BinaryAlgebra	BinaryAlgebra.getCommutatorWith(BinaryAlgebra a, boolean collect_terms) Calculates the commutator of an element a1 of the algebra with another one a2.
static BinaryAlgebra	BinaryAlgebra.getDifference(BinaryAlgebra a1, BinaryAlgebra a2)
abstract BinaryAlgebra	BinaryAlgebra.getGrade(int grade)
static BinaryAlgebra	BinaryAlgebra.getGradedInnerProduct(BinaryAlgebra a1, BinaryAlgebra a2, boolean with_grade_0)
BinaryAlgebra	BinaryAlgebra.getLeftCovariantDerivative(BinaryAlgebra covariant_deriv_op, BinaryAlgebra h) The covariant derivative of the hypernumber is calculated.
static BinaryAlgebra	BinaryAlgebra.getOuterProduct(BinaryAlgebra a1, BinaryAlgebra a2)
static BinaryAlgebra	BinaryAlgebra.getProduct(BinaryAlgebra a, BinaryAlgebra b)
static BinaryAlgebra	BinaryAlgebra.getScalarProduct(BinaryAlgebra a1, BinaryAlgebra a2) The scalar product (= real inner product) <.|.> of two algebra a1 and a2 is defined as = 1/2(a1a2*+a2a1*)
static BinaryAlgebra	BinaryAlgebra.getSum(BinaryAlgebra a1, BinaryAlgebra a2)
static BinaryAlgebra	BinaryAlgebra.getTernaryInnerProduct(BinaryAlgebra a1, BinaryAlgebra a2, BinaryAlgebra a3) 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)
BinaryAlgebra	BinaryAlgebra.rightMultiplyWith(BinaryAlgebra a)
BinaryAlgebra	BinaryAlgebra.subtract(BinaryAlgebra a) Subtracts an element from an algebra.

Methods in jhypercomplex.algebras with parameters of type BinaryAlgebra

Modifier and Type	Method and Description
static BinaryAlgebra	BinaryAlgebra.applyLeibnizRule(BinaryAlgebra h) TODO: meanwhile see 'getLeftCovariantDerivative ()'
BinaryAlgebra	BinaryAlgebra.calculateBCHWith(BinaryAlgebra a, int from_order, int to_order) The Baker Campbell Hausdorff formula (BCH) is calculated for a specified range of orders.
BinaryAlgebra	BinaryAlgebra.getAntiCommutatorWith(BinaryAlgebra a) 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
BinaryAlgebra	BinaryAlgebra.getCommutatorWith(BinaryAlgebra a)
BinaryAlgebra	BinaryAlgebra.getCommutatorWith(BinaryAlgebra a, boolean collect_terms) Calculates the commutator of an element a1 of the algebra with another one a2.
static BinaryAlgebra	BinaryAlgebra.getDifference(BinaryAlgebra a1, BinaryAlgebra a2)
static BinaryAlgebra	BinaryAlgebra.getGradedInnerProduct(BinaryAlgebra a1, BinaryAlgebra a2, boolean with_grade_0)
BinaryAlgebra	BinaryAlgebra.getLeftCovariantDerivative(BinaryAlgebra covariant_deriv_op, BinaryAlgebra h) The covariant derivative of the hypernumber is calculated.
static BinaryAlgebra	BinaryAlgebra.getOuterProduct(BinaryAlgebra a1, BinaryAlgebra a2)
static BinaryAlgebra	BinaryAlgebra.getProduct(BinaryAlgebra a, BinaryAlgebra b)
static BinaryAlgebra	BinaryAlgebra.getScalarProduct(BinaryAlgebra a1, BinaryAlgebra a2) The scalar product (= real inner product) <.|.> of two algebra a1 and a2 is defined as = 1/2(a1a2*+a2a1*)
static BinaryAlgebra	BinaryAlgebra.getSum(BinaryAlgebra a1, BinaryAlgebra a2)
static BinaryAlgebra	BinaryAlgebra.getTernaryInnerProduct(BinaryAlgebra a1, BinaryAlgebra a2, BinaryAlgebra a3) 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)
static boolean	BinaryAlgebra.isCommutative(BinaryAlgebra a1, BinaryAlgebra a2)
static boolean	BinaryAlgebra.isOrthogonal(BinaryAlgebra a1, BinaryAlgebra a2)
boolean	BinaryAlgebra.isOrthogonalTo(BinaryAlgebra a)
BinaryAlgebra	BinaryAlgebra.rightMultiplyWith(BinaryAlgebra a)
BinaryAlgebra	BinaryAlgebra.subtract(BinaryAlgebra a) Subtracts an element from an algebra.

Constructors in jhypercomplex.algebras with parameters of type BinaryAlgebra

Constructor and Description
TensoredAlgebra(BinaryAlgebra algebra1, BinaryAlgebra algebra2) Constructor for the two algebras to be tensored, according to (algebra1) x (algebra2).

Uses of BinaryAlgebra in jhypercomplex.algebras.cayley_dickson_algebras

Subclasses of BinaryAlgebra in jhypercomplex.algebras.cayley_dickson_algebras

Modifier and Type	Class and Description
class	CayleyDicksonAlgebra Copyright © 2005-2015 by Markus Maute.
class	ComplexNumber Copyright © 2005-2015 by Markus Maute.
class	OctonarySubAlgebra Copyright © 2005-2015 by Markus Maute.
class	Octonion Copyright © 2005-2015 by Markus Maute.
class	Quaternion Copyright © 2005-2015 by Markus Maute.
class	Sedenion Copyright © 2005-2015 by Markus Maute.
class	Trigintaduonion Copyright © 2005-2015 by Markus Maute.

Methods in jhypercomplex.algebras.cayley_dickson_algebras that return BinaryAlgebra

Modifier and Type	Method and Description
BinaryAlgebra	OctonarySubAlgebra.getClone()
BinaryAlgebra	Trigintaduonion.getGrade(int grade)
BinaryAlgebra	OctonarySubAlgebra.getGrade(int grade)
BinaryAlgebra	OctonarySubAlgebra.getNewInstance()

Methods in jhypercomplex.algebras.cayley_dickson_algebras with parameters of type BinaryAlgebra

Modifier and Type	Method and Description
Octonion	Octonion.add(BinaryAlgebra o)
static Octonion	Octonion.getAntiAssociator(BinaryAlgebra h1, BinaryAlgebra h2, BinaryAlgebra h3)
Octonion	Octonion.getAntiCommutatorWith(BinaryAlgebra h)
Octonion	Octonion.getCommutatorWith(BinaryAlgebra o)
static Octonion	Octonion.getNumericalInverse(BinaryAlgebra h)
static Octonion	Octonion.getProductWithScalar(BinaryAlgebra h, java.lang.String scalar)
Octonion	Octonion.subtract(BinaryAlgebra o)

Constructors in jhypercomplex.algebras.cayley_dickson_algebras with parameters of type BinaryAlgebra

Constructor and Description
OctonarySubAlgebra(BinaryAlgebra a, MultiplicationTable mult_tab)

Uses of BinaryAlgebra in jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras

Subclasses of BinaryAlgebra in jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras

Modifier and Type	Class and Description
class	ComplexOctonion Copyright © 2005-2015 by Markus Maute.
class	ComplexQuaternion Copyright © 2005-2015 by Markus Maute.
class	ComplexSedenion Copyright © 2005-2015 by Markus Maute.

Methods in jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras that return BinaryAlgebra

Modifier and Type	Method and Description
BinaryAlgebra	ComplexSedenion.getGrade(int grade)
BinaryAlgebra	ComplexQuaternion.getGrade(int grade)
BinaryAlgebra	ComplexOctonion.getGrade(int grade)

Uses of BinaryAlgebra in jhypercomplex.algebras.cayley_dickson_algebras.discrete

Methods in jhypercomplex.algebras.cayley_dickson_algebras.discrete that return BinaryAlgebra

Modifier and Type	Method and Description
BinaryAlgebra[]	HypercomplexLattice.getElements(int from, int to)

Methods in jhypercomplex.algebras.cayley_dickson_algebras.discrete with parameters of type BinaryAlgebra

Modifier and Type	Method and Description
int	HypercomplexLattice.getNumberOfUnitElement(BinaryAlgebra h)
boolean	HypercomplexLattice.isIntegralUnitElement(BinaryAlgebra h)
boolean	HypercomplexLattice.isUnitElement(BinaryAlgebra h, boolean zero_allowed)

Uses of BinaryAlgebra in jhypercomplex.algebras.clifford_algebras

Subclasses of BinaryAlgebra in jhypercomplex.algebras.clifford_algebras

Modifier and Type	Class and Description
class	CliffordAlgebra Copyright © 2005-2015 by Markus Maute.
class	DeSitterAlgebra Copyright © 2005-2015 by Markus Maute.
class	PauliAlgebra Copyright © 2005-2015 by Markus Maute.
class	PlaneAlgebra Copyright © 2005-2015 by Markus Maute.
class	SpacetimeAlgebra Copyright © 2005-2015 by Markus Maute.

Methods in jhypercomplex.algebras.clifford_algebras that return BinaryAlgebra

Modifier and Type	Method and Description
BinaryAlgebra	PlaneAlgebra.getClone()
BinaryAlgebra	PauliAlgebra.getClone()
BinaryAlgebra	DeSitterAlgebra.getClone()
BinaryAlgebra	SpacetimeAlgebra.getClone(BinaryAlgebra a)
BinaryAlgebra	PlaneAlgebra.getClone(BinaryAlgebra a)
BinaryAlgebra	PauliAlgebra.getClone(BinaryAlgebra pa)
BinaryAlgebra	DeSitterAlgebra.getClone(BinaryAlgebra a)
abstract BinaryAlgebra	CliffordAlgebra.getClone(BinaryAlgebra a)
abstract BinaryAlgebra	CliffordAlgebra.getNewInstance()

Methods in jhypercomplex.algebras.clifford_algebras with parameters of type BinaryAlgebra

Modifier and Type	Method and Description
BinaryAlgebra	SpacetimeAlgebra.getClone(BinaryAlgebra a)
BinaryAlgebra	PlaneAlgebra.getClone(BinaryAlgebra a)
BinaryAlgebra	PauliAlgebra.getClone(BinaryAlgebra pa)
BinaryAlgebra	DeSitterAlgebra.getClone(BinaryAlgebra a)
abstract BinaryAlgebra	CliffordAlgebra.getClone(BinaryAlgebra a)

Uses of BinaryAlgebra in jhypercomplex.algebras.identities

Methods in jhypercomplex.algebras.identities that return BinaryAlgebra

Modifier and Type	Method and Description
static BinaryAlgebra	AlgebraicFunctions.getAntiAssociator(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c)
static BinaryAlgebra	AlgebraicFunctions.getAntiCommutator(BinaryAlgebra a, BinaryAlgebra b)
static BinaryAlgebra	AlgebraicFunctions.getAssociationType(int nr, BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d) There are 5 ways to put the brackets in a product of 4 Algebras.
static BinaryAlgebra	AlgebraicFunctions.getAssociationType(int nr, BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d, BinaryAlgebra e) There are 14 ways to put the brackets in a product of 5 Algebras.
static BinaryAlgebra	AlgebraicFunctions.getAssociationType(int nr, BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d, BinaryAlgebra e, boolean commutator) "Switch"-method, that allows for an invocation of the association type method or alternatively the commutator association type method.
static BinaryAlgebra	AlgebraicFunctions.getAssociationType(int nr, BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d, boolean commutator) "Switch"-method, that allows for an invocation of the association type method or alternatively the commutator association type method.
static BinaryAlgebra	AlgebraicFunctions.getAssociationTypeCommutator(int nr, BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d) 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]]
static BinaryAlgebra	AlgebraicFunctions.getAssociationTypeCommutator(int nr, BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d, BinaryAlgebra e) 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]
static BinaryAlgebra	AlgebraicFunctions.getAssociator(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c)
static BinaryAlgebra	AlgebraicFunctions.getBMQuaternator1(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d) First quaternator as defined by Murray R.
static BinaryAlgebra	AlgebraicFunctions.getBMQuaternator2(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d) Second quaternator as defined by Murray R.
static BinaryAlgebra	AlgebraicFunctions.getBMQuaternatorIdentity1(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getBMQuaternatorIdentity2(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getBMQuaternatorIdentity3(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getBMQuaternatorIdentity4(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getCommuAssociator(BinaryAlgebra h1, BinaryAlgebra h2, BinaryAlgebra h3, BinaryAlgebra h4)
static BinaryAlgebra	AlgebraicFunctions.getCommutator(BinaryAlgebra a, BinaryAlgebra b)
static BinaryAlgebra	AlgebraicFunctions.getCommutator(BinaryAlgebra a, BinaryAlgebra b, boolean collect_terms)
static BinaryAlgebra	AlgebraicFunctions.getCommutatorBMQuaternator1(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d) First quaternator as defined by Murray R.
static BinaryAlgebra	AlgebraicFunctions.getCommutatorJacobian(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c)
static BinaryAlgebra	AlgebraicFunctions.getCommutatorSaglian(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getFirstHetztelPeresian(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d, BinaryAlgebra e)
static BinaryAlgebra	AlgebraicFunctions.getJacobian(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c)
static BinaryAlgebra	AlgebraicFunctions.getJordanAssociator(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c)
static BinaryAlgebra	AlgebraicFunctions.getKleinfeldFunction(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getQuaternator(BinaryAlgebra h1, BinaryAlgebra h2, BinaryAlgebra h3, BinaryAlgebra h4)
static BinaryAlgebra	AlgebraicFunctions.getQuaternator1(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getQuaternator2(BinaryAlgebra h1, BinaryAlgebra h2, BinaryAlgebra h3, BinaryAlgebra h4)
static BinaryAlgebra	AlgebraicFunctions.getSabininator(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getSabininQuaternator(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getSecondHetztelPeresian(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)

Methods in jhypercomplex.algebras.identities with parameters of type BinaryAlgebra

Modifier and Type	Method and Description
static BinaryAlgebra	AlgebraicFunctions.getAntiAssociator(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c)
static BinaryAlgebra	AlgebraicFunctions.getAntiCommutator(BinaryAlgebra a, BinaryAlgebra b)
static BinaryAlgebra	AlgebraicFunctions.getAssociationType(int nr, BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d) There are 5 ways to put the brackets in a product of 4 Algebras.
static BinaryAlgebra	AlgebraicFunctions.getAssociationType(int nr, BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d, BinaryAlgebra e) There are 14 ways to put the brackets in a product of 5 Algebras.
static BinaryAlgebra	AlgebraicFunctions.getAssociationType(int nr, BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d, BinaryAlgebra e, boolean commutator) "Switch"-method, that allows for an invocation of the association type method or alternatively the commutator association type method.
static BinaryAlgebra	AlgebraicFunctions.getAssociationType(int nr, BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d, boolean commutator) "Switch"-method, that allows for an invocation of the association type method or alternatively the commutator association type method.
static BinaryAlgebra	AlgebraicFunctions.getAssociationTypeCommutator(int nr, BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d) 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]]
static BinaryAlgebra	AlgebraicFunctions.getAssociationTypeCommutator(int nr, BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d, BinaryAlgebra e) 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]
static BinaryAlgebra	AlgebraicFunctions.getAssociator(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c)
static BinaryAlgebra	AlgebraicFunctions.getBMQuaternator1(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d) First quaternator as defined by Murray R.
static BinaryAlgebra	AlgebraicFunctions.getBMQuaternator2(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d) Second quaternator as defined by Murray R.
static BinaryAlgebra	AlgebraicFunctions.getBMQuaternatorIdentity1(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getBMQuaternatorIdentity2(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getBMQuaternatorIdentity3(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getBMQuaternatorIdentity4(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getCommuAssociator(BinaryAlgebra h1, BinaryAlgebra h2, BinaryAlgebra h3, BinaryAlgebra h4)
static BinaryAlgebra	AlgebraicFunctions.getCommutator(BinaryAlgebra a, BinaryAlgebra b)
static BinaryAlgebra	AlgebraicFunctions.getCommutator(BinaryAlgebra a, BinaryAlgebra b, boolean collect_terms)
static BinaryAlgebra	AlgebraicFunctions.getCommutatorBMQuaternator1(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d) First quaternator as defined by Murray R.
static BinaryAlgebra	AlgebraicFunctions.getCommutatorJacobian(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c)
static BinaryAlgebra	AlgebraicFunctions.getCommutatorSaglian(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getFirstHetztelPeresian(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d, BinaryAlgebra e)
static BinaryAlgebra	AlgebraicFunctions.getJacobian(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c)
static BinaryAlgebra	AlgebraicFunctions.getJordanAssociator(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c)
static BinaryAlgebra	AlgebraicFunctions.getKleinfeldFunction(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getQuaternator(BinaryAlgebra h1, BinaryAlgebra h2, BinaryAlgebra h3, BinaryAlgebra h4)
static BinaryAlgebra	AlgebraicFunctions.getQuaternator1(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getQuaternator2(BinaryAlgebra h1, BinaryAlgebra h2, BinaryAlgebra h3, BinaryAlgebra h4)
static BinaryAlgebra	AlgebraicFunctions.getSabininator(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getSabininQuaternator(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static BinaryAlgebra	AlgebraicFunctions.getSecondHetztelPeresian(BinaryAlgebra a, BinaryAlgebra b, BinaryAlgebra c, BinaryAlgebra d)
static boolean	AlgebraicProperties.isAlternative(BinaryAlgebra h1, BinaryAlgebra h2) Alternativity means right- and left-alternative.
static boolean	AlgebraicProperties.isInLeftNucleus(BinaryAlgebra h)
static boolean	AlgebraicProperties.isInMiddleNucleus(BinaryAlgebra h)
static boolean	AlgebraicProperties.isInNucleus(BinaryAlgebra h)
static boolean	AlgebraicProperties.isInRightNucleus(BinaryAlgebra h)
static boolean	AlgebraicProperties.isLeftAlternative(BinaryAlgebra h1, BinaryAlgebra h2) Left-alternativity is defined by means of the associator identity [h1,h1,h2] = 0.
static boolean	AlgebraicProperties.isRightAlternative(BinaryAlgebra h1, BinaryAlgebra h2) Right-alternativity is defined by means of the associator identity [h1,h2,h2] = 0.

Uses of BinaryAlgebra in jhypercomplex.multiplication_tables

Methods in jhypercomplex.multiplication_tables with parameters of type BinaryAlgebra

Modifier and Type	Method and Description
static java.lang.String[][]	MultiplicationTableDoubling.getDoubledMultiplicationTable(int doubling_type, BinaryAlgebra orig_algebra, java.lang.String[] new_base_elements, int sign)