Question: Defining a 4-vector in Maple 16

Hi all,

I'm trying to initialize a 4-vector and promote it as a tensor in Maple 16 using the Physics package. My attempt so far has been unsuccessful :) 

This 4-vector needs to be a function of the coordinates X. What I'm trying to do is to allocate terms by terms my tensor as indicated in my attempt below. Everything looks fine (the query is telling me F2 is a tensor) but when I'm trying to compute contravariant quantities, I can't obtain an answer for a given coordinate (here F2[~n](X) is not equal du v_1(X))... Finally, the last line, computing the sum over all the indexes is not giving me an answer... 

restart; with(Physics):
Setup(mathematicalnotation=true):
Setup(coordinatesystems = cartesian):
Define();
g_[]:

F2[1]:=(x,y,z,t)->v_1(X);F2[2]:=(x,y,z,t)->v_2(X);F2[3]:=(x,y,z,t)->v_3(X);F2[4]:=(x,y,z,t)->1;

Define(F2[mu](X));

Define(F2,query);

F2[1](X);F2[2](X);

F2[~1](X);F2[~2](X);

F2[~nu].F2[nu]

Surely, something is wrong in my way of defining a spacetime tensor. What would be the solution to obtain a decent contravariant F2?

Another more or less related question would be to know how to compute a taylor expansion of a function itself i.e. 1/(1+f(X))~ 1-f(X) since f<<1? Would there be a built-in fonction to do such a thing?

Many thanks!

Vincent