- the ring of the integer numbers,
- the ring of the integer modulo for ,
- the ring of univariate polynomials over ,
- the ring of univariate polynomials over for .

**If you choose to work with MAPLE, you must implement your own univariate
polynomial arithmetic by means of a canonical representation.
To do do, you can adapt the
file polynomials.input which implements multivariate
polynomial arithmetic by means of a canonical representation.
This is needed since in your implementation of the Karatsuba's algorithm
you must control which algorithm is used during the recursive calls.
If you would be using the built-in polynomial multiplication of MAPLE, then you would not know.
As you can guess, the MAPLE polynomial multiplication already uses
the Karatsuba's algorithm and other tricks.
**

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2008-01-07