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

Packages that use Ring

Package	Description
org.episteme.benchmarks.audit.mathematics.linearalgebra
org.episteme.client.client.mathematics.linearalgebra.backends
org.episteme.core.mathematics.algebra	Defines fundamental algebraic concepts:
org.episteme.core.mathematics.algebra.algebras
org.episteme.core.mathematics.algebra.polynomials
org.episteme.core.mathematics.algebra.rings
org.episteme.core.mathematics.analysis.functions
org.episteme.core.mathematics.analysis.functions.algorithms
org.episteme.core.mathematics.linearalgebra
org.episteme.core.mathematics.linearalgebra.backends
org.episteme.core.mathematics.linearalgebra.matrices
org.episteme.core.mathematics.linearalgebra.matrices.storage
org.episteme.core.mathematics.linearalgebra.providers
org.episteme.core.mathematics.linearalgebra.spaces
org.episteme.core.mathematics.linearalgebra.vectors
org.episteme.core.mathematics.linearalgebra.vectors.storage
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.core.mathematics.structures.spaces
org.episteme.core.mathematics.symbolic
org.episteme.core.technical.algorithm
org.episteme.nativ.mathematics.linearalgebra.backends
org.episteme.nativ.mathematics.linearalgebra.matrices
org.episteme.nativ.mathematics.linearalgebra.matrices.storage
org.episteme.nativ.mathematics.linearalgebra.vectors.storage
org.episteme.nativ.mathematics.numbers.real

Uses of Ring in org.episteme.benchmarks.audit.mathematics.linearalgebra

Methods in org.episteme.benchmarks.audit.mathematics.linearalgebra with parameters of type Ring

Modifier and Type	Method	Description
static <E> void	LinearAlgebraAuditSuite.runFullAudit(LinearAlgebraProvider<E> p, LinearAlgebraProvider<E> ref, int n, LinearAlgebraAuditSuite.AuditAction action, Ring<E> ring, String prefix, double tolerance)

Uses of Ring in org.episteme.client.client.mathematics.linearalgebra.backends

Methods in org.episteme.client.client.mathematics.linearalgebra.backends with parameters of type Ring

Modifier and Type	Method	Description
boolean	GRPCLinearAlgebraBackend.isCompatible(Ring<?> ring)

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

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

Subinterfaces of Ring 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	LieAlgebra<E,S>	Represents a Lie Algebra.

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

Modifier and Type	Class	Description
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 Ring in org.episteme.core.mathematics.algebra.polynomials

Classes in org.episteme.core.mathematics.algebra.polynomials with type parameters of type Ring

Modifier and Type	Class	Description
static class	PolynomialDivision.DivisionResult<R extends Ring<R>>	Result of polynomial division: A = B * Q + R

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

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

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

Methods in org.episteme.core.mathematics.algebra.rings that return Ring

Modifier and Type	Method	Description
Ring<E>	PolynomialRing.getCoefficientRing()

Constructors in org.episteme.core.mathematics.algebra.rings with parameters of type Ring

Modifier	Constructor	Description
	PolynomialRing(Ring<E> coefficientRing, String variableName)

Uses of Ring in org.episteme.core.mathematics.analysis.functions

Methods in org.episteme.core.mathematics.analysis.functions with parameters of type Ring

Modifier and Type	Method	Description
static <R> Polynomial<R>	Polynomial.constant(R value, Ring<R> ring)	Creates constant polynomial.
static <R> Polynomial<R>	Polynomial.monomial(R coefficient, int degree, Ring<R> ring)	Creates monomial: coefficient * x^degree.
static <R> Polynomial<R>	Polynomial.of(Ring<R> ring, R... coefficients)	Creates a polynomial from coefficients.
static <R> Polynomial<R>	Polynomial.x(Ring<R> ring)	Creates the polynomial x.
static <R> Polynomial<R>	Polynomial.zero(Ring<R> ring)	Creates zero polynomial.

Constructors in org.episteme.core.mathematics.analysis.functions with parameters of type Ring

Modifier	Constructor	Description
	Polynomial(List<R> coefficients, Ring<R> ring)	Creates a polynomial from coefficients (lowest degree first).

Uses of Ring in org.episteme.core.mathematics.analysis.functions.algorithms

Methods in org.episteme.core.mathematics.analysis.functions.algorithms with parameters of type Ring

Modifier and Type	Method	Description
static <R> List<R>	KaratsubaOptimizer.multiply(List<R> a, List<R> b, Ring<R> ring)	Multiplies two sequences of coefficients using the Karatsuba algorithm.

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

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

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

Methods in org.episteme.core.mathematics.linearalgebra that return Ring

Modifier and Type	Method	Description
Ring<E>	Matrix.getScalarRing()

Methods in org.episteme.core.mathematics.linearalgebra with parameters of type Ring

Modifier and Type	Method	Description
static <E> Matrix<E>	Matrix.identity(int size, Ring<E> ring)	Creates an identity matrix.
default boolean	LinearAlgebraProvider.isCompatible(Ring<?> ring)	Checks if this provider is compatible with the given ring.
static <E> Matrix<E>	Matrix.of(E[][] data, Ring<E> ring)	Creates a matrix from a 2D array.
static <E> Matrix<E>	Matrix.of(List<List<E>> data, Ring<E> ring)	Creates a matrix from a 2D list.
static <E> Vector<E>	Vector.of(E[] data, Ring<E> ring)	Creates a vector from an array of elements.
static <E> Vector<E>	Vector.of(List<E> data, Ring<E> ring)	Creates a vector from a list of elements.
static <E> Vector<E>	Vector.of(Ring<E> ring, E... elements)	Creates a vector from a variable number of elements.
static <E> Matrix<E>	Matrix.triangular(List<List<E>> data, Ring<E> ring)	Creates a triangular matrix from a 2D list.
static <E> Matrix<E>	Matrix.tridiagonal(List<List<E>> data, Ring<E> ring)	Creates a tridiagonal matrix from a 2D list.
static <E> Matrix<E>	Matrix.zeros(int rows, int cols, Ring<E> ring)	Creates a matrix of zeros.
static <E> Vector<E>	Vector.zeros(int dimension, Ring<E> ring)	Creates a vector of zeros.

Uses of Ring in org.episteme.core.mathematics.linearalgebra.backends

Methods in org.episteme.core.mathematics.linearalgebra.backends with parameters of type Ring

Modifier and Type	Method	Description
boolean	ColtBackend.isCompatible(Ring<?> ring)
boolean	CommonsMathBackend.isCompatible(Ring<?> ring)
boolean	EJMLBackend.isCompatible(Ring<?> ring)
boolean	EpistemeLinearAlgebraBackend.isCompatible(Ring<?> ring)
boolean	JBlasBackend.isCompatible(Ring<?> ring)

Constructors in org.episteme.core.mathematics.linearalgebra.backends with parameters of type Ring

Modifier	Constructor	Description
	EpistemeLinearAlgebraBackend(Ring<E> ring)

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

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

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).

Fields in org.episteme.core.mathematics.linearalgebra.matrices declared as Ring

Modifier and Type	Field	Description
protected Ring<E>	GenericMatrix.ring

Methods in org.episteme.core.mathematics.linearalgebra.matrices that return Ring

Modifier and Type	Method	Description
Ring<E>	GenericMatrix.getField()
Ring<E>	GenericMatrix.getScalarRing()
Ring<Real>	MMapMatrix.getScalarRing()
Ring<Real>	SIMDRealDoubleMatrix.getScalarRing()
Ring<Real>	SIMDRealFloatMatrix.getScalarRing()

Methods in org.episteme.core.mathematics.linearalgebra.matrices with parameters of type Ring

Modifier and Type	Method	Description
static <E> SparseMatrix<E>	SparseMatrix.fromDense(List<List<E>> rows, Ring<E> ring)
static <E> SparseMatrix<E>	SparseMatrix.identity(int size, Ring<E> ring)
static <E> Matrix<E>	DenseMatrix.of(E[][] data, Ring<E> ring)	Creates a DenseMatrix with automatic storage optimization.
static <E> Matrix<E>	DenseMatrix.of(List<List<E>> rows, Ring<E> ring)	Creates a DenseMatrix with automatic storage optimization.
static <E> SparseMatrix<E>	SparseMatrix.of(int rows, int cols, E zero, Ring<E> ring)
static <E> SparseMatrix<E>	SparseMatrix.of(int rows, int cols, Ring<E> ring)
static <E> SparseMatrix<E>	SparseMatrix.zeros(int rows, int cols, Ring<E> ring)

Constructors in org.episteme.core.mathematics.linearalgebra.matrices with parameters of type Ring

Modifier	Constructor	Description
	DenseMatrix(E[][] data, Ring<E> ring)	Creates a DenseMatrix with automatic storage optimization.
	DenseMatrix(E[] flatData, int rows, int cols, LinearAlgebraProvider<E> provider, Ring<E> ring)
	DenseMatrix(E[] flatData, int rows, int cols, Ring<E> ring)
	DenseMatrix(List<List<E>> rows, Ring<E> ring)	Creates a DenseMatrix with automatic storage optimization.
	DenseMatrix(MatrixStorage<E> storage, LinearAlgebraProvider<E> provider, Ring<E> ring)
	DenseMatrix(MatrixStorage<E> storage, Ring<E> ring)
	GenericMatrix(E[][] data, Ring<E> ring)	Creates a GenericMatrix with automatic storage selection.
	GenericMatrix(MatrixStorage<E> storage, LinearAlgebraProvider<E> provider, Ring<E> ring)	Public constructor for Providers and internal use.
	SparseMatrix(int rows, int cols, Ring<E> ring)
	SparseMatrix(E[][] data, Ring<E> ring)	Creates a SparseMatrix with automatic storage optimization.
	SparseMatrix(List<List<E>> rows, Ring<E> ring)
	SparseMatrix(MatrixStorage<E> storage, LinearAlgebraProvider<E> provider, Ring<E> ring)
	SparseMatrix(MatrixStorage<E> storage, Ring<E> ring)
	TiledMatrix(int rows, int cols, int tileSize, Ring<E> ring)	Creates an empty TiledMatrix with specified dimensions.

Uses of Ring in org.episteme.core.mathematics.linearalgebra.matrices.storage

Methods in org.episteme.core.mathematics.linearalgebra.matrices.storage with parameters of type Ring

Modifier and Type	Method	Description
<E> MatrixStorage<E>	MatrixStorageFactory.createDense(int rows, int cols, Ring<E> ring)	Creates a new dense matrix storage.

Constructors in org.episteme.core.mathematics.linearalgebra.matrices.storage with parameters of type Ring

Modifier	Constructor	Description
	DenseMatrixStorage(int rows, int cols, Ring<E> ring)
	DiagonalMatrixStorage(E[] diagonal, Ring<E> ring)
	SymmetricMatrixStorage(List<List<E>> data, Ring<E> ring)

Uses of Ring in org.episteme.core.mathematics.linearalgebra.providers

Fields in org.episteme.core.mathematics.linearalgebra.providers declared as Ring

Modifier and Type	Field	Description
protected final Ring<E>	CPUSparseLinearAlgebraProvider.ring

Methods in org.episteme.core.mathematics.linearalgebra.providers with parameters of type Ring

Modifier and Type	Method	Description
boolean	CPUDenseLinearAlgebraProvider.isCompatible(Ring<?> ring)
boolean	CPUSparseLinearAlgebraProvider.isCompatible(Ring<?> ring)
boolean	DistributedLinearAlgebraProvider.isCompatible(Ring<?> ring)

Constructors in org.episteme.core.mathematics.linearalgebra.providers with parameters of type Ring

Modifier	Constructor	Description
	CPUSparseLinearAlgebraProvider(Ring<E> ring)
	DistributedLinearAlgebraProvider(Ring<E> ring)

Uses of Ring in org.episteme.core.mathematics.linearalgebra.spaces

Methods in org.episteme.core.mathematics.linearalgebra.spaces that return Ring

Modifier and Type	Method	Description
Ring<Real>	VectorSpace2D.getScalarRing()
Ring<Real>	VectorSpace3D.getScalarRing()

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

Fields in org.episteme.core.mathematics.linearalgebra.vectors declared as Ring

Modifier and Type	Field	Description
protected final Ring<E>	GenericVector.ring

Methods in org.episteme.core.mathematics.linearalgebra.vectors that return Ring

Modifier and Type	Method	Description
Ring<E>	GenericVector.getField()
Ring<E>	GenericVector.getScalarRing()

Methods in org.episteme.core.mathematics.linearalgebra.vectors with parameters of type Ring

Modifier and Type	Method	Description
static <E> Vector<E>	DenseVector.of(List<E> elements, Ring<E> ring)
static <E> SparseVector<E>	SparseVector.of(int dimension, Ring<E> ring)
static <E> SparseVector<E>	SparseVector.of(List<E> elements, Ring<E> ring)
static <E> DenseVector<E>	DenseVector.zeros(int dimension, Ring<E> ring)
static <E> SparseVector<E>	SparseVector.zeros(int dimension, Ring<E> ring)

Constructors in org.episteme.core.mathematics.linearalgebra.vectors with parameters of type Ring

Modifier	Constructor	Description
	DenseVector(List<E> elements, Ring<E> ring)	Creates a DenseVector with automatic storage optimization.
	DenseVector(VectorStorage<E> storage, LinearAlgebraProvider<E> provider, Ring<E> ring)
protected	DenseVector(VectorStorage<E> storage, Ring<E> ring)
	GenericVector(List<E> data, Ring<E> ring)	Creates a GenericVector with automatic storage selection.
	GenericVector(VectorStorage<E> storage, LinearAlgebraProvider<E> provider, Ring<E> ring)
	SparseVector(int dimension, Ring<E> ring)
	SparseVector(List<E> elements, Ring<E> ring)	Creates a SparseVector with automatic storage selection.
protected	SparseVector(VectorStorage<E> storage, Ring<E> ring)

Uses of Ring in org.episteme.core.mathematics.linearalgebra.vectors.storage

Methods in org.episteme.core.mathematics.linearalgebra.vectors.storage with parameters of type Ring

Modifier and Type	Method	Description
<E> VectorStorage<E>	VectorStorageFactory.createDense(int dimension, Ring<E> ring)	Creates a new dense vector storage.

Constructors in org.episteme.core.mathematics.linearalgebra.vectors.storage with parameters of type Ring

Modifier	Constructor	Description
	DenseVectorStorage(int dimension, Ring<E> ring)

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

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

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).

Methods in org.episteme.core.mathematics.numbers.complex that return Ring

Modifier and Type	Method	Description
Ring<Complex>	Complex.getScalarRing()
static Ring<Complex>	Complex.ring()	Returns the ring structure for complex numbers.

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

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

Modifier and Type	Class	Description
class	Integer	Abstract base class for integers (ℤ = {..., -2, -1, 0, 1, 2, ...}).

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

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

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

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

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

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.

Fields in org.episteme.core.mathematics.numbers.real declared as Ring

Modifier and Type	Field	Description
static final Ring<RealDouble>	RealDouble.RING
static final Ring<RealFloat>	RealFloat.RING

Methods in org.episteme.core.mathematics.numbers.real that return Ring

Modifier and Type	Method	Description
Ring<Real>	Real.getScalarRing()	Returns the ring structure for real numbers.
static Ring<Real>	Real.ring()

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

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

Modifier and Type	Class	Description
final class	Complexes	The structure of complex numbers (â„‚).
final class	Integers	The structure of integers (ℤ = {..., -2, -1, 0, 1, 2, ...}).
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 Ring in org.episteme.core.mathematics.structures.rings

Subinterfaces of Ring 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.

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

Methods in org.episteme.core.mathematics.structures.spaces that return Ring

Modifier and Type	Method	Description
Ring<R>	Module.getScalarRing()	Returns the ring of scalars for this module.

Uses of Ring in org.episteme.core.mathematics.symbolic

Classes in org.episteme.core.mathematics.symbolic with type parameters of type Ring

Modifier and Type	Class	Description
class	ConstantExpression<T extends Ring<T>>	Represents a constant value as a symbolic expression. *
class	DivisionExpression<T extends Ring<T>>	Represents a division of two expressions.
interface	Expression<T extends Ring<T>>	Represents a symbolic mathematical expression.
class	FunctionExpression<T extends Ring<T>>	Represents a transcendental function as a symbolic expression.
class	IntegralExpression<T extends Ring<T>>	Represents a symbolic integral.
class	Monomial<T extends Ring<T>>	Represents a monomial, which is a product of variables raised to non-negative integer powers.
class	PolynomialExpression<T extends Ring<T>>	Represents a multivariate polynomial expression.
class	ProductExpression<T extends Ring<T>>	Represents a product of two expressions.
class	Series<T extends Ring<T>>	Represents a power series Σ aₙxⁿ.
class	SumExpression<T extends Ring<T>>	Represents a sum of two expressions.
class	Variable<T extends Ring<T>>	Represents a symbolic variable (e.g., "x", "y", "theta").

Methods in org.episteme.core.mathematics.symbolic with type parameters of type Ring

Modifier and Type	Method	Description
static <T extends Ring<T>> Expression<T>	Simplifier.collectLikeTerms(Expression<T> expr)	Collects like terms in an expression.
static <T extends Ring<T>> FunctionExpression<T>	FunctionExpression.cos(Expression<T> arg)	Creates a cosine function expression.
static <T extends Ring<T>> FunctionExpression<T>	FunctionExpression.exp(Expression<T> arg)	Creates an exponential function expression.
static <T extends Ring<T>> Expression<T>	Simplifier.expandProducts(Expression<T> expr)	Expands products in an expression.
static <T extends Ring<T>> FunctionExpression<T>	FunctionExpression.log(Expression<T> arg)	Creates a natural logarithm function expression.
static <T extends Ring<T>> Series<T>	Series.maclaurin(List<T> coefficients, Ring<T> ring)	Creates a Maclaurin series (expansion around xâ‚€ = 0).
static <T extends Ring<T>> Monomial<T>	Monomial.of(Variable<T> v)
static <E extends Ring<E>> ConstantExpression<E>	ConstantExpression.ofConstant(E value, Ring<E> ring)	Returns a constant expression for the given value and ring.
static <T extends Ring<T>> PolynomialExpression<T>	PolynomialExpression.ofConstant(T value, Ring<T> ring)
static <T extends Ring<T>> PolynomialExpression<T>	PolynomialExpression.ofVariable(Variable<T> v, Ring<T> ring)
static <T extends Ring<T>> Monomial<T>	Monomial.one()
static <T extends Ring<T>> FunctionExpression<T>	FunctionExpression.pow(Expression<T> base, Expression<T> exp)	Creates a power function expression.
static <T extends Ring<T>> Expression<T>	Simplifier.simplify(Expression<T> expr)	Simplifies an LegacyExpression using all available rules.
static <T extends Ring<T>> Expression<T>	Simplifier.simplifyAlgebraic(Expression<T> expr)	Simplifies algebraic expressions.
static <T extends Ring<T>> Expression<T>	Simplifier.simplifyArithmetic(Expression<T> expr)	Simplifies arithmetic operations.
static <T extends Ring<T>> Expression<T>	Simplifier.simplifyTrigonometric(Expression<T> expr)	Simplifies trigonometric expressions.
static <T extends Ring<T>> FunctionExpression<T>	FunctionExpression.sin(Expression<T> arg)	Creates a sine function expression.
static <T extends Ring<T>> FunctionExpression<T>	FunctionExpression.sqrt(Expression<T> arg)	Creates a square root function expression.
static <T extends Ring<T>> FunctionExpression<T>	FunctionExpression.tan(Expression<T> arg)	Creates a tangent function expression.

Methods in org.episteme.core.mathematics.symbolic that return Ring

Modifier and Type	Method	Description
Ring<T>	ConstantExpression.getRing()	Returns the ring structure.
Ring<T>	DivisionExpression.getRing()	Returns the ring structure.
Ring<T>	Expression.getRing()	Returns the ring this expression belongs to.
Ring<T>	FunctionExpression.getRing()
Ring<T>	IntegralExpression.getRing()
Ring<T>	PolynomialExpression.getRing()
Ring<T>	ProductExpression.getRing()	Returns the ring structure.
Ring<T>	SumExpression.getRing()	Returns the ring structure.
Ring<T>	Variable.getRing()

Methods in org.episteme.core.mathematics.symbolic with parameters of type Ring

Modifier and Type	Method	Description
static <T extends Ring<T>> Series<T>	Series.maclaurin(List<T> coefficients, Ring<T> ring)	Creates a Maclaurin series (expansion around xâ‚€ = 0).
static <E extends Ring<E>> ConstantExpression<E>	ConstantExpression.ofConstant(E value, Ring<E> ring)	Returns a constant expression for the given value and ring.
static <T extends Ring<T>> PolynomialExpression<T>	PolynomialExpression.ofConstant(T value, Ring<T> ring)
static <T extends Ring<T>> PolynomialExpression<T>	PolynomialExpression.ofVariable(Variable<T> v, Ring<T> ring)

Constructors in org.episteme.core.mathematics.symbolic with parameters of type Ring

Modifier	Constructor	Description
	ConstantExpression(T value, Ring<T> ring)	Creates a constant expression.
	DivisionExpression(Expression<T> numerator, Expression<T> denominator, Ring<T> ring)	Creates a division expression.
	IntegralExpression(Expression<T> integrand, Variable<T> variable, Ring<T> ring)	Creates an integral expression.
	PolynomialExpression(Map<Monomial<T>, T> terms, Ring<T> ring)	Creates a polynomial expression.
	ProductExpression(Expression<T> left, Expression<T> right, Ring<T> ring)	Creates a product expression.
	Series(List<T> coefficients, T center, Ring<T> ring)	Creates a power series with given coefficients.
	Series(List<T> coefficients, T center, Ring<T> ring, Real convergenceRadius)	Creates a power series with given coefficients and convergence radius.
	SumExpression(Expression<T> left, Expression<T> right, Ring<T> ring)	Creates a sum expression.
	Variable(String symbol, Ring<T> ring)	Creates a new variable with the given symbol and ring.

Uses of Ring in org.episteme.core.technical.algorithm

Methods in org.episteme.core.technical.algorithm with parameters of type Ring

Modifier and Type	Method	Description
<E> MatrixStorage<E>	ProviderRegistry.createStorage(int rows, int cols, Ring<E> ring, double density)	Creates optimal storage based on data and density context.
<E> VectorStorage<E>	ProviderRegistry.createVectorStorage(int dim, Ring<E> ring, double density)	Creates optimal vector storage.
<E> LinearAlgebraProvider<E>	ProviderRegistry.getDenseLinearAlgebraProvider(Ring<E> ring)
<E> LinearAlgebraProvider<E>	ProviderRegistry.getLinearAlgebraProvider(Ring<E> ring)
<E> LinearAlgebraProvider<E>	ProviderRegistry.getSparseLinearAlgebraProvider(Ring<E> ring)	Gets a sparse linear algebra provider.
<E> LinearAlgebraProvider<E>	ProviderRegistry.selectLinearAlgebraProvider(OperationContext ctx, Ring<E> ring)	Gets a linear algebra provider suited for the given operation context and ring.

Uses of Ring in org.episteme.nativ.mathematics.linearalgebra.backends

Fields in org.episteme.nativ.mathematics.linearalgebra.backends declared as Ring

Modifier and Type	Field	Description
protected final Ring<E>	AbstractNativeCPULinearAlgebraBackend.ring
protected final Ring<E>	AbstractNativeSIMDLinearAlgebraBackend.ring

Methods in org.episteme.nativ.mathematics.linearalgebra.backends with parameters of type Ring

Modifier and Type	Method	Description
boolean	AbstractNativeCPULinearAlgebraBackend.isCompatible(Ring<?> ring)
boolean	AbstractNativeFFMBLASBackend.isCompatible(Ring<?> ring)
boolean	AbstractNativeSIMDLinearAlgebraBackend.isCompatible(Ring<?> ring)
boolean	NativeCUDADenseLinearAlgebraDoubleBackend.isCompatible(Ring<?> ring)
boolean	NativeCUDADenseLinearAlgebraFloatBackend.isCompatible(Ring<?> ring)
boolean	NativeCUDASparseLinearAlgebraDoubleBackend.isCompatible(Ring<?> ring)
boolean	NativeCUDASparseLinearAlgebraFloatBackend.isCompatible(Ring<?> ring)
boolean	NativeFFMBLASComplexBackend.isCompatible(Ring<?> ring)
boolean	NativeFFMBLASRealBackend.isCompatible(Ring<?> ring)
boolean	NativeMPFRDenseLinearAlgebraBackend.isCompatible(Ring<?> ring)
boolean	NativeMPFRSparseLinearAlgebraBackend.isCompatible(Ring<?> ring)
boolean	NativeND4JLinearAlgebraBackend.isCompatible(Ring<?> ring)
boolean	NativeOpenCLDenseLinearAlgebraDoubleBackend.isCompatible(Ring<?> ring)
boolean	NativeOpenCLDenseLinearAlgebraFloatBackend.isCompatible(Ring<?> ring)
boolean	NativeOpenCLSparseLinearAlgebraDoubleBackend.isCompatible(Ring<?> ring)
boolean	NativeOpenCLSparseLinearAlgebraFloatBackend.isCompatible(Ring<?> ring)

Constructors in org.episteme.nativ.mathematics.linearalgebra.backends with parameters of type Ring

Modifier	Constructor	Description
protected	AbstractNativeCPULinearAlgebraBackend(Ring<E> ring)
protected	AbstractNativeSIMDLinearAlgebraBackend(Ring<E> ring)

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

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

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 Ring in org.episteme.nativ.mathematics.linearalgebra.matrices.storage

Methods in org.episteme.nativ.mathematics.linearalgebra.matrices.storage with parameters of type Ring

Modifier and Type	Method	Description
<E> MatrixStorage<E>	NativeMatrixStorageFactory.createDense(int rows, int cols, Ring<E> ring)

Uses of Ring in org.episteme.nativ.mathematics.linearalgebra.vectors.storage

Methods in org.episteme.nativ.mathematics.linearalgebra.vectors.storage with parameters of type Ring

Modifier and Type	Method	Description
<E> VectorStorage<E>	NativeVectorStorageFactory.createDense(int dim, Ring<E> ring)

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

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

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