Package org.tensorics.core.math.structures.grouplike

Class AbstractAbelianGroup<E>

java.lang.Object

org.tensorics.core.math.structures.grouplike.AbstractAbelianGroup<E>

All Implemented Interfaces:

java.io.Serializable, AbelianGroup<E>, CommutativeMonoid<E>, CommutativeSemigroup<E>, Group<E>, GrouplikeStructure<E>, Magma<E>, Monoid<E>, Semigroup<E>, Structure<E>

public class AbstractAbelianGroup<E>
extends java.lang.Object
implements AbelianGroup<E>, java.io.Serializable

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
AbstractAbelianGroup(CommutativeAssociativeOperation<E> operation, E identity, UnaryOperation<E> inversion)

Method Summary

Modifier and Type	Method	Description
boolean	equals(java.lang.Object obj)
int	hashCode()
E	identity()	Has to return the element of the set, which represents the identity of the operation of the monoid.
UnaryOperation<E>	inversion()	Has to return the inversion operation for elements.
CommutativeAssociativeOperation<E>	operation()	Has to return the binary operation (M x M = M) for this Magma.
java.lang.String	toString()

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

AbstractAbelianGroup

public AbstractAbelianGroup(CommutativeAssociativeOperation<E> operation,
                            E identity,
                            UnaryOperation<E> inversion)

Method Detail

operation

public CommutativeAssociativeOperation<E> operation()

Description copied from interface: GrouplikeStructure

Has to return the binary operation (M x M = M) for this Magma.

Specified by:

operation in interface CommutativeSemigroup<E>

Specified by:

operation in interface GrouplikeStructure<E>

Specified by:

operation in interface Semigroup<E>

Returns:

the binary operation.

identity

public E identity()

Description copied from interface: Monoid

Has to return the element of the set, which represents the identity of the operation of the monoid.

Specified by:

identity in interface Monoid<E>

Returns:

the identity element of the monoid.

inversion

public UnaryOperation<E> inversion()

Description copied from interface: Group

Has to return the inversion operation for elements.

Specified by:

inversion in interface Group<E>

Returns:

the inversion operation

hashCode

public int hashCode()

Overrides:

hashCode in class java.lang.Object

equals

public boolean equals(java.lang.Object obj)

Overrides:

equals in class java.lang.Object

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object