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# conformalBlockRank -- computes the rank of the conformal block vector bundle

- Usage:
    `conformalBlockRank(V)`
- Inputs:
  - V, an instance of the type ConformalBlockVectorBundle,
- Outputs:
  - r, an integer,

## Description

This function uses propagation and factorization to recursively compute ranks in terms of the ranks on $\bar{M}_{0,3}$. These are determined by the so-called fusion rules and are computed via the function fusionCoefficient in the LieAlgebraRepresentations package. See [Beauville] for details on these topics.

In the example below we compute the rank of the conformal block bundle $V(sl_3,2,(\omega_1,\omega_1,\omega_2,\omega_2))$.

    i1 : sl_3=simpleLieAlgebra("A",2);

    i2 : V=conformalBlockVectorBundle(sl_3,2,{{1,0},{1,0},{0,1},{0,1}},0)

    o2 = V

    o2 : Conformal block vector bundle on M-0-4-bar

    i3 : conformalBlockRank(V)

    o3 = 2

## Ways to use conformalBlockRank:

- `conformalBlockRank(ConformalBlockVectorBundle)`

## For the programmer

The object conformalBlockRank is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/ConformalBlocks.m2:1452:0.