#14888: Make FiniteField_pari_ffelt the default for generic finite fields
-------------------------------------+-------------------------------------
       Reporter:  pbruin             |        Owner:  cpernet
           Type:  enhancement        |       Status:  positive_review
       Priority:  major              |    Milestone:  sage-5.13
      Component:  finite rings       |   Resolution:
       Keywords:  FiniteField        |    Merged in:
  performance                        |    Reviewers:  Jean-Pierre Flori,
        Authors:  Peter Bruin        |  Jeroen Demeyer
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
   Dependencies:  #12142, #15124,    |     Stopgaps:
  #15125                             |
-------------------------------------+-------------------------------------

Comment (by jdemeyer):

 This happens sometimes:
 {{{
 **********************************************************************
 File "devel/sage/sage/schemes/plane_conics/con_finite_field.py", line 110,
 in
 sage.schemes.plane_conics.con_finite_field.ProjectiveConic_finite_field.?
 Failed example:
     C.has_rational_point(point = True)  # output is random
 Exception raised:
     Traceback (most recent call last):
       File "/scratch/release/merger/sage-5.13.beta0/local/lib/python2.7
 /site-packages/sage/doctest/forker.py", line 479, in _run
         self.execute(example, compiled, test.globs)
       File "/scratch/release/merger/sage-5.13.beta0/local/lib/python2.7
 /site-packages/sage/doctest/forker.py", line 838, in execute
         exec compiled in globs
       File "<doctest
 sage.schemes.plane_conics.con_finite_field.ProjectiveConic_finite_field.?[9]>",
 line 1, in <module>
         C.has_rational_point(point = True)  # output is random
       File "/scratch/release/merger/sage-5.13.beta0/local/lib/python2.7
 /site-packages/sage/schemes/plane_conics/con_finite_field.py", line 132,
 in has_rational_point
         s, pt = self.has_singular_point(point = True)
       File "/scratch/release/merger/sage-5.13.beta0/local/lib/python2.7
 /site-packages/sage/schemes/plane_conics/con_field.py", line 595, in
 has_singular_point
         return True, self.point(Sequence(D.right_kernel().gen()))
       File "/scratch/release/merger/sage-5.13.beta0/local/lib/python2.7
 /site-packages/sage/schemes/plane_conics/con_field.py", line 886, in point
         p = ProjectiveCurve_generic.point(self, v, check=check)
       File "/scratch/release/merger/sage-5.13.beta0/local/lib/python2.7
 /site-packages/sage/schemes/generic/scheme.py", line 370, in point
         return self.point_homset() (v, check=check)
       File "/scratch/release/merger/sage-5.13.beta0/local/lib/python2.7
 /site-packages/sage/schemes/generic/homset.py", line 263, in __call__
         return Set_generic.__call__(self, *args, **kwds)
       File "parent.pyx", line 1011, in
 sage.structure.parent.Parent.__call__ (sage/structure/parent.c:8392)
       File "coerce_maps.pyx", line 427, in
 sage.structure.coerce_maps.ListMorphism._call_with_args
 (sage/structure/coerce_maps.c:8035)
       File "coerce_maps.pyx", line 100, in
 sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args
 (sage/structure/coerce_maps.c:4278)
       File "coerce_maps.pyx", line 90, in
 sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args
 (sage/structure/coerce_maps.c:4089)
       File "/scratch/release/merger/sage-5.13.beta0/local/lib/python2.7
 /site-packages/sage/schemes/generic/homset.py", line 455, in
 _element_constructor_
         return self.codomain()._point(self, v, **kwds)
       File "/scratch/release/merger/sage-5.13.beta0/local/lib/python2.7
 /site-packages/sage/schemes/generic/algebraic_scheme.py", line 583, in
 _point
         return self.__A._point(*args, **kwds)
       File "/scratch/release/merger/sage-5.13.beta0/local/lib/python2.7
 /site-packages/sage/schemes/projective/projective_space.py", line 835, in
 _point
         return SchemeMorphism_point_projective_finite_field(*args, **kwds)
       File "/scratch/release/merger/sage-5.13.beta0/local/lib/python2.7
 /site-packages/sage/schemes/projective/projective_point.py", line 764, in
 __init__
         X.extended_codomain()._check_satisfies_equations(v)
       File "/scratch/release/merger/sage-5.13.beta0/local/lib/python2.7
 /site-packages/sage/schemes/generic/algebraic_scheme.py", line 967, in
 _check_satisfies_equations
         raise TypeError, "Coordinates %s do not define a point on
 %s"%(coords,self)
     TypeError: Coordinates [0, 0, 1] do not define a point on Projective
 Conic Curve over Finite Field in a of size 7^20 defined by x^2 + (a)*y^2 +
 2*z^2
 **********************************************************************
 }}}
 Note the code path in the traceback showing that Sage thinks the conic is
 singular.

--
Ticket URL: <http://trac.sagemath.org/ticket/14888#comment:16>
Sage <http://www.sagemath.org>
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