This webpage contains GAP3 programs that allow to write any word in the generators of the generic Hecke algebra associated with the group G

The user should run the file corresponding to the group they are interested in G

well) does not calculate determinants with indterminates to negative powers.

_{n}, for n=4,5,6,7,8,13, as a linear combination of the elements of the basis B_{n}, used in the papers BCCK and BCC for the proof of the BMM symmetrising trace conjecture. The algorithm is explained in detail in Section 3.3 of the associated paper.**INSTRUCTIONS**The user should run the file corresponding to the group they are interested in G

_{4}, G_{5}, G_{6}, G_{7}, G_{8}, G_{13}and then:**If they want to express a word w as a linear combination of elements of B**

_{n}:**Step 1.**Write w as a list l of integers 1,2,3,-1,-2,-3 for s

_{1}, s

_{2}, s

_{3}, s

_{1}

^{-1}, s

_{2}

^{-1}, s

_{3}

^{-1}respectively. For example, for w=s

_{1}

^{2}s

_{2}s

_{1}

^{-1}s

_{2}

^{-2}, take l=[1,1,2,-1,-2,-2].

**Step 2.**Calculate F(l); The output is a list where each element is the coefficient of the corresponding element in B

_{n}.

**If they want to check whether a family of |G**

_{n}| words is a basis of the generic Hecke algebra:**Step 1.**Create a list B where each word is presented as a list of integers as in Step 1 above.

**Step 2.**Calculate M:=FindMat(B); This is the change of basis matrix.

**Step 3.**Calculate DeterminantMat(r*M); If this is a unit, then the initial family is a basis. The factor r is used, because GAP3 (and SAGE as

well) does not calculate determinants with indterminates to negative powers.

**PARABOLIC BASES**

In the following files we give parabolic bases for the generic Hecke algebras
for the groups discussed: G_{4},
G_{5}, G_{6},
G_{7}, G_{8}, G_{13}.