# classFunction -- Converts symmetric function to class function

## Synopsis

• Usage:
ch = classFunction(f)
• Inputs:
• f, , element of a Symmetric ring
• Outputs:
• ch,

## Description

Given a symmetric function f, homogeneous of degree N, the method computes the corresponding virtual character of the symmetric group S_N.

The character of the standard representation of S_5 is

 i1 : R = symmetricRing(QQ,5); i2 : classFunction(jacobiTrudi({4,1},R)) o2 = ClassFunction{{1, 1, 1, 1, 1} => 4} {2, 1, 1, 1} => 2 {3, 1, 1} => 1 {3, 2} => -1 {5} => -1 o2 : ClassFunction

The character of the second exterior power of the standard representation of S_5 is

 i3 : R = symmetricRing(QQ,5); i4 : classFunction(jacobiTrudi({3,1,1},R)) o4 = ClassFunction{{1, 1, 1, 1, 1} => 6} {2, 2, 1} => -2 {5} => 1 o4 : ClassFunction

## For the programmer

The object classFunction is .