org.ojalgo.algebra

Interface Group

All Known Subinterfaces:

DecompositionStore<N>, Field<S>, Group.Additive<S>, Group.Multiplicative<S>, MatrixStore<N>, NormedVectorSpace<V,F>, PhysicalStore<N>, Ring<S>, Scalar<N>, Tensor<N>, VectorSpace<V,F>

All Known Implementing Classes:

BigScalar, ComplexMatrix, ComplexNumber, ComplexNumber.Normalised, ExactDecimal, GenericDenseStore, Money, PrimitiveDenseStore, PrimitiveMatrix, PrimitiveScalar, Quaternion, Quaternion.Versor, QuaternionMatrix, RationalMatrix, RationalNumber, RawStore, SparseStore

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.

Author:

apete

See Also:

Group

Nested Class Summary

Nested Classes

Modifier and Type	Interface and Description
static interface	Group.Additive<S>
static interface	Group.Multiplicative<S>