**
You must implement a generator of random univariate polynomials
parametrized by the desired degree and the coefficient ring.
In MAPLE
**
- there is already a generator of random univariate polynomials,
- and you may choose to write one generator per desired coefficient ring.

**
In AXIOM
**
- there is less support for generating random polynomials,
- but it is still quite easy.

**
For each coefficient ring, the degree
should vary from
to a value large enough (typically
) in order to show
that the Karatsuba's algorithm is asymptotically faster.
For each value of
, it is recommended
**
- to pick several random pairs and run both algorithms for this pair,
- to compute the average time for each algorithm.

**
Both MAPLE and AXIOM have graphical facilities
that you can use for displaying your experimental results.
You may also use **`gnuplot` or any other tool that you
are familiar with.

*Marc Moreno Maza *

2008-01-07