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Charts (a), (b), (c). For univariate polynomial data types, DUP outperforms SUP and, for the multivariate polynomial data types, MMA outperforms DRMP, which outperforms NSMP. For the largest degrees, the timing ratio between the best combination, DUP + MMA, and the worst one, SUP + NSMP is in the range 2 · · · 3. Charts (d), (e), (f). The best and the worst combinations are the same as above, however the timing ratio is in the range 3 · · · 4. Interestingly, the second best combination is SUP + MMA for small coeﬃcients and DUP + DRMP for larger ones.

This feature is suﬃcient to generate Tpic special codes. Thus, we have developed a macro package of Maple (version V and later): KETpic (abbreviation of Kisarazu Educational Tpic). KETpic as well as Maple covers the major platforms. We have already released two versions of KETpic for Mac and Windows which generate codes with diﬀerent end-of-line characters according to each platform. 5 and later)[8]. Table 1. 1 functions sets line width adds x, y to the path draws a line on the current path draws a circle or arc shades a closed object Design Concept and Advantages of KETpic Pursuing operability and economy for KETpic, we designed KETpic so as to carry out calculations on Maple as much as possible, and not to depend on the PC and the peripherals (such as a PostScript printer etc).

Fateman. Vector-based polynomial recursive representation arithmetic. dylan, 1999. 7. A. Filatei. Implementation of fast polynomial arithmetic in Aldor, 2006. University of Western Ontario. ´ Schost. Implementation techniques 8. A. Filatei, X. Li, M. Moreno Maza, and E for fast polynomial arithmetic in a high-level programming environment. In Proc. ISSAC’06. ACM Press, 2006. 9. Free Software Foundation. GNU Multiple Precision Arithmetic Library. com/gmp/. 10. J. von zur Gathen and J. Gerhard. Modern Computer Algebra.