Class JSci.maths.Group
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Class JSci.maths.Group
java.lang.Object
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+----JSci.maths.Set
|
+----JSci.maths.Group
- public class Group
- extends Set
The Group class provides an abstract encapsulation for groups.
-
Group()
- Constructs a group.
-
compose(Object, Object)
- The group composition law.
-
identity()
- Returns the identity element.
-
inverse(Object)
- Returns the inverse element.
-
isIdentity(Object)
- Returns true if the element is the identity element of this group.
-
isInverse(Object, Object)
- Returns true if one element is the inverse of the other.
-
isMember(Object)
- Returns true if the object is a member of this group.
Group
public Group()
- Constructs a group.
compose
public abstract Object compose(Object a,
Object b)
- The group composition law.
- Parameters:
- a - a group element
- b - a group element
identity
public abstract Object identity()
- Returns the identity element.
inverse
public abstract Object inverse(Object a)
- Returns the inverse element.
isMember
public abstract boolean isMember(Object a)
- Returns true if the object is a member of this group.
- Parameters:
- a - an object
isIdentity
public abstract boolean isIdentity(Object a)
- Returns true if the element is the identity element of this group.
- Parameters:
- a - a group element
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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