Uses of Interface
org.episteme.core.mathematics.structures.rings.Semiring

Packages that use Semiring

Package	Description
org.episteme.core.mathematics.algebra	Defines fundamental algebraic concepts:
org.episteme.core.mathematics.algebra.algebras
org.episteme.core.mathematics.algebra.rings
org.episteme.core.mathematics.linearalgebra
org.episteme.core.mathematics.linearalgebra.matrices
org.episteme.core.mathematics.numbers.complex
org.episteme.core.mathematics.numbers.integers
org.episteme.core.mathematics.numbers.rationals
org.episteme.core.mathematics.numbers.real
org.episteme.core.mathematics.sets
org.episteme.core.mathematics.structures.rings
org.episteme.nativ.mathematics.linearalgebra.matrices
org.episteme.nativ.mathematics.numbers.real

Uses of Semiring in org.episteme.core.mathematics.algebra

Subinterfaces of Semiring in org.episteme.core.mathematics.algebra

Modifier and Type	Interface	Description
interface	Algebra<E,F>	An algebra over a field is a vector space equipped with a bilinear product.

Uses of Semiring in org.episteme.core.mathematics.algebra.algebras

Subinterfaces of Semiring in org.episteme.core.mathematics.algebra.algebras

Modifier and Type	Interface	Description
interface	BanachAlgebra<E,F>	Represents a Banach algebra - a complete normed algebra.
interface	CStarAlgebra<E,F>	Represents a C*-algebra (C-star algebra).
interface	GradedAlgebra<E,F>	Represents a graded algebra - an algebra that can be decomposed into a direct sum of subspaces indexed by a grading group (typically integers).
interface	KleeneAlgebra<E>	A Kleene Algebra is an idempotent semiring with a closure operator (Kleene star).
interface	LieAlgebra<E,S>	Represents a Lie Algebra.

Classes in org.episteme.core.mathematics.algebra.algebras that implement Semiring

Modifier and Type	Class	Description
final class	BooleanAlgebra	Boolean algebra - a special algebraic structure for logic operations.
class	CliffordAlgebra<E>	Represents a Clifford Algebra (Geometric Algebra) over a field.
class	MatrixLieAlgebra<E>	A concrete Lie Algebra where elements are square matrices and the bracket is the commutator [A, B] = AB - BA.

Uses of Semiring in org.episteme.core.mathematics.algebra.rings

Classes in org.episteme.core.mathematics.algebra.rings that implement Semiring

Modifier and Type	Class	Description
class	PolynomialRing<E>	Represents a Polynomial Ring R[x] over a ring R.

Uses of Semiring in org.episteme.core.mathematics.linearalgebra

Subinterfaces of Semiring in org.episteme.core.mathematics.linearalgebra

Modifier and Type	Interface	Description
interface	Matrix<E>	Represents a matrix of scalar elements.

Uses of Semiring in org.episteme.core.mathematics.linearalgebra.matrices

Classes in org.episteme.core.mathematics.linearalgebra.matrices that implement Semiring

Modifier and Type	Class	Description
class	DenseMatrix<E>	A dense matrix implementation.
class	GenericMatrix<E>	A generic matrix implementation with smart storage and provider selection.
class	MMapMatrix	Memory-Mapped Matrix implementation for Out-of-Core processing.
class	RealDoubleMatrix	A specialized Matrix implementation for Doubles with SIMD and Native optimization.
class	SIMDRealDoubleMatrix	SIMD-accelerated Matrix implementation using JDK Vector API.
class	SIMDRealFloatMatrix	SIMD-accelerated Matrix implementation using JDK Vector API for Float (Single) precision.
class	SparseMatrix<E>	A sparse matrix implementation.
class	TiledMatrix<E>	A matrix decomposed into smaller tiles (blocks).

Uses of Semiring in org.episteme.core.mathematics.numbers.complex

Classes in org.episteme.core.mathematics.numbers.complex that implement Semiring

Modifier and Type	Class	Description
final class	Complex	Represents a complex number (â„‚), defined as a + bi where a, b are Real numbers.
class	Octonion	Represents an octonion number (8-dimensional hypercomplex number).
final class	Quaternion	Represents a Quaternion number (H).

Uses of Semiring in org.episteme.core.mathematics.numbers.integers

Classes in org.episteme.core.mathematics.numbers.integers that implement Semiring

Modifier and Type	Class	Description
final class	Boolean	Boolean algebraic type - matches Real/Integer pattern.
class	Integer	Abstract base class for integers (ℤ = {..., -2, -1, 0, 1, 2, ...}).
class	Natural	Abstract base class for natural numbers (â„• = {0, 1, 2, ...}).

Uses of Semiring in org.episteme.core.mathematics.numbers.rationals

Classes in org.episteme.core.mathematics.numbers.rationals that implement Semiring

Modifier and Type	Class	Description
final class	Rational	Represents a rational number (â„š), defined as the quotient of two integers.

Uses of Semiring in org.episteme.core.mathematics.numbers.real

Classes in org.episteme.core.mathematics.numbers.real that implement Semiring

Modifier and Type	Class	Description
final class	DoubleField	Field implementation for primitive Double wrappers.
class	Real	Abstract base class for real numbers (ℝ).
final class	RealBig	Real number backed by arbitrary-precision BigDecimal.
final class	RealDouble	Real number backed by a 64-bit double.
final class	RealFloat	Real number backed by a 32-bit float.

Uses of Semiring in org.episteme.core.mathematics.sets

Classes in org.episteme.core.mathematics.sets that implement Semiring

Modifier and Type	Class	Description
final class	Booleans	The structure of Boolean values (𝔹 = {0, 1}).
final class	Complexes	The structure of complex numbers (â„‚).
final class	Integers	The structure of integers (ℤ = {..., -2, -1, 0, 1, 2, ...}).
final class	Naturals	The structure of natural numbers (â„• = {0, 1, 2, 3, ...}).
final class	Octonions	The structure of Octonions (O).
final class	Quaternions	The structure of Quaternions (H).
final class	Rationals	The structure of rational numbers (â„š).
final class	Reals	The structure of real numbers (ℝ).
final class	SquareMatrices<E>	The structure of n×n square matrices over a field, forming a ring.

Uses of Semiring in org.episteme.core.mathematics.structures.rings

Subinterfaces of Semiring in org.episteme.core.mathematics.structures.rings

Modifier and Type	Interface	Description
interface	DivisionRing<E>	A division ring (also known as a skew field) is a ring in which every non-zero element has a multiplicative inverse.
interface	Field<E>	A field is a commutative ring where every non-zero element has a multiplicative inverse.
interface	Ring<E>	A ring is an abelian group with a second binary operation (multiplication).

Uses of Semiring in org.episteme.nativ.mathematics.linearalgebra.matrices

Classes in org.episteme.nativ.mathematics.linearalgebra.matrices that implement Semiring

Modifier and Type	Class	Description
class	NativeRealDoubleMatrix	High-performance Real Double Matrix backed by a persistent native MemorySegment.
class	NativeRealFloatMatrix	High-performance Real Float Matrix backed by a persistent native MemorySegment.

Uses of Semiring in org.episteme.nativ.mathematics.numbers.real

Classes in org.episteme.nativ.mathematics.numbers.real that implement Semiring

Modifier and Type	Class	Description
final class	NativeRealBig	High-precision real number backed by the native MPFR library.