Multi-index notation is used to shorten expressions that contain many indices. Let 
and write 
.
A multi-index 
is an 
-tuple
of integers 
with 
,
..., 
.
The notation 
is used to denote the length 
.
For monomial expressions in coordinates 
, multi-index notation provides a convenient shorthand. For
example, writing 
,
gives a compact notation
 |
for the partial derivative.
