Am Samstag, 24. November 2018 23:11:26 UTC+1 schrieb parisse:
>
>
> Giac supports double revlex ordering, this is the order used by the
> eliminate command of Giac. Geogebra has many examples of eliminate commands
> there https://dev.geogebra.org/trac/browser/trunk/geogebra/giac/src/test
>
Nice. It would probably be good to have this function in the Sage interface
for giac, as well. Is it also possible to obtain the full Gröbner basis
with respect to the revlex/revlex block order, but without elimination?
Meanwhile, Roman Pearce's website [5] is back online and I used those
polynomial systems to compare the Sage interfaces libsingular, giacpy_sage
and fgb_sage. I created a gist of the code [6].
Versions of libraries used:
• Sage 8.5.beta4
• libSingular-4.1.1
• giacpy_sage-0.6.6, giac-1.4.9.45.p4
• fgb_sage-0.1, fgb-20150719 (14538, 14539)
Primes used: singular: 2^31-1, giac: 16777213, fgb: 65521.
Machine: CentOS 7.5.1804, Intel(R) Xeon(R) CPU E5-2660 0 @ 2.20GHz, 32
cores, 196 G memory.
Number of threads in parentheses. Computation time in seconds.
ℤ/p | singular (1) | giac (4) giac (16) | fgb (4)
fgb (16)
cyclic8 | 62.01 | 7.71 4.88 | 1.86
1.38
cyclic9 | 11519.16 | 258.85 191.30 | 112.31
55.37
katsura11 | 107.91 | 12.62 11.10 | 4.04
2.43
katsura12 | 1090.37 | 67.07 60.25 | 23.09
12.59
bayes148 | 7.19 | 92.63 92.15 | 571.28
471.59
gametwo7 | 934.69 | 122.65 116.37 | 20.78
14.30
jason210 | 2.67 | 23.71 23.39 | 24.58
22.44
mayr42 | 124.74 | 169.94 166.56 | 139.12
111.08
yang1 | 49.79 | [3] [3] | 257.96
177.65
ℚ | singular (1) | giac (4) giac (16) | fgb (1)
cyclic7 | [1] | 10.71 10.62 | 4.20
cyclic8 | [2] | 120.44 205.57 | 77.22
katsura9 | 19.19 | 27.30 27.23 | 3.04
katsura10 | 236.62 | 241.32 238.23 | 18.58
alea6 | 35724.62 | 578.94 548.39 | [4] 331.64
eco12 | [1] | 4748.24 4811.32 | 102.06
jason210 | 13.43 | 65.24 83.82 | 49.38
noon9 | 132.82 | 3146.97 3159.49 | 136.55
I am a bit surprised about some of the Singular results being a lot worse
than reported in [5], cyclic7 in particular. Perhaps starting this
computation with some different options can help here.
[1] Aborted after 13.5 hours.
[2] Skipped.
[3] Error, problem too large.
[4] Excessive memory usage of about 300 G; computed on a different machine.
[5] http://www.cecm.sfu.ca/~rpearcea/mgb.html
[6] https://gist.github.com/mwageringel/213a4a980e338ec8ea5a75482b1bcb2b
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