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# qdim -- Compute principal specialization of character or quantum dimension

- Usage:
    `qdim M`
    `qdim(M,l)`
- Inputs:
  - M, an instance of the type LieAlgebraModule,
  - l, an integer,
- Outputs:
  - P, a ring element,

## Description

qdim M computes the principal specialization of the character of M. qdim (M,l) evaluates it modulo the appropriate cyclotomic polynomial, so that upon specialization of the variable $q$ to be the corresponding root of unity of smallest positive argument, it provides the quantum dimension of M.

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

    o1 = g

    o1 : simple LieAlgebra

    i2 : W=weylAlcove(g,3)

    o2 = {{0, 0}, {0, 1}, {0, 2}, {0, 3}, {1, 0}, {1, 1}, {1, 2}, {2, 0}, {2, 1},
         ------------------------------------------------------------------------
         {3, 0}}

    o2 : List

    i3 : L=LL_(1,1) (g)

    o3 = L

    o3 : irreducible LieAlgebraModule over g

    i4 : M=matrix table(W,W,(v,w)->fusionCoefficient(L,LL_v g,LL_w g,3))

    o4 = | 0 0 0 0 0 1 0 0 0 0 |
         | 0 1 0 0 0 0 1 1 0 0 |
         | 0 0 1 0 1 0 0 0 1 0 |
         | 0 0 0 0 0 1 0 0 0 0 |
         | 0 0 1 0 1 0 0 0 1 0 |
         | 1 0 0 1 0 2 0 0 0 1 |
         | 0 1 0 0 0 0 1 1 0 0 |
         | 0 1 0 0 0 0 1 1 0 0 |
         | 0 0 1 0 1 0 0 0 1 0 |
         | 0 0 0 0 0 1 0 0 0 0 |

                  10       10
    o4 : Matrix ZZ   <-- ZZ

    i5 : first eigenvalues M

    o5 = 2.999999999999997

    o5 : CC (of precision 53)

    i6 : qdim L

          4     2         -2    -4
    o6 = q  + 2q  + 2 + 2q   + q

    o6 : ZZ[q]

    i7 : qdim (L,3)

    o7 = 3

            ZZ[q]
    o7 : -----------
          4    2
         q  - q  + 1

## Ways to use qdim:

- `qdim(LieAlgebraModule)`
- `qdim(LieAlgebraModule,ZZ)`

## For the programmer

The object qdim is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/LieAlgebraRepresentations/documentation.m2:1154:0.