dev.nm.algebra.structure

Interface Monoid<G>

Type Parameters:

G - a monoid

All Known Subinterfaces:

Field<F>, GenericMatrix<T,F>, Matrix, MatrixRing, Ring<R>, SparseMatrix

All Known Implementing Classes:

BidiagonalMatrix, BorderedHessian, CauchyPolynomial, ColumnBindMatrix, Complex, ComplexMatrix, CongruentMatrix, CorrelationMatrix, CSRSparseMatrix, DenseMatrix, DiagonalMatrix, DiagonalSum, DOKSparseMatrix, DPolynomial, FastKroneckerProduct, GenericFieldMatrix, GivensMatrix, GoldfeldQuandtTrotter, Hessian, HilbertMatrix, ImmutableMatrix, Inverse, Jacobian, KroneckerProduct, LILSparseMatrix, LowerTriangularMatrix, MAT, MatrixRootByDiagonalization, MatthewsDavies, OuterProduct, PermutationMatrix, Polynomial, PositiveDefiniteMatrixByPositiveDiagonal, PositiveSemiDefiniteMatrixNonNegativeDiagonal, Pow, PseudoInverse, QuadraticMonomial, Real, RealMatrix, ReturnsMatrix, SampleCovariance, ScaledPolynomial, SimilarMatrix, SubMatrixRef, SymmetricKronecker, SymmetricMatrix, TridiagonalMatrix, UpperTriangularMatrix, VariancebtX

public interface Monoid<G>

A monoid is a group with a binary operation (×), satisfying the group axioms:

1. closure
2. associativity
3. existence of multiplicative identity

See Also:

Wikipedia: Monoid

Method Summary

Modifier and Type	Method and Description
G	multiply(G that) × : G × G → G
G	ONE() The multiplicative element 1 in the group such that for any elements a in the group, the equation 1 × a = a × 1 = a holds.

Method Detail

multiply

G multiply(G that)

× : G × G → G

Parameters:

that - the multiplicand

Returns:

this × that

ONE

G ONE()

The multiplicative element 1 in the group such that for any elements a in the group, the equation 1 × a = a × 1 = a holds.

Returns:

1