[GAP Forum] Fox derivatives
Joachim Neubueser
joachim.neubueser at math.rwth-aachen.de
Fri Jul 30 10:27:29 BST 2004
Dear Karol Palka
You wrote:
> Dear Forum,
>
> is it possible to compute the Fox derivatives of a word in GAP ?
> It's quite important and not very difficult tool in homology theory of
> finitely presented groups. (Maybe somebody can implement it ?)
>
> Karol Palka,
> Warsaw Univ.
This letter to the GAP Forum of July 10 was unfortunately held up
until yesterday, because you are not a member of the GAP Forum and so
your letter did not get posted automatically to all Forum members but
was only found in a revision 'by hand' of mail to the Forum. So
independently of the following, may I recommend that you register as a
Forum member as explained on the GAP website for future cases.
I have yesterday forwarded your letter to Professor Derek Holt at
Warwick and got the folowing answer, which I hope will help you.
If you have further questions feel free to write either to Professor
Holt or to the address gap-support as explained on the GAP website.
Kind regards and apologies for the delay,
Joachim Neubueser
----------------------------------------------------------------------
I think the (rather easy) function below computes the required Fox
derivatives. This is for right actions, however, and it is quite likely that
he would prefer it for left actions. Maybe he can adapt it himself? Anyway,
let me know if there are any problems.
Derek.
FoxDerivative := function(F,i,w)
## F should be a free group of rank r, i an integer with 1 <= i <= r,
## and w a word in F.
## The value of the i-th Fox derivative of F on w is returned as a list
## of pairs [k,v] (v in F, k = 1 or -1) representing the element
## sum k * v of the group algebra ZF.
local len, er, j, fd;
fd := [];
len := Length(w);
for j in [1..len] do
er := ExtRepOfObj(Subword(w,j,j));
if er[1] = i and er[2] = 1 then Add(fd,[1,Subword(w,j+1,len)]); fi;
if er[1] = i and er[2] = -1 then Add(fd,[-1,Subword(w,j,len)]); fi;
od;
return fd;
end;
------------------------------------------------------------------------
More information about the Forum
mailing list