Uses of Interface
org.episteme.core.mathematics.analysis.Relation

Packages that use Relation

Package	Description
org.episteme.core.mathematics.analysis
org.episteme.core.mathematics.analysis.chaos
org.episteme.core.mathematics.analysis.series
org.episteme.core.mathematics.analysis.transform
org.episteme.core.mathematics.geometry
org.episteme.core.mathematics.geometry.curves
org.episteme.core.mathematics.geometry.surfaces
org.episteme.core.mathematics.statistics
org.episteme.core.mathematics.statistics.distributions

Uses of Relation in org.episteme.core.mathematics.analysis

Subinterfaces of Relation in org.episteme.core.mathematics.analysis

Modifier and Type	Interface	Description
interface	Bijection<D,C>	A bijective function (one-to-one and onto mapping).
interface	ContinuousFunction<D,C>	Represents a continuous function.
interface	DifferentiableFunction<D,C>	Represents a differentiable function.
interface	Function<D,C>	Represents a mathematical function from a domain D to a codomain C.
interface	IntegrableFunction<D,C>	Represents an integrable function.
interface	MultivariateFunction	Multivariate function (multiple variables: ℝⁿ → ℝ).
interface	MultivariateRealFunction	Represents a real-valued function of multiple real variables (R^n -> R).
interface	RealFunction	Represents a real-valued function of a real variable (R -> R).
interface	ScalarField<V>	Represents a scalar field: f: ℝⁿ → ℝ
interface	ScalarFunction<D>	Scalar-valued function (returns a single real number).
interface	UnivariateFunction	Univariate function (single variable: ℝ → ℝ).
interface	VectorField<V>	Represents a vector field: F: ℝⁿ → ℝⁿ
interface	VectorFunction<F extends Field<F>>	Represents a function from a vector space to another (F^n -> F^m).

Classes in org.episteme.core.mathematics.analysis that implement Relation

Modifier and Type	Class	Description
class	PolynomialFunction<R>	Represents a polynomial function P(x) over a Ring R.

Uses of Relation in org.episteme.core.mathematics.analysis.chaos

Subinterfaces of Relation in org.episteme.core.mathematics.analysis.chaos

Modifier and Type	Interface	Description
interface	DiscreteMap<T>	A discrete dynamical system defined by an iterative map.

Classes in org.episteme.core.mathematics.analysis.chaos that implement Relation

Modifier and Type	Class	Description
class	ArnoldCatMap	Arnold's Cat Map: x_{n+1} = (2x_n + y_n) mod 1 y_{n+1} = (x_n + y_n) mod 1
class	GingerbreadManMap	The Gingerbread Man Map - a chaotic discrete dynamical system.
class	HenonMap	The Hénon Map: x_{n+1} = 1 - a * x_n^2 + y_n y_{n+1} = b * x_n
class	LogisticMap	The Logistic Map: x_{n+1} = r * x_n * (1 - x_n).
class	StandardMap	The Standard Map (Chirikov-Taylor map): p_{n+1} = (p_n + K * sin(theta_n)) mod 2Ï€ theta_{n+1} = (theta_n + p_{n+1}) mod 2Ï€

Uses of Relation in org.episteme.core.mathematics.analysis.series

Subinterfaces of Relation in org.episteme.core.mathematics.analysis.series

Modifier and Type	Interface	Description
interface	ConvergentSequence<T>	Represents a sequence that converges to a limit.
interface	IntegerSequence	A sequence of integers (ℤ).
interface	Sequence<T>	A mathematical sequence a(n) for n ≥ 0.

Classes in org.episteme.core.mathematics.analysis.series that implement Relation

Modifier and Type	Class	Description
class	BellSequence	Bell numbers sequence (OEIS A000110).
class	CatalanSequence	Catalan numbers: C(0)=1, C(n) = (2n)!
class	FactorialSequence	Factorial sequence: n!
class	FibonacciSequence	Fibonacci sequence: F(0) = 0, F(1) = 1, F(n) = F(n-1) + F(n-2).
class	PrimePiSequence	Prime counting function π(n) (OEIS A000720).
class	PrimeSequence	Prime number sequence: 2, 3, 5, 7, 11, ...
class	RecursiveSequence<T>	Represents a sequence defined by a recurrence relation.
class	SquareSequence	Square numbers sequence: a(n) = n².
class	TriangularSequence	Triangular numbers sequence: T(n) = n(n+1)/2.

Uses of Relation in org.episteme.core.mathematics.analysis.transform

Subinterfaces of Relation in org.episteme.core.mathematics.analysis.transform

Modifier and Type	Interface	Description
interface	Transform<D,C>	Represents a mathematical transform (e.g., Fourier, Laplace, Wavelet).

Classes in org.episteme.core.mathematics.analysis.transform that implement Relation

Modifier and Type	Class	Description
class	DiscreteFourierTransform	Discrete Fourier Transform (DFT) using Fast Fourier Transform (FFT) algorithm.

Uses of Relation in org.episteme.core.mathematics.geometry

Subinterfaces of Relation in org.episteme.core.mathematics.geometry

Modifier and Type	Interface	Description
interface	ParametricCurve	Represents a parametric curve in N-dimensional space.
interface	ParametricSurface	Represents a parametric surface in 3D space.

Uses of Relation in org.episteme.core.mathematics.geometry.curves

Classes in org.episteme.core.mathematics.geometry.curves that implement Relation

Modifier and Type	Class	Description
class	BezierCurve	Represents a Bézier curve.
class	Circle	Represents a circle as a parametric curve.
class	Ellipse	Represents an ellipse curve.
class	Helix	Represents a 3D helix (spiral) curve.

Uses of Relation in org.episteme.core.mathematics.geometry.surfaces

Classes in org.episteme.core.mathematics.geometry.surfaces that implement Relation

Modifier and Type	Class	Description
class	Cone	Represents a conical surface.
class	Cylinder	Represents a cylindrical surface.
class	Ellipsoid	Represents an ellipsoidal surface.
class	Paraboloid	Represents a paraboloidal surface.
class	Sphere	Represents a sphere as a parametric surface.
class	Torus	Represents a torus as a parametric surface.

Uses of Relation in org.episteme.core.mathematics.statistics

Subinterfaces of Relation in org.episteme.core.mathematics.statistics

Modifier and Type	Interface	Description
interface	ProbabilityDistribution	A probability distribution P(X ≤ x).

Classes in org.episteme.core.mathematics.statistics that implement Relation

Modifier and Type	Class	Description
class	ContinuousDistribution	Abstract base class for continuous probability distributions.
class	DiscreteDistribution	Abstract base class for discrete probability distributions.

Uses of Relation in org.episteme.core.mathematics.statistics.distributions

Classes in org.episteme.core.mathematics.statistics.distributions that implement Relation

Modifier and Type	Class	Description
class	BetaDistribution
class	BinomialDistribution	Binomial distribution Bin(n, p).
class	CauchyDistribution	Cauchy distribution (also called Lorentz distribution).
class	ChiSquareDistribution
class	ExponentialDistribution	Exponential distribution Exp(λ).
class	GammaDistribution
class	GeometricDistribution
class	LogNormalDistribution	LogNormal distribution.
class	NormalDistribution	Normal (Gaussian) distribution N(μ, σ²).
class	PoissonDistribution	*
class	StudentTDistribution
class	UniformDistribution
class	WeibullDistribution	Weibull distribution.