By Secchi S.

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**Example text**

Optimization of Maple outputs remained as a problem. 2 Solution: KETpic Tpic is a graphic extension of TEX which uses a simpler set of embedded commands. Currently, Tpic is popular world-wide and only requires some special dvi drivers. When Tpic special codes are generated by some computer algebra software, they can be expected to produce very accurate graphs of any function. A famous computer algebra system: Maple enables us to manipulate raw data of plots and strings. This feature is suﬃcient to generate Tpic special codes.

However, one can further improve the performance by writing assembly code. We have also implemented this trick in Assembly language for the Pentium IA-32 with SSE2 support. The SSE/SSE2 instruction sets use XMM registers. Each of these registers is of 128-bit and can be used to pack 2 double precision ﬂoating point numbers. In fact, SSE/SSE2 instructions can compute on multiple data packed in one register, in parallel. Our implementation of the FFT-based polynomial multiplication over Z/pZ uses this technique.

4. ), texture mapping, light sources of diﬀerent colors and positions, interactive manipulation (coloring, zooming, rotation), etc. are applied. These illumination eﬀects allow us to simulate the mechanical part with a high level of quality. In addition to their aesthetic eﬀect, the illumination models are important to detect irregularities on surfaces, for example, by using some illumination lines called isophotes [10]. This procedure does reproduce the real situation of looking for the diﬀerent reﬂection lines on the surface of a car body.

### A note on closed geodesics for a class of non-compact Riemannian manifolds by Secchi S.

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