Class JSci.maths.Group
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Class JSci.maths.Group

java.lang.Object
   |
   +----JSci.maths.Set
           |
           +----JSci.maths.Group

public class Group
extends Set
The Group class provides an abstract encapsulation for groups.

Constructor Index

 o Group()
Constructs a group.

Method Index

 o compose(Object, Object)
The group composition law.
 o identity()
Returns the identity element.
 o inverse(Object)
Returns the inverse element.
 o isIdentity(Object)
Returns true if the element is the identity element of this group.
 o isInverse(Object, Object)
Returns true if one element is the inverse of the other.
 o isMember(Object)
Returns true if the object is a member of this group.

Constructors

 o Group
  public Group()
Constructs a group.

Methods

 o compose
  public abstract Object compose(Object a,
                                 Object b)
The group composition law.
Parameters:
a - a group element
b - a group element
 o identity
  public abstract Object identity()
Returns the identity element.
 o inverse
  public abstract Object inverse(Object a)
Returns the inverse element.
 o isMember
  public abstract boolean isMember(Object a)
Returns true if the object is a member of this group.
Parameters:
a - an object
 o isIdentity
  public abstract boolean isIdentity(Object a)
Returns true if the element is the identity element of this group.
Parameters:
a - a group element
 o isInverse
  public final boolean isInverse(Object a,
                                 Object b)
Returns true if one element is the inverse of the other.
Parameters:
a - a group element
b - a group element

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