repthy
Class PermGpElt

Object
  PermGpElt

All Implemented Interfaces:

Comparable, GroupElt

public class PermGpElt

extends Object

implements GroupElt, Comparable

Stores a permutation of the integers 0, 1, ..., deg-1. The permutation is a one-to-one function from this set of integers to itself, as expressed by the method apply(int). The toString() method expresses the permutation in cycle notation; parseCycles(int, java.lang.String) goes in the other direction.

In this implementation, the object is immutable.

Author:

Mark McConnell

Constructor Summary

PermGpElt(int[] perm)
Constructs the PermGpElt from an array of length n containing a permutation of the integers 0, 1, ..., n-1.

Method Summary

int	apply(int i) Returns this(i).
int	bruhatLength() Returns the number of "consecutive permutations" (0 1), (1 2), up to (n-2 n-1) in a minimal product equal to this.
boolean	commutesWith(GroupElt y) Returns whether this and the argument commute.
int	compareTo(Object o)
GroupElt	conjugate(GroupElt y) Returns y * this * y^(-1).
GroupElt	conjugateYinvXY(GroupElt y) Returns y^(-1) * this * y.
boolean	equals(Object o) Tests for equality in the mathematical sense--same degree and same permutation.
int	getDegree()
GroupElt	getIdentity() Returns the identity element of the same class as this.
int	getOrder(Group G) This implementation ignores G.
int	getSign() Returns the sign of the permutation as +1 or -1.
int	hashCode() Must be consistent with equals(java.lang.Object).
GroupElt	inverse() Returns the inverse element for this.
boolean	isIdentity() Tests whether this is the identity element among GroupElts of its class.
static void	main(String[] args) For testing.
GroupElt	mult(GroupElt y) Returns this * y, that is, the permutation whose value on i is this(y(i)).
static PermGpElt	parseCycles(int deg, String x) Converts a cycle like (2 0 4)(3 1) to a PermGpElt of the specified degree.
GroupElt	power(int i) Returns the i-th power of this element.
String	toString() Expresses this permutation in disjoint cycle notation.

Methods inherited from class Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Detail

PermGpElt

public PermGpElt(int[] perm)

Constructs the PermGpElt from an array of length n containing a permutation of the integers 0, 1, ..., n-1. As a function, this permutation maps i to perm[i].

The array is cloned, so later changes to the argument won't affect what's created here.

Throws:

IllegalArgumentException - If perm is not a permutation of the specified form.

Method Detail

equals

public boolean equals(Object o)

Tests for equality in the mathematical sense--same degree and same permutation. As a side effect, sets the hash code.

Specified by:

equals in interface GroupElt

hashCode

public int hashCode()

Description copied from interface: GroupElt

Must be consistent with GroupElt.equals(java.lang.Object).

Specified by:

hashCode in interface GroupElt

compareTo

public int compareTo(Object o)

Specified by:

compareTo in interface Comparable

getDegree

public final int getDegree()

apply

public final int apply(int i)

Returns this(i). See the comment on the class.

Throws:

ArrayIndexOutOfBoundsException - if i is outside the range 0 leq i less than the degree.

mult

public GroupElt mult(GroupElt y)

Returns this * y, that is, the permutation whose value on i is this(y(i)).

Specified by:

mult in interface GroupElt

Throws:

IllegalArgumentException - if the degrees don't match.

inverse

public GroupElt inverse()

Description copied from interface: GroupElt

Returns the inverse element for this.

Specified by:

inverse in interface GroupElt

conjugate

public GroupElt conjugate(GroupElt y)

Returns y * this * y^(-1). This obeys the classical rule: if this = (a b c ...) in cycle notation, the result is (y(a) y(b) y(c) ...).

Specified by:

conjugate in interface GroupElt

Throws:

IllegalArgumentException - if the degrees don't match.

conjugateYinvXY

public GroupElt conjugateYinvXY(GroupElt y)

Description copied from interface: GroupElt

Returns y^(-1) * this * y. Compare GroupElt.conjugate(repthy.GroupElt).

Specified by:

conjugateYinvXY in interface GroupElt

isIdentity

public boolean isIdentity()

Description copied from interface: GroupElt

Tests whether this is the identity element among GroupElts of its class.

Specified by:

isIdentity in interface GroupElt

getIdentity

public GroupElt getIdentity()

Description copied from interface: GroupElt

Returns the identity element of the same class as this.

Specified by:

getIdentity in interface GroupElt

getSign

public int getSign()

Returns the sign of the permutation as +1 or -1.

commutesWith

public boolean commutesWith(GroupElt y)

Returns whether this and the argument commute.

Specified by:

commutesWith in interface GroupElt

Throws:

IllegalArgumentException - if the degrees don't match.

bruhatLength

public int bruhatLength()

Returns the number of "consecutive permutations" (0 1), (1 2), up to (n-2 n-1) in a minimal product equal to this.

toString

public String toString()

Expresses this permutation in disjoint cycle notation. Use parseCycles(int, java.lang.String) to go in the other direction.

parseCycles

public static PermGpElt parseCycles(int deg,
                                    String x)

Converts a cycle like (2 0 4)(3 1) to a PermGpElt of the specified degree. Use toString() to go in the other direction.

Throws:

IllegalArgumentException - If there is a syntax error.

NumberFormatException - If some entry is not an integer.

ArrayIndexOutOfBoundsException - If some entry is outside the range 0, 1, ...,deg-1.

getOrder

public int getOrder(Group G)

This implementation ignores G.

Specified by:

getOrder in interface GroupElt

Parameters:

G - A group containing this element. It can be null, but if it's not, we can use a more efficient algorithm.

power

public GroupElt power(int i)

Description copied from interface: GroupElt

Returns the i-th power of this element. Implementations may be based on Group.power(repthy.GroupElt, int), which uses an efficient squaring algorithm.

Specified by:

power in interface GroupElt

main

public static void main(String[] args)

For testing. Give it deg perm where perm is in cycle notation.