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# weightDiagram -- computes the weights in a Lie algebra module and their multiplicities

- Usage:
    `weightDiagram(V)`
- Inputs:
  - V, an instance of the type LieAlgebraModule,
- Optional inputs:
  - Strategy => ..., default value null
- Outputs:
  - T, a virtual tally,

## Description

Let $V$ be the irreducible $\mathbf{g}$-module with highest weight $v$. This function returns a tally whose keys are the weights appearing in $V$ and whose values are the multiplicities of these weights. An optional argument "Strategy" allows to specify which algorithm to use, see character.

    i1 : g=simpleLieAlgebra("A",2)

    o1 = g

    o1 : simple LieAlgebra

    i2 : V=irreducibleLieAlgebraModule({2,1},g)

    o2 = V

    o2 : irreducible LieAlgebraModule over g

    i3 : weightDiagram(V)

    o3 = VirtualTally{{-1, -2} => 1}
                      {-1, 1} => 2
                      {-2, 0} => 1
                      {-2, 3} => 1
                      {-3, 2} => 1
                      {0, -1} => 2
                      {0, 2} => 1
                      {1, -3} => 1
                      {1, 0} => 2
                      {2, -2} => 1
                      {2, 1} => 1
                      {3, -1} => 1

    o3 : VirtualTally

## See also

- multiplicity(List,LieAlgebraModule) -- compute the multiplicity of a weight in a Lie algebra module
- character -- Computes the character of a Lie algebra module

## Ways to use weightDiagram:

- `weightDiagram(LieAlgebra,List)`
- `weightDiagram(LieAlgebra,Vector)`
- `weightDiagram(LieAlgebraModule)`

## For the programmer

The object weightDiagram is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/LieAlgebraRepresentations/documentation.m2:791:0.