** Let
be a commutative ring and let
be a power of
.
Let
and
be two polynomials in
with degrees less than
and
respectively.
The product
has degree less than
and we can write
**

**
where
belong to
.
The goal of this exercise is to show that one can compute
the coefficients
at the cost of multiplying
two polynomials in
with degree
.
The polynomial
is called the ***middle product* of
and
and plays an important role as we shall see in class.

*Marc Moreno Maza *

2008-03-18