com.numericalmethod.suanshu.mathstructure
Interface Monoid<G>

Type Parameters:

G - a monoid

All Known Subinterfaces:

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

All Known Implementing Classes:

BidiagonalMatrix, BorderedHessian, Complex, ComplexMatrix, CovarianceMatrix, CsrSparseMatrix, DenseMatrix, DiagonalMatrix, DokSparseMatrix, DPolynomial, GenericMatrix, GivensMatrix, GoldfeldQuandtTrotter, Gradient, Hessian, HilbertMatrix, ImmutableKroneckerProduct, ImmutableMatrix, Inverse, Jacobian, JordanExchange, KroneckerProduct, LilSparseMatrix, LowerTriangularMatrix, MatrixMathImpl, MatrixStorageImpl, MatthewsDavies, PermutationMatrix, Polynomial, Pow, PseudoInverse, Real, RealMatrix, SubMatrixRef, SymmetricMatrix, TriangularMatrix, TridiagonalMatrix, UpperTriangularMatrix

public interface Monoid<G>

This interface represents a monoid.

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

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