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# Interface JSci.maths.groups.AbelianGroup

public interface AbelianGroup
extends Member

This interface defines an abelian group.

##

isNegative(AbelianGroupMember, AbelianGroupMember)
  Returns true if one member is the negative of the other.
isZero(AbelianGroupMember)
  Returns true if the member is the identity element of this group.
zero()
  Returns the identity element.

##

zero

     public abstract AbelianGroupMember zero()

  Returns the identity element.

isZero

     public abstract boolean isZero(AbelianGroupMember g)

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

  Parameters:
    g - a group member

isNegative

     public abstract boolean isNegative(AbelianGroupMember a,
                                        AbelianGroupMember b)

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

  Parameters:
    a - a group member
    b - a group member

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