#11455: Add algorithm Magma to Conic methods
----------------------------------+-----------------------------------------
   Reporter:  mstreng             |          Owner:  AlexGhitza            
       Type:  enhancement         |         Status:  needs_work            
   Priority:  major               |      Milestone:  sage-5.0              
  Component:  algebraic geometry  |       Keywords:  magma conic           
Work_issues:                      |       Upstream:  N/A                   
   Reviewer:                      |         Author:  Marco Streng          
     Merged:                      |   Dependencies:  #10621, #11454, #11456
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Changes (by mstreng):

  * status:  needs_review => needs_work


Old description:

> This patch adds the option algorithm='magma' to (has_)rational_point for
> conics.
>
> #12154 is required for making all optional Magma doctests pass (even an
> unpatched Sage currently has failing optional Magma doctests)

New description:

 This patch adds the option algorithm='magma' to (has_)rational_point for
 conics.

 Some optional magma doctests fail on current Sage. This is unrelated to
 this ticket, and is fixed by #12154.

--

Comment:

 Something is wrong, in 5.0.prealpha1, I get
 {{{
 sage: K.<i> = QuadraticField(-1)
 sage: C = Conic(K,[1,1,1])
 sage: C.rational_point(algorithm='magma')
 NotImplementedError: No correct conversion implemented for converting the
 Magma point (-i : 1 : 0) on Conic over Number Field with defining
 polynomial t^2 + 1 over the Rational Field defined by
 X^2 + Y^2 + Z^2 to a correct Sage point on self (=Projective Conic Curve
 over Number Field in i with defining polynomial x^2 + 1 defined by x^2 +
 y^2 + z^2)
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11455#comment:6>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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