Q:

mathematica -creating lists and vectors of specific length

In Mathematica,

How can I create a list of length n
and fill with zeroes?
How can I
create a vector of length n and fill
with zeroes?

A:

Version 6.0 and up include a new function ConstantArray for doing exactly this, and is more efficient than using Table:
In[2]:= ConstantArray[0,10]
Out[2]= {0,0,0,0,0,0,0,0,0,0}

Documentation here:
http://reference.wolfram.com/mathematica/ref/ConstantArray.html

A:

In Mathematica, there's no distinction between lists and vectors.  You can use the Table function to generate a list of length n:
x = Table[0, {n}]
(* If n was 4, x would now be the list {0, 0, 0, 0} *)

