Package org.ojalgo.algebra
Interface Group
-
- All Known Subinterfaces:
DecompositionStore<N>
,Field<T>
,Group.Additive<T>
,Group.Multiplicative<T>
,Matrix2D<N,M>
,MatrixStore<N>
,NormedVectorSpace<T,N>
,PhysicalStore<N>
,PolynomialFunction<N>
,Ring<T>
,Scalar<N>
,SelfDeclaringScalar<S>
,Tensor<N,T>
,VectorSpace<T,N>
- All Known Implementing Classes:
AboveBelowStore
,AbstractPolynomial
,AbstractStore
,Amount
,AnyTensor
,ArrayBasedTensor
,BasicMatrix
,BigScalar
,ColumnsStore
,ColumnsSupplier
,ComplexNumber
,ComposingStore
,ConjugatedStore
,DiagonalStore
,ExactDecimal
,FactoryStore
,GenericStore
,IdentityStore
,ImageData
,ImageData.SingleChannel
,IterativeASS.SchurComplementSolver
,LeftRightStore
,LimitStore
,LogicalStore
,LowerHessenbergStore
,LowerSymmetricStore
,LowerTriangularStore
,MatrixC128
,MatrixH256
,MatrixQ128
,MatrixR032
,MatrixR064
,MatrixR128
,MatrixTensor
,Money
,OffsetStore
,PolynomialC128
,PolynomialQ128
,PolynomialR032
,PolynomialR064
,PolynomialR128
,PolynomialR256
,Price
,PrimitiveScalar
,Quadruple
,Quantity
,Quaternion
,R032Store
,R064Store
,RationalNumber
,RawStore
,RepeatedColumnsStore
,RepeatedRowsStore
,RowsStore
,RowsSupplier
,ScalarPolynomial
,SelectingStore
,ShadingStore
,SingleStore
,SparseStore
,SuperimposedStore
,TransjugatedStore
,TransposedStore
,UnaryOperatoStore
,UpperHessenbergStore
,UpperSymmetricStore
,UpperTriangularStore
,VectorTensor
,WrapperStore
,ZeroStore
public interface Group
A group is a set of elements paired with a binary operation. Four conditions called the group axioms must be satisfied:
- Closure: If A and B are both members of the set then the result of A op B is also a member.
- Associativity: Invocation/execution order doesn't matter - ((A op B) op C) == (A op (B op C))
- The identity property: There is an identity element in the set, I, so that I op A == A op I == A
- The inverse property: For each element in the set there must be an inverse element (opposite or reciprocal) so that A-1 op A == A op A-1 == I
Note that commutativity is not a requirement - A op B doesn't always have to be equal to B op A. If the operation is commutative then the group is called an abelian group or simply a commutative group.
- See Also:
- Group
-
-
Nested Class Summary
Nested Classes Modifier and Type Interface Description static interface
Group.Additive<T>
static interface
Group.Multiplicative<T>
-