# How to write an involution in Weyl group as a product of $2$-cycles?

Is there some method in Sage to decompose an involution in Weyl group as a product of $2$-cycles (transpositions)?

For example, I define

```
W=WeylGroup(['A', 3], prefix='s')
t1=[1,2,3,1,2,1]
t2=W.from_reduced_word(t1)
```

How to write t2 as a product of $2$-cycles? The result should be $(1,4)(2,3)$. Thank you very much.

Something along these lines should do the job:

@max, thank you very much! But the result I got is [(1, 12), (2, 11), (3, 10), (4, 9), (5, 8), (6, 7)] not (1,4)(2,3). Do you know what is the problem? Thank you very much.

It depends on how you interpret

`t2`

as a permutation. In the code above I consider it as a permutation of the 12 roots. If you have something else in mind, modify the code accordingly.E.g. try to change

`.roots()`

to`.simple_roots()`

.@max, thank you very much. I tried simple_roots() but it has errors. The t2 is the product of simple reflections $s_1s_2s_3s_1s_2s_1$.