jsci.maths.groups

Interface AbelianGroup

All Known Subinterfaces:

BanachSpace, Field, Module, Ring, VectorSpace

All Known Implementing Classes:

ComplexField, ComplexPolynomialRing, CyclicGroup, DoubleMatrixAlgebra, Hilb.OperatorSpace, HilbertSpace, IntegerMatrixAlgebra, IntegerRing, RealField, RealPolynomialRing

public interface AbelianGroup

This interface defines an abelian group.

Nested Class Summary

Nested Classes

Modifier and Type	Interface and Description
static interface	AbelianGroup.Member This interface defines a member of an abelian group.

Method Summary

Modifier and Type	Method and Description
boolean	isNegative(AbelianGroup.Member a, AbelianGroup.Member b) Returns true if one member is the negative of the other.
boolean	isZero(AbelianGroup.Member g) Returns true if the member is the identity element of this group.
AbelianGroup.Member	zero() Returns the identity element.

Method Detail

zero

AbelianGroup.Member zero()

Returns the identity element.

isZero

boolean isZero(AbelianGroup.Member g)

Returns true if the member is the identity element of this group.

Parameters:

g - a group member

isNegative

boolean isNegative(AbelianGroup.Member a,
                   AbelianGroup.Member b)

Returns true if one member is the negative of the other.

Parameters:

a - a group member

b - a group member