Package dk.jonaslindstrom.ruffini.permutations.structures

Class SymmetricGroup

java.lang.Object

dk.jonaslindstrom.ruffini.permutations.structures.SymmetricGroup

All Implemented Interfaces:

Group<Permutation>, Monoid<Permutation>, Semigroup<Permutation>, Set<Permutation>

public class SymmetricGroup
extends Object
implements Group<Permutation>

Constructor Summary

Constructors

Constructor	Description
SymmetricGroup(int n)

Method Summary

Modifier and Type	Method	Description
boolean	equals(Permutation a, Permutation b)	Returns true if and only if a = b as elements of this set.
Permutation	identity()	Return the identity element of this monoid.
Permutation	invert(Permutation a)	Return the inverse a-1.
Permutation	multiply(Permutation a, Permutation b)	Return the result of the product ab in this group.
String	toString()
String	toString(Permutation a)	Returns a human-readable string representation of an element in this set.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Group

divide

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Monoid

isIdentity, power

Methods inherited from interface dk.jonaslindstrom.ruffini.common.abstractions.Semigroup

multiply, multiply

Constructor Details

SymmetricGroup

public SymmetricGroup(int n)

Method Details

identity

public Permutation identity()

Description copied from interface: Monoid

Return the identity element of this monoid.

Specified by:

identity in interface Monoid<Permutation>

multiply

public Permutation multiply(Permutation a,
 Permutation b)

Description copied from interface: Semigroup

Return the result of the product ab in this group.

Specified by:

multiply in interface Semigroup<Permutation>

toString

public String toString(Permutation a)

Description copied from interface: Set

Returns a human-readable string representation of an element in this set.

Specified by:

toString in interface Set<Permutation>

equals

public boolean equals(Permutation a,
 Permutation b)

Description copied from interface: Set

Returns true if and only if a = b as elements of this set.

Specified by:

equals in interface Set<Permutation>

invert

public Permutation invert(Permutation a)

Description copied from interface: Group

Return the inverse a^-1.

Specified by:

invert in interface Group<Permutation>

toString

public String toString()

Overrides:

toString in class Object