Let $R$ be a reduced root system, $W$ the associated Weyl group, and $w\_0 \in W$ the longest element of $W$. In general $w\_0$ admits more than one reduced decomposition into a product of reflections, a number which we denote by $d\_R$. Where can one find a list of values of $d\_R$ for low-dimensional root systems?


For example are the explicit values of $d\_R$ known for the exceptional root systems?



Number of reduced decompositions of the longest element of the Weyl group
This is easy to do in [SageMath](https://www.sagemath.org/). E.g. the following code



```
G = WeylGroup("F4")
w = G.long_element_hardcoded()
print(w)
rw = w.reduced_words() 
len(rw)

```

outputs 2144892. If you want to look at some of these reduced words just examine the list rw. To create a list for classical types of different rank do



```
res = {}
for n in range(2,5):
    G = WeylGroup(["A", n])
    w = G.long_element_hardcoded()
    print("Calculating rank ", n)
    res[n] = len(w.reduced_words())

```

