#14888: Make FiniteField_pari_ffelt the default for generic finite fields
-------------------------------------+-------------------------------------
       Reporter:  pbruin             |        Owner:  cpernet
           Type:  enhancement        |       Status:  needs_work
       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):

 Some more news from the debugging camp: I added
 {{{
 #!diff
 diff --git a/sage/rings/finite_rings/element_pari_ffelt.pyx
 b/sage/rings/finite_rings/element_pari_ffelt.pyx
 --- a/sage/rings/finite_rings/element_pari_ffelt.pyx
 +++ b/sage/rings/finite_rings/element_pari_ffelt.pyx
 @@ -450,6 +450,7 @@
          pari_catch_sig_on()
          x.construct(FF_add((<FiniteFieldElement_pari_ffelt>self).val,
                             (<FiniteFieldElement_pari_ffelt>right).val))
 +        print "%s + %s = %s"%(self, right, x)
          return x

      cpdef ModuleElement _sub_(FiniteFieldElement_pari_ffelt self,
 ModuleElement right):
 @@ -482,6 +483,7 @@
          pari_catch_sig_on()
          x.construct(FF_mul((<FiniteFieldElement_pari_ffelt>self).val,
                             (<FiniteFieldElement_pari_ffelt>right).val))
 +        print "%s * %s = %s"%(self, right, x)
          return x

      cpdef RingElement _div_(FiniteFieldElement_pari_ffelt self,
 RingElement right):
 }}}
 and adjusted some doctests. This clearly shows the error in the conversion
 to PARI:
 {{{
 sage -t devel/sage/sage/schemes/plane_conics/con_finite_field.py
 **********************************************************************
 File "devel/sage/sage/schemes/plane_conics/con_finite_field.py", line 108,
 in
 sage.schemes.plane_conics.con_finite_field.ProjectiveConic_finite_field.?
 Failed example:
     C = Conic([1, a, -5]); C
 Expected:
     a * 1 = a
     0 + a = a
     0 + 2 = 2
     Projective Conic Curve over Finite Field in a of size 7^20 defined by
 x^2 + (a)*y^2 + 2*z^2
 Got:
     a * 0 = 0
     0 + 0 = 0
     0 + 2 = 2
     Projective Conic Curve over Finite Field in a of size 7^20 defined by
 x^2 + (a)*y^2 + 2*z^2
 **********************************************************************
 File "devel/sage/sage/schemes/plane_conics/con_finite_field.py", line 113,
 in
 sage.schemes.plane_conics.con_finite_field.ProjectiveConic_finite_field.?
 Failed example:
     C._coefficients
 Expected:
     [1, 0, 0, a, 0, 2]
 Got:
     [1, 0, 0, 0, 0, 2]
 **********************************************************************
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/14888#comment:33>
Sage <http://www.sagemath.org>
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