FYI: Giac 1.5.0-49 released, cyclic10 Groebner basis on Q solved.

[parisse]

Thanks to W. Stein, I could run Giac on cocalc server during the last 3 months, improve the Groebner basis source code, and eventually I could solve the huge cyclic10 benchmark on Q : 2225 primes were required for Chinese remaindering, 217G of memory, and more than 200 sequential days computation (10 days real time).

For more details, see this report

Giac source code: https://www-fourier.ujf-grenoble.fr/~parisse/debian/dists/stable/main/source/giac_1.5.0-49.tar.gz

[rpea...@gmail.com]

This is interesting.  One thing we discovered with Maple, which I think is known by others, is that when degree drops occur in the modular computations, you can stop F4 and output the new polynomials that have lower than expected degree, together with a flag saying the computation is incomplete.  An outer loop computing over Q can focus on reconstructing those polynomials, which also tend to be small, before restarting with them in the generating set.  This strategy was effective for cyclic-n, however, we found other systems where the degree fluctuates rapidly over hundreds of steps.

[parisse]

Le vendredi 29 mars 2019 19:25:05 UTC+1, rpea...@gmail.com a écrit :

This is interesting.  One thing we discovered with Maple, which I think is known by others, is that when degree drops occur in the modular computations, you can stop F4 and output the new polynomials that have lower than expected degree, together with a flag saying the computation is incomplete.

Interesting, I did not know about that trick. It's really different from what I do, I only add basis elements.

By the way, did you try cyclic10 on Q with mgb?

[Samuel Lelievre]

Hacker News: https://news.ycombinator.com/item?id=19526653