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# classFunction -- Converts symmetric function to class function

- Usage:
    `ch = classFunction(f)`
- Inputs:
  - f, a ring element, element of a Symmetric ring
- Outputs:
  - ch, a Class function,

## 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

## See also

- symmetricFunction -- Converts class function to symmetric function

## Ways to use classFunction:

- `classFunction(RingElement)`
- classFunction(BasicList) -- Character of irreducible representation of symmetric group

## For the programmer

The object classFunction is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/SchurRings.m2:2815:0.