repthy
Class ClassFunction

Object
  ClassFunction

Direct Known Subclasses:

GpCharacter

public class ClassFunction

extends Object

A complex-valued function on the Group G that is constant on conjugacy classes. For characters, see the subclass GpCharacter.

Operations that combine two class functions will throw an IllegalArgumentException if the underlying groups aren't equal.

Author:

Mark McConnell

Constructor Summary

ClassFunction(Group G, Complex[] val)
Constructs the class function on G whose value on the i-th conjugacy class (as returned by Group.getConjClass(int)) is val[i].

Method Summary

Complex	apply(GroupElt g) Returns the value of the function at g.
ClassFunction	conjugate() Returns the conjugate of this.
Group	getGroup() Returns the underlying group.
Complex	getValue(int i) Returns the value for the i-th conjugacy class.
Complex	innerProduct(ClassFunction chi) Returns the Hermitian inner product (1 / order(G)) * Sum_(g in G) [this(g) * chi(g)^conjugate] on the space of class functions.
ClassFunction	minus(ClassFunction chi) Returns this - chi.
Complex	normSq() Returns the innerProduct(repthy.ClassFunction) of this with itself.
ClassFunction	sum(ClassFunction chi) Returns this + chi.
ClassFunction	times(ClassFunction chi) Returns the pointwise product this * chi.
ClassFunction	times(int n) Returns n * this.
String	toString()

Methods inherited from class Object

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

Constructor Detail

ClassFunction

public ClassFunction(Group G,
                     Complex[] val)

Constructs the class function on G whose value on the i-th conjugacy class (as returned by Group.getConjClass(int)) is val[i]. The argument val is cloned.

Throws:

IllegalArgumentException - if val.length isn't equal to the number of conjugacy classes.

Method Detail

getGroup

public final Group getGroup()

Returns the underlying group.

apply

public Complex apply(GroupElt g)

Returns the value of the function at g. Expect exceptions if g is not in the group.

getValue

public final Complex getValue(int i)

Returns the value for the i-th conjugacy class.

innerProduct

public Complex innerProduct(ClassFunction chi)

Returns the Hermitian inner product
(1 / order(G)) * Sum_(g in G) [this(g) * chi(g)^conjugate]
on the space of class functions.

normSq

public Complex normSq()

Returns the innerProduct(repthy.ClassFunction) of this with itself.

sum

public ClassFunction sum(ClassFunction chi)

Returns this + chi. Compare GpCharacter.sum(repthy.GpCharacter).

minus

public ClassFunction minus(ClassFunction chi)

Returns this - chi. Compare GpCharacter.minus(repthy.GpCharacter).

times

public ClassFunction times(int n)

Returns n * this. Compare GpCharacter.sumTimes(int).

times

public ClassFunction times(ClassFunction chi)

Returns the pointwise product this * chi. Compare GpCharacter.tensor(repthy.GpCharacter).

conjugate

public ClassFunction conjugate()

Returns the conjugate of this. Compare GpCharacter.dual().

toString

public String toString()