Uses of Interface
org.episteme.core.mathematics.structures.groups.Monoid

Packages that use Monoid

Package	Description
org.episteme.core.mathematics.algebra	Defines fundamental algebraic concepts:
org.episteme.core.mathematics.algebra.algebras
org.episteme.core.mathematics.algebra.groups
org.episteme.core.mathematics.algebra.rings
org.episteme.core.mathematics.algebra.spaces
org.episteme.core.mathematics.geometry
org.episteme.core.mathematics.linearalgebra
org.episteme.core.mathematics.linearalgebra.matrices
org.episteme.core.mathematics.linearalgebra.spaces
org.episteme.core.mathematics.linearalgebra.vectors
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.groups
org.episteme.core.mathematics.structures.rings
org.episteme.core.mathematics.structures.spaces
org.episteme.nativ.mathematics.linearalgebra.matrices
org.episteme.nativ.mathematics.linearalgebra.vectors
org.episteme.nativ.mathematics.numbers.real

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

Subinterfaces of Monoid 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.
interface	NonAssociativeAlgebra<E,S>	A non-associative algebra over a field (or ring).

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

Subinterfaces of Monoid 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 Monoid

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 Monoid in org.episteme.core.mathematics.algebra.groups

Subinterfaces of Monoid in org.episteme.core.mathematics.algebra.groups

Modifier and Type	Interface	Description
interface	FiniteGroup<E>	Represents a Finite Group.
interface	OrderedGroup<E>	Represents an Ordered Group.

Classes in org.episteme.core.mathematics.algebra.groups that implement Monoid

Modifier and Type	Class	Description
class	CyclicGroup	Represents a Cyclic Group of order n (Z_n).
class	DihedralGroup	Represents a Dihedral Group D_n of order 2n.
class	FreeGroup	Represents a Free Group over a set of generators.
class	LieGroup	A Lie group is a group that is also a differentiable manifold.
class	QuaternionGroup	Represents the Quaternion Group Q8.
class	SO3_1Group	The group of all linear transformations of Minkowski space that preserve the spacetime interval ds²=-c²dt²+dx²+dy²+dz².
class	SU2Group	The group of 2x2 unitary matrices with determinant 1.
class	SU3Group	The group of 3x3 unitary matrices with determinant 1.
class	SymmetricGroup	Represents the Symmetric Group S_n (group of all permutations of n elements).
class	U1Group	Represents the Unitary Group U(1).

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

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

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

Uses of Monoid in org.episteme.core.mathematics.algebra.spaces

Subinterfaces of Monoid in org.episteme.core.mathematics.algebra.spaces

Modifier and Type	Interface	Description
interface	BanachSpace<E,S>	Represents a Banach Space.
interface	HilbertSpace<E,S>	Represents a Hilbert Space.

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

Classes in org.episteme.core.mathematics.geometry that implement Monoid

Modifier and Type	Class	Description
final class	Vector2D	A 2D vector in Euclidean space. * @author Silvere Martin-Michiellot
class	Vector3D	Represents a 3D vector.
class	Vector4D	Represents a 4D vector, typically used for spacetime coordinates (ct, x, y, z).
class	VectorND	Represents an N-dimensional geometric vector.

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

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

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

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

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

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 Monoid in org.episteme.core.mathematics.linearalgebra.spaces

Classes in org.episteme.core.mathematics.linearalgebra.spaces that implement Monoid

Modifier and Type	Class	Description
class	VectorSpace2D	2D Vector Space.
class	VectorSpace3D	3D Vector Space.

Uses of Monoid in org.episteme.core.mathematics.linearalgebra.vectors

Classes in org.episteme.core.mathematics.linearalgebra.vectors that implement Monoid

Modifier and Type	Class	Description
class	DenseVector<E>	A dense vector implementation.
class	GenericVector<E>	A generic vector implementation using abstract storage and provider delegation.
class	RealDoubleVector	An optimized Vector implementation for Real numbers.
class	RealFloatVector	An optimized Vector implementation for Single-Precision Real numbers.
class	SparseVector<E>	A sparse vector implementation.

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

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

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 Monoid in org.episteme.core.mathematics.numbers.integers

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

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 Monoid in org.episteme.core.mathematics.numbers.rationals

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

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

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

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

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 Monoid in org.episteme.core.mathematics.sets

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

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 Monoid in org.episteme.core.mathematics.structures.groups

Subinterfaces of Monoid in org.episteme.core.mathematics.structures.groups

Modifier and Type	Interface	Description
interface	AbelianGroup<E>	An abelian group is a commutative group.
interface	AbelianMonoid<E>	An abelian monoid is a commutative monoid.
interface	Group<E>	A group is a set with an associative binary operation, an identity element, and inverse elements.

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

Subinterfaces of Monoid 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).
interface	Semiring<E>	A semiring (or rig) is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse.

Uses of Monoid in org.episteme.core.mathematics.structures.spaces

Subinterfaces of Monoid in org.episteme.core.mathematics.structures.spaces

Modifier and Type	Interface	Description
interface	Module<M,R>	A module is a generalization of a vector space over a ring instead of a field.
interface	VectorSpace<V,F>	A vector space is a module over a field.

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

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

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 Monoid in org.episteme.nativ.mathematics.linearalgebra.vectors

Classes in org.episteme.nativ.mathematics.linearalgebra.vectors that implement Monoid

Modifier and Type	Class	Description
class	NativeRealDoubleVector	High-performance Real Double Vector backed by a persistent native MemorySegment.

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

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

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