# Create an alternative: W(E8) act on positive roots to get some roots

W=WeylGroup(['E',8])

R = RootSystem(['E',8]).root_lattice()

alpha = R.simple_roots();alpha

[w for w in W if w.action(alpha[1])==(alpha[1]+alpha[2])]

Output shows : gap: cannot extend the workspace any more!

**Is their any alternative calculation to simplify the above **

Does this work with A4 or A6 or A8 instead of E8 ? it could be that E8 is too big, for some reason.

yes it works for A4 or A6 or A8 . E8 is too big

Up to multiplication by the simple reflection $s_1$, these elements live in the stabilizer of $\alpha_1$. you should rather iterate over this stabilizer.