switch to nauty for generating posets

[fchapoton]

as there is now a direct method in nauty and we have added the interface previously

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[mantepse]

This is a very impressive speedup:

sage: %time n=7; sum(1 for dig in DiGraphGenerators()(n, is_poset))
CPU times: user 5.85 s, sys: 0 ns, total: 5.85 s
Wall time: 5.85 s
2045
sage: %time n=7; sum(1 for dig in DiGraphGenerators().nauty_posetg(f"{n} o"))
CPU times: user 57.3 ms, sys: 0 ns, total: 57.3 ms
Wall time: 66.7 ms
2045
sage: %time n=8; sum(1 for dig in DiGraphGenerators().nauty_posetg(f"{n} o"))
CPU times: user 395 ms, sys: 0 ns, total: 395 ms
Wall time: 399 ms
16999

[dcoudert]

Actually, there is another issue: nauty_posetg works only for $n\leq 16$. You could use a switch to use it only in this case and use the previous (slower) method otherwise.

[mantepse]

Actually, there is another issue: nauty_posetg works only for n ≤ 16 . You could use a switch to use it only in this case and use the previous (slower) method otherwise.

Great catch!

To avoid such oversights in future (not in this pull request!), wouldn't it be better to have intermediate methods that call nauty_posetg and do the argument parsing? I am frequently wasting time looking up the precise string for nauty_geng to generate connected graphs only :-)

[mantepse]

I think that the issue pointed out by @dcoudert still needs fixing.

[fchapoton]

We lose a lot of speed in the relabeling..

[dcoudert]

I don't see how to avoid the topological sort. However, you can avoid a copy of the graph

-            yield FinitePoset(dig.relabel(label_dict, inplace=False))
+            yield FinitePoset(dig.relabel(label_dict, inplace=True))

note also that instead of dig.order(), you can use self._n. All graphs have the same number of vertices.

[fchapoton]

merci pour les suggestions