Archaon's profile - activity

I apologise in advance for the following extremely elementary question:

If a T basis element T_omega of the Iwahori-Hecke algebra attached to A_n is given, how do I extract the permutation omega from the basis element? I couldn't find the function which returns omega (when applied to T_omega).

Following the kind suggestion in the comments, here is some basic code:

R.<q> = LaurentPolynomialRing(ZZ)
H = IwahoriHeckeAlgebra('A12', q)
T = H.T()

Now produce a random element in the Hecke algebra:

P = T[4,3,2,5,6,4,7,8,2]*T[7, 6, 5, 4, 3, 2, 1, 5, 4, 3, 2, 5, 4, 3, 5, 4, 7, 6, 5, 7, 6, 7]

It will be a big sum of certain basis elements in T which can be extracted via:

for x in P.terms():     
    for y in x.coefficients(): 
        print(x/y)

Every x/y will be an element in T indexed by some element (a permutation) omega in A_12. How to extract this element from x/y?

I thank you very much in advance for your help!