** **

**Project 2** (Rational function reconstruction in AXIOM)

*
Similar to Project 1, but with an implementation
in AXIOM.
*

**Project 3** (FFT-based multiplication in

in AXIOM)

*
The goal of this project is to implement in AXIOM the algorithms of the course
for FFT-based multiplication in
.
Benchmarks versus the Karatsuba and classical quadratic multiplication algorithms
are needed for
.
*

**Project 4** (Fast Interpolation in M

APLE)

*
We have seen during the course how to perform interpolation
with more than two moduli.
Section 10.2 in [GG99] propose an elegant divide-and-conquer
strategy to improve the performances of the interpolation
Algorithm.
The goal of this project is to implementation this algorithm in MAPLE
and realize benchmarks with
and
.
*

**Project 5** (Fast Chinese Remaindering in M

APLE)

*
We have seen during the course how to perform Chinese Remaindering
with more than two moduli.
Section 10.3 in [GG99] propose an elegant divide-and-conquer
strategy to improve the performances of the Chinese Remaindering
Algorithm.
The goal of this project is to implementation this algorithm in MAPLE
and realize benchmarks with
or
.
*

**Project 6** (Fast Interpolation in AXIOM)

*
Similar to Project 4, but with an implementation
in AXIOM.
*

**Project 7** (Fast Chinese Remaindering in AXIOM)

*
Similar to Project 5, but with an implementation
in AXIOM.
*

**Project 8** (Project of your choice in M

APLE or AXIOM)

*
During your reading of [GG99], you may have been seduced or puzzled
by an algorithm.
Please discuss it with the instrutor, to determine if it can
be turned into a project.
*

*Marc Moreno Maza *

2008-01-07