Compute rank of elliptic curve defined over relative number field

[mmasdeu]

Currently the following fails:

sage: x = QQ['x'].gen()
sage: F.<a> = QuadraticField(5)
sage: K.<b> = F.extension(x^2-3)
sage: E = EllipticCurve(K,[0,0,0,b,1])
sage: E.rank()

This is because the sage function wrapping around Denis Simon's two-descent script does not consider relative number fields.

I propose an easy fix for it.

[mmasdeu]

New commits:

​1dcdf8d	Allow for relative number fields to be passed to two_descent function.
​78bb894	Fixed a doctest.
​2085e0c	Added some comments.

[pbruin]

Looks good and passes all tests. The new doctest does take a long time (4 minutes), but that is probably hard to avoid. Two comments:

• use your real name for the "Authors" field
• the documentation line starting with "An example with" should be indented

After fixing those, feel free to set this to positive review.

[cremona]

Please try to find a shorter doctest! Even when tagged with "long time" 4 minutes is going to add quite a lot to the testing time.

But thanks for doing this, anyway.

[git]

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

​6a54aa4

Fixed indentation problem in doctest.

[git]

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

​522aa2f

Found an example for the doctest that takes much less to terminate (about 4s).

[pbruin]

This long example, and the special lim1 and limtriv in your last commit, make it sound like a good moment to look into #9322, which should generally speed up simon_two_descent() by changing the parameters.

[pbruin]

The old example would be more than twice as fast with Simon's default parameters:

sage: %timeit -n 1 -r 1 E.rank(lim1=2,lim3=4,limtriv=2)
1 loops, best of 1: 1min 42s per loop

So indeed fixing #9322 would help.

Another thing: E.torsion_subgroup() fails as well, I've opened ticket #16011 for it.

[pbruin]

The doctest in the last commit turns out to break (return an incorrect result) after #11005. Marc and I could reproduce this using Simon's script inside gp. We will mark the doctest with # known bug and report the bug to Denis Simon.

[git]

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

​db79035	Merge branch 'develop' into gp_simon_relative
​a92a80e	Changed the doctest to make it independent of variable output.
​275e4be	fix a bug in Denis Simon's 2-descent program
​8bceb36	Merge branch 'u/pbruin/16022-simon_two_descent_bug' of trac.sagemath.org:sage into gp_simon_relative

[mmasdeu]

I merged #16022 and now the it passes the doctests.