Make big_oh notation work for any element that has a big_oh() method

[tkluck]

One can use the big-oh notation

O(xⁿ)

when x is a generator of a power series or a laurent series. It is convenient to also be able to use this notation when the parent of x is another ring (for example, a subclass of a power series ring).

The current implementation in rings/big_oh.py imports a large number of types, which slows down the Sage startup. Elements should implement their own big_oh() methods, and the function O(x) should simply call x.big_oh().

[tkluck]

patch for sage.rings.big_oh

[tkluck]

I just added the patch in the right format, i.e. the output of hg_sage.export() instead of a normal diff.

[mariah]

Applied patch to sage-4.7.1.alpha2, did 'sage -b', then 'make testlong'. All tests passed. Positive review!

[jdemeyer]

I think this patch needs an extra doctest to demonstrate what it does and that it works as expected.

[was]

The following behavior is bad. In both cases, I think one should get an error.

sage: R.<x> = QQ[[]]
sage: O(1+x^10)
O(x^10)
sage: f = x*(1/x + x^9); type(f)
<type 'sage.rings.laurent_series_ring_element.LaurentSeries'>
sage: O(f)
O(x^0)

[was]

Tom Boothby is currently working on this. See also #11726 and #11729.

[boothby]

apply only this patch

[tkluck]

I could have reviewed this sooner, sorry about that. However, the ticket's dependencies are still open, so maybe we should still wait for them to be accepted?

This doesn't apply to v5.4 anymore. I also couldn't easily fix that myself. I'll set the status to needs_work.