Package dev.nm.algebra.structure
Interface AbelianGroup<G>
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- Type Parameters:
G- an Abelian group
- All Known Subinterfaces:
BanachSpace<B,F>,Field<F>,GenericMatrix<T,F>,HilbertSpace<H,F>,Matrix,MatrixRing,Ring<R>,SparseMatrix,Vector,VectorSpace<V,F>
- All Known Implementing Classes:
Basis,BidiagonalMatrix,BorderedHessian,CauchyPolynomial,ColumnBindMatrix,CombinedVectorByRef,Complex,ComplexMatrix,CongruentMatrix,CorrelationMatrix,CSRSparseMatrix,DenseMatrix,DenseVector,DiagonalMatrix,DiagonalSum,DOKSparseMatrix,DPolynomial,FastKroneckerProduct,GenericFieldMatrix,GivensMatrix,GoldfeldQuandtTrotter,Gradient,Hessian,HilbertMatrix,ImmutableMatrix,ImmutableVector,Inverse,Jacobian,KroneckerProduct,LILSparseMatrix,LowerTriangularMatrix,MAT,MatrixRootByDiagonalization,MatthewsDavies,OuterProduct,PermutationMatrix,Polynomial,PositiveDefiniteMatrixByPositiveDiagonal,PositiveSemiDefiniteMatrixNonNegativeDiagonal,Pow,PseudoInverse,QuadraticMonomial,Real,RealMatrix,ReturnsMatrix,SampleCovariance,ScaledPolynomial,SimilarMatrix,SparseVector,SubMatrixRef,SubVectorRef,SVEC,SymmetricKronecker,SymmetricMatrix,TridiagonalMatrix,UpperTriangularMatrix,VariancebtX
public interface AbelianGroup<G>An Abelian group is a group with a binary additive operation (+), satisfying the group axioms:- closure
- associativity
- existence of additive identity
- existence of additive opposite
- commutativity of addition
- See Also:
- Wikipedia: Abelian group
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Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method Description Gadd(G that)+ : G × G → GGminus(G that)- : G × G → GGopposite()For each a in G, there exists an element b in G such that a + b = b + a = 0.GZERO()The additive element 0 in the group, such that for all elements a in the group, the equation 0 + a = a + 0 = a holds.
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Method Detail
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minus
G minus(G that)
- : G × G → G The operation "-" is not in the definition of of an additive group but can be deduced. This function is provided for convenience purpose. It is equivalent to
.this.add(that.opposite())- Parameters:
that- the object to be subtracted (subtrahend)- Returns:
- this - that
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opposite
G opposite()
For each a in G, there exists an element b in G such that a + b = b + a = 0. That is, it is the object such asthis.add(this.opposite()) == this.ZERO- Returns:
- -this, the additive opposite
- See Also:
- Wikipedia: Additive inverse
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ZERO
G ZERO()
The additive element 0 in the group, such that for all elements a in the group, the equation 0 + a = a + 0 = a holds.- Returns:
- 0, the additive identity
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