Uses of Class
jhypercomplex.BinaryProductStructure

Packages that use BinaryProductStructure

Package	Description
jhypercomplex
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.external_systems
jhypercomplex.loops
jhypercomplex.matrices
jhypercomplex.multiplication_tables

Uses of BinaryProductStructure in jhypercomplex

Methods in jhypercomplex that return BinaryProductStructure

Modifier and Type	Method and Description
BinaryProductStructure	BinaryProductStructure.conjugate()
static BinaryProductStructure	BinaryProductStructure.dual() // TODO Implementation not clear, as we have to distinguish between a left- and // a right dual ...
abstract BinaryProductStructure	BinaryProductStructure.getClone()
static BinaryProductStructure	BinaryProductStructure.getConjugate(BinaryProductStructure h)
static BinaryProductStructure	BinaryProductStructure.getDual(BinaryProductStructure h)
BinaryProductStructure	BinaryProductStructure.getHermitianConjugate() 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.
static BinaryProductStructure	BinaryProductStructure.getImaginaryPart(BinaryProductStructure h)
static BinaryProductStructure	BinaryProductStructure.getInstance(java.lang.Class class_)
static BinaryProductStructure	BinaryProductStructure.getNegated(BinaryProductStructure h)
abstract BinaryProductStructure	BinaryProductStructure.getNewInstance()
static BinaryProductStructure	BinaryProductStructure.getNormSquared(BinaryProductStructure h)
static BinaryProductStructure	BinaryProductStructure.getNumericalInverse(BinaryProductStructure h) The inverse of a hypernumber h is calculated.
static BinaryProductStructure	BinaryProductStructure.getProduct(BinaryProductStructure h1, BinaryProductStructure h2) Multiplies two hypernummers according to the order of the arguments of the method.
static BinaryProductStructure	BinaryProductStructure.getProductWithScalar(BinaryProductStructure h, java.lang.String scalar)
static BinaryProductStructure[]	BinaryProductStructure.getRandomClosedPair(BinaryProductStructure[] h) From the given set of hypernumbers a random pair is chosen (non trivial, i.a. the two elements are supposed to be different).
static BinaryProductStructure[]	BinaryProductStructure.getRandomNonClosedPair(BinaryProductStructure[] h) From the given set of hypernumbers a random pair is chosen (non trivial, i.a. the two elements are supposed to be different).
static BinaryProductStructure	BinaryProductStructure.getTrace(BinaryProductStructure h) The trace of a hypernumber is defined as tr(h) = h + conjugate(h) = 2*real part (h).
static BinaryProductStructure	BinaryProductStructure.getVectorDerivative(BinaryProductStructure direction, BinaryProductStructure function) Derivative in direction of a vector 'a' for a hypernumber-valued function F: (a*d)F with '*' being the inner product and 'd' a
static BinaryProductStructure	BinaryProductStructure.getVectorProduct(BinaryProductStructure h1, BinaryProductStructure h2) 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.
BinaryProductStructure	BinaryProductStructure.multiplyWithScalar(java.lang.String scalar) Multiplication with a scalar.
BinaryProductStructure	BinaryProductStructure.negate() Negates the hypernumber: h --> -h.
BinaryProductStructure	BinaryProductStructure.rightMultiplyWith(BinaryProductStructure h2)
BinaryProductStructure	BinaryProductStructure.rightMultiplyWith(BinaryProductStructure h, boolean collect_terms) Multiply with another hypercomplex number.
BinaryProductStructure	BinaryProductStructure.square()

Methods in jhypercomplex that return types with arguments of type BinaryProductStructure

Modifier and Type	Method and Description
static java.util.HashSet<BinaryProductStructure>	MonteCarlo.getIdemotents(java.lang.Class class_, int nonzero_elements) Idempotents (modulo '-1') are determined.

Methods in jhypercomplex with parameters of type BinaryProductStructure

Modifier and Type	Method and Description
static java.util.HashSet<java.lang.String>	BinaryProductStructure.getClosedPairsAsString(BinaryProductStructure[] h)
static BinaryProductStructure	BinaryProductStructure.getConjugate(BinaryProductStructure h)
static BinaryProductStructure	BinaryProductStructure.getDual(BinaryProductStructure h)
static BinaryProductStructure	BinaryProductStructure.getImaginaryPart(BinaryProductStructure h)
int	BinaryProductStructure.getMultiplicativeOrder(BinaryProductStructure h, int max_steps)
int	BinaryProductStructure.getMultiplicativeOrder(BinaryProductStructure h, int mult_steps, double zero_precision) Multiplicative order n, defined by: {min n: h1*(h2^n) = l*h1} with l a scalar factor.
static BinaryProductStructure	BinaryProductStructure.getNegated(BinaryProductStructure h)
static BinaryProductStructure	BinaryProductStructure.getNormSquared(BinaryProductStructure h)
static int	BinaryProductStructure.getNumberOfClosedElements(BinaryProductStructure[] h) 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.
static int	BinaryProductStructure.getNumberOfClosedPairs(BinaryProductStructure[] h) For every posssible pair of the given set of hypernumbers it is checked if the prodeuct is again contained in the set.
static BinaryProductStructure	BinaryProductStructure.getNumericalInverse(BinaryProductStructure h) The inverse of a hypernumber h is calculated.
static BinaryProductStructure	BinaryProductStructure.getProduct(BinaryProductStructure h1, BinaryProductStructure h2) Multiplies two hypernummers according to the order of the arguments of the method.
static BinaryProductStructure	BinaryProductStructure.getProductWithScalar(BinaryProductStructure h, java.lang.String scalar)
static BinaryProductStructure[]	BinaryProductStructure.getRandomClosedPair(BinaryProductStructure[] h) From the given set of hypernumbers a random pair is chosen (non trivial, i.a. the two elements are supposed to be different).
static BinaryProductStructure[]	BinaryProductStructure.getRandomNonClosedPair(BinaryProductStructure[] h) From the given set of hypernumbers a random pair is chosen (non trivial, i.a. the two elements are supposed to be different).
static BinaryProductStructure	BinaryProductStructure.getTrace(BinaryProductStructure h) The trace of a hypernumber is defined as tr(h) = h + conjugate(h) = 2*real part (h).
double	BinaryProductStructure.getTraceRespDeterminant(BinaryProductStructure h)
static BinaryProductStructure	BinaryProductStructure.getVectorDerivative(BinaryProductStructure direction, BinaryProductStructure function) Derivative in direction of a vector 'a' for a hypernumber-valued function F: (a*d)F with '*' being the inner product and 'd' a
static BinaryProductStructure	BinaryProductStructure.getVectorProduct(BinaryProductStructure h1, BinaryProductStructure h2) 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.
boolean	BinaryProductStructure.isAutomorphism(BinaryProductStructure x, BinaryProductStructure y) Checks if given hypernumber is related to the hypernumbers x, y via the automorphism map: (a x a^{-1}) (a y a^{-1}) = l (a xy a^{-1}) with l a constant, i.e. we do not require an appropriate normalisation of the hypernumbers.
static boolean	BinaryProductStructure.isLinearlyDependent(BinaryProductStructure h1, BinaryProductStructure h2, boolean pos_and_neg) Tests linear dependency, i.e. if h1 = c*h2 is satisfied, with "c" a (real) non-zero constant.
static boolean	BinaryProductStructure.isNumericalityDetected(BinaryProductStructure h) Detects if all the components are numerical.
static boolean	BinaryProductStructure.isProductClosed(BinaryProductStructure[] h) REQUIRES: Mode must be set to numerical.
BinaryProductStructure	BinaryProductStructure.rightMultiplyWith(BinaryProductStructure h2)
BinaryProductStructure	BinaryProductStructure.rightMultiplyWith(BinaryProductStructure h, boolean collect_terms) Multiply with another hypercomplex number.

Uses of BinaryProductStructure in jhypercomplex.algebras

Subclasses of BinaryProductStructure in jhypercomplex.algebras

Modifier and Type	Class and Description
class	BinaryAlgebra Copyright © 2005-2015 by Markus Maute.
class	TensoredAlgebra Tensor product of two algebras.

Methods in jhypercomplex.algebras that return types with arguments of type BinaryProductStructure

Modifier and Type	Method and Description
static java.util.HashSet<BinaryProductStructure>	BinaryAlgebra.getIntersection(BinaryProductStructure[] h1, BinaryProductStructure[] h2) Two sets of hypernumbers are compared.

Methods in jhypercomplex.algebras with parameters of type BinaryProductStructure

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 java.util.HashSet<BinaryProductStructure>	BinaryAlgebra.getIntersection(BinaryProductStructure[] h1, BinaryProductStructure[] h2) Two sets of hypernumbers are compared.
static java.util.HashSet<BinaryProductStructure>	BinaryAlgebra.getIntersection(BinaryProductStructure[] h1, BinaryProductStructure[] h2) Two sets of hypernumbers are compared.
boolean	BinaryAlgebra.isEqual(BinaryProductStructure h) Compares the components of the hypernumber with those of another one.

Uses of BinaryProductStructure in jhypercomplex.algebras.cayley_dickson_algebras

Subclasses of BinaryProductStructure 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 BinaryProductStructure

Modifier and Type	Method and Description
BinaryProductStructure	Trigintaduonion.getClone(BinaryProductStructure s)
BinaryProductStructure	Trigintaduonion.getNewInstance()
BinaryProductStructure	Sedenion.getNewInstance()
BinaryProductStructure	Quaternion.getNewInstance()
BinaryProductStructure	ComplexNumber.getNewInstance()

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

Modifier and Type	Method and Description
BinaryProductStructure	Trigintaduonion.getClone(BinaryProductStructure s)
Trigintaduonion	Trigintaduonion.rightMultiplyWith(BinaryProductStructure t)
Sedenion	Sedenion.rightMultiplyWith(BinaryProductStructure s)

Uses of BinaryProductStructure in jhypercomplex.algebras.cayley_dickson_algebras.complex_algebras

Subclasses of BinaryProductStructure 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 BinaryProductStructure

Modifier and Type	Method and Description
BinaryProductStructure	ComplexSedenion.getNewInstance()
BinaryProductStructure	ComplexQuaternion.getNewInstance()
BinaryProductStructure	ComplexOctonion.getNewInstance()

Uses of BinaryProductStructure in jhypercomplex.algebras.cayley_dickson_algebras.discrete

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

Modifier and Type	Method and Description
abstract BinaryProductStructure[]	HypercomplexLattice.getAllUnitElements()
BinaryProductStructure[]	HypercomplexLattice.getBasis()
BinaryProductStructure	HypercomplexLattice.getUnitElement(int nr)

Uses of BinaryProductStructure in jhypercomplex.algebras.clifford_algebras

Subclasses of BinaryProductStructure 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 with parameters of type BinaryProductStructure

Modifier and Type	Method and Description
SpacetimeAlgebra	SpacetimeAlgebra.add(BinaryProductStructure h)
PauliAlgebra	PauliAlgebra.add(BinaryProductStructure h)
DeSitterAlgebra	DeSitterAlgebra.add(BinaryProductStructure h)
DeSitterAlgebra	DeSitterAlgebra.getClone(BinaryProductStructure dsa)

Uses of BinaryProductStructure in jhypercomplex.external_systems

Methods in jhypercomplex.external_systems that return BinaryProductStructure

Modifier and Type	Method and Description
static BinaryProductStructure	Mathematica.differentiate(BinaryProductStructure nabla, BinaryProductStructure function)
static BinaryProductStructure	Mathematica.processComponentwise(BinaryProductStructure hypernumber) The expression of each component of a hypernumber is sent to Mathematica and the result is written back to the respective component.

Methods in jhypercomplex.external_systems with parameters of type BinaryProductStructure

Modifier and Type	Method and Description
static BinaryProductStructure	Mathematica.differentiate(BinaryProductStructure nabla, BinaryProductStructure function)
static BinaryProductStructure	Mathematica.processComponentwise(BinaryProductStructure hypernumber) The expression of each component of a hypernumber is sent to Mathematica and the result is written back to the respective component.

Uses of BinaryProductStructure in jhypercomplex.loops

Subclasses of BinaryProductStructure in jhypercomplex.loops

Modifier and Type	Class and Description
class	OctonionLoop Copyright © 2005-2015 by Markus Maute.
class	SedenionLoop Copyright © 2005-2015 by Markus Maute.

Uses of BinaryProductStructure in jhypercomplex.matrices

Subclasses of BinaryProductStructure in jhypercomplex.matrices

Modifier and Type	Class and Description
class	Vector Copyright © 2005-2015 by Markus Maute.

Methods in jhypercomplex.matrices that return BinaryProductStructure

Modifier and Type	Method and Description
BinaryProductStructure	Vector.getGrade(int grade)
BinaryProductStructure	Vector.getNewInstance()

Uses of BinaryProductStructure in jhypercomplex.multiplication_tables

Methods in jhypercomplex.multiplication_tables with parameters of type BinaryProductStructure

Modifier and Type	Method and Description
static java.lang.String[][]	MultiplicationTableTripling.getTripledMultiplicationTable(BinaryProductStructure orig_algebra, java.lang.String[] new_base_elements, int sign1, int sign2) 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.