#9342: rank method for elliptic curves over number fields
------------------------------------+---------------------------------------
   Reporter:  ljpk                  |       Owner:  cremona   
       Type:  enhancement           |      Status:  needs_work
   Priority:  minor                 |   Milestone:  sage-4.5  
  Component:  elliptic curves       |    Keywords:            
     Author:  ljpk                  |    Upstream:  N/A       
   Reviewer:                        |      Merged:            
Work_issues:  docstring formatting  |  
------------------------------------+---------------------------------------
Changes (by davidloeffler):

  * status:  needs_review => needs_work
  * work_issues:  => docstring formatting


Comment:

 This is very nice -- good stuff! I have only a few tiny criticisms, mostly
 to do with docstring formatting.

 (1)
 {{{
 1347    def rank_bounds(self,verbose=0, lim1=5, lim3=50, limtriv=10,
 maxprob=20, limbigprime=30):
 1348        r"""
 1349        Returns the lower and upper bounds using simon_two_descent.
 The results of simon_two_descent are cached.
 }}}
 There is a ReST syntax for cross-referencing between docstrings, which
 should be used here:
 {{{... using :meth:`~simon_two_descent`. The results ...}}}.

 (2)
 {{{
 1435        .. NOTE::
 1436
 1437           Note: For non-quadratic number fields, this code does
 1438           return, but it takes a long time.
 }}}
 The output is "Note: Note: For ...". The second "Note" should go. This
 mistake is made in two of the three new docstrings.

 (2) If it does terminate for non-quadratic fields, but it takes a long
 time, then throw in an example and flag it as long:
 {{{
 sage: EllipticCurve('11a').base_extend(NumberField(x^3 - 3,'c')).rank() #
 long time
 0
 }}}
 This example only takes about 15 seconds on my machine.

 (3)
 {{{
 1459        IMPLEMENTATION:
 1460
 1461        Uses Denis Simon's GP/PARI scripts from
 1462        \url{http://www.math.unicaen.fr/~simon/}.
 }}}
 This should just be "{{{ from http://www.math.unicaen.fr/~simon/.}}}"; The
 ReST documentation parser is clever enough to spot URL's without help, and
 the LaTeX-style syntax you've used just gets copied into the output. This
 mistake is in all three of the new docstrings.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9342#comment:4>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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