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 G
add(G that)
+ : G × G → GG
minus(G that)
- : G × G → GG
opposite()
For each a in G, there exists an element b in G such that a + b = b + a = 0.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.
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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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