[with patch, with positive review *BUT* see comments] Wrap Simon's new gp two descent code

[robertwb]

Scripts were recently updated  http://www.math.unicaen.fr/~simon/

It now handles two-torsion more uniformly, works on more curves, and actually returns points on the curve given.

[robertwb]

John Cremona and I worked on this during Sage Days 6.

The attached patches have the new version of the code (to be applied to extcode) and a revised interface.

This also includes an implementation of transformations between different Weierstrass models.

[was]

WARNING: This is full of bugs and issues.

E.g.,

sage: E = EllipticCurve([0, 0, 1/216, -7/1296, 1/7776])
sage: F = E.global_integral_model(); F
outputs a non-integral model!

DO NOT apply this until further patche(s) are posted.

I'm working on some now.

ALSO -- there are many new functions with no doctets.

[was]

Some missing doctests or things that will cause latex problems:

a/sage/schemes/elliptic_curves/ell_generic.py
integral_model
change_weierstrass_model

a/sage/rings/complex_double.pyx
argument

* number_field_element.pyx -- nth_root has \ but no r"""
* same prob in WeierstrassIsomorphism
* no doctest in init method for WeierstrassIsomorphism
* no doctest in init method for WeierstrassIsomorphism _call_

[was]

[11:14pm] wstein-rvw-1239: It might be easy for you to fix the problems.
[11:14pm] wstein-rvw-1239: E.g.,            sage: E = EllipticCurve([0, 0, 1/216, -7/1296, 1/7776])
[11:14pm] wstein-rvw-1239:             sage: F = E.global_integral_model(); F
[11:14pm] wstein-rvw-1239: doesn't return an integral model.
[11:14pm] wstein-rvw-1239: E = EllipticCurve([1/3, 5]); E
[11:14pm] wstein-rvw-1239: E.integral_model()
[11:14pm] wstein-rvw-1239: returns a non-integral model

[was]

tentative_trac-1239.patch

[was]

[good review -- on extcode] The extcode bundle is *OK* -- no problems.

[robertwb]

The global_integral_model / integral_model code in question is John Cremona's. I'll look into it more.

WARNING: The extcode patch can't go in without this one (due to interface changes).

[robertwb]

Turned out to be an indentation issue. Also added another doctest.

Should be ready to go in now.

[mabshoff]

Merged in 2.9.rc0.