speed up Schur to fundamental

[mantepse]

Old:

sage: s = SymmetricFunctions(QQ).schur()
sage: F = QuasiSymmetricFunctions(QQ).Fundamental()
sage: %timeit [F(s(la)) for la in Partitions(7)]
1 loop, best of 3: 2.04 s per loop
sage: %timeit [F(s(la)) for la in Partitions(8)]
1 loop, best of 3: 8.8 s per loop

New:

sage: s = SymmetricFunctions(QQ).schur()
sage: F = QuasiSymmetricFunctions(QQ).Fundamental()
sage: %timeit [F(s(la)) for la in Partitions(7)]
10 loops, best of 3: 97.9 ms per loop
sage: %timeit [F(s(la)) for la in Partitions(8)]
1 loop, best of 3: 331 ms per loop

[mantepse]

New commits:

​dc41651

add dedicated coercion from the Schur basis to the Fundamental basis

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​068d937

fix wrong replacements

[tscrim]

With _Partitions/Partitions(), we decided to make that a global object permanently fixed in memory because it appears in so many different contexts within combinatorics and could appear in tighter loops (e.g., the cycle type of a permutation). So I am not sure about doing the same for _Combinations/Combinations(). Moreover, it should not have such a significant impact on timings because of the UniqueRepresentation behavior. Thus, I think this is something we need to take into more careful consideration. Nevertheless, it should be something on an independent ticket because it is a bigger change.

In _from_schur_on_basis, you can (I would probably even say should) use self._indices instead of Compositions() as self._indices has a little more context.

[tscrim]

However, this is a good change to do and is quite a speedup.

[mantepse]

done, and yes indeed, the _Compositions was nonsense, thanks!

[tscrim]

I wouldn't say it was nonsense, but just something that would warrant a little more consideration.

Anyways, LGTM. Thanks.

[mantepse]

Thanks. Nonsense, because it did not give any speedup with respect to the topic of this ticket.

[embray]

Retarging tickets optimistically to the next milestone. If you are responsible for this ticket (either its reporter or owner) and don't believe you are likely to complete this ticket before the next release (8.7) please retarget this ticket's milestone to sage-pending or sage-wishlist.