Fix performance issue in hilbn and friends

[8d1h]

Hi! I was playing with the Hodge diamonds of K3^[n] and I noticed there is a huge performance issue. It appears that power series does not allow access of individual coefficients, and series.coefficients() creates a large dictionary which contains a lot of redundant info. So it's a lot faster to convert a power series to a polynomial then access its coefficients.

The same issue happens in nestedhilbn and complete_intersection too.

Also I fixed the variable names in cyclic_cover :)

[pbelmans]

Thanks! I knew it wasn't very efficient, but it served it purpose for things of the size that I was interested in so far :).

I've been running a documentation-adding branch offline, that I need to finish up asap. I'll include your changes there, unless an upstream merge happens to still be possible somehow.

[8d1h]

Sure!

[pbelmans]

I have now finally finished writing documentation and unit tests, and after that I could copy-paste your changes and quickly verify that all unit tests still pass :). Hurray for unit tests! But it sure was a tedious task...

The automated testing went from 18s or so to 5s.

For those who want a sneak peek of the documentation, check out https://pbelmans.ncag.info/hodge-diamond-cutter/

[8d1h]

The automated testing went from 18s or so to 5s.

Yes already hilbn(K3, 5) was very slow and I think your tests computed it twice... Now we can easily compute K3^[10] :)

BTW, although I doubt anyone would really want to compute this, but for abelian(g) with large g it is a lot faster using curve(1)^g instead.

sage: time a = abelian(100)
CPU times: user 15.2 s, sys: 0 ns, total: 15.2 s
Wall time: 15.2 s
sage: time b = curve(1)^100
CPU times: user 329 ms, sys: 0 ns, total: 329 ms
Wall time: 329 ms
sage: a == b
True

For those who want a sneak peek of the documentation, check out https://pbelmans.ncag.info/hodge-diamond-cutter/

This is really nice! :)

[pbelmans]

Excellent point about the computation for abelian varieties! This is now the computation method. Thanks!