- intermediate expression swell,
- complexity of symbolic computations
- implementing fast algorithms.

**We iluustrate below the gap between naive and optimized implementations
of the same algorithm.
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**Next, we show benchmarks between classical and FFT-based
univariate polynomial multiplication.
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**The maple work sheet Bareiss.mw iluustrates
the problem of intermediate expression swell.
In many situations, this problem is solved by means of modular
methods. Here's an example of such method that will study
in detail later
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**Input:**- a square matrix over of order with for .
**Output:**- .

**Another example of intermediate expression swell
is given below. Consider the polynomials
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(1) |

**We will study modular methods for the Euclidean Algorithm too.
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2008-01-07