symmetry properties



Hi,
 
First,
thanks to Viktor for his help concerning my last question.

This
time, I would like to differentiate a function by a symmetrical tensor.
If
I do for example:
    load(itensor);
    decsym(T,2,0,[sym(all)],[]);
    ishow(diff(T([i,j],[]),T([k,l],[])))$
The
result will correspond to the case where T is not symmetric.
To
take into account this property, I have to replace T([i,j],[]) by 0.5(T([i,j],[])+
T([j,i],[])) and then the result will be right.

Is
there a better way? 
Maybe
Maxima can be modified to take into account the symmetry properties itself when
it differentiates?
 
Thank
by advance for your help and remarks.
Guenhael.