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= Final Pynac Switchover Push for Sage-4.0 =

See also http://trac.sagemath.org/sage_trac/ticket/5930

<<TableOfContents>>

== Number Fields ==
 * _pow_ in number_field_element and _rational_ has some hacks since the Pynac library will cause infinite recursions.

== Formal Derivatives ==
 
 * Handling of fderivatives so that we can convert to Maxima.

== Doctest Grunt Work ==

 * There's a lot of "grunt work" to be done to fix doctests to work with the new output format. In each case somebody has to verify that the two things are equal.

== Massive Speed Regressions ==

 * The massive speed regressions, making pynac symbolics *slower* than Maxima for some benchmarks.

== I = sqrt(-1) ==

 * The current handling of I as a wrapper around a number field element is a bit awkward since (I+2)*x can't be expanded as I+2 is "atomic". This also means that I.imag() returns 1.0 instead of 1. This causes issues in algebraic.
  
 Idea to solve this:
{{{
Mike: I think what we want is just a QQ*I ring which automatically goes to SR when you do arithmetic with anything outside of it.
 me: ok.
You suggested that before, and it makes some sense.
Can't we just make a quadratic number field, and enhance it a tiny spec.
 Mike: I think if we had that, then everything should work out.
 Sent at 11:31 AM on Thursday
 me: That sounds easy enough, and it would be super fast, since quadratic fields are very very fast.
 Mike: We just don't have an exact way to work with complex numbers.
 me: robertwb could whip it out, as he wrote quadratic fields, etc.
 Mike: Yep
For RR we have QQ, but we don't have quite an analogue for CC.
}}}

== Doctest status ==

As of right now -- May 7 at 11:38 am, doing
   sage -tp 20 devel/sage/sage
results in
{{{
The following tests failed:

 sage -t devel/sage/sage/quadratic_forms/quadratic_form__mass__Siegel_densities.py # 2 doctests failed
 sage -t devel/sage/sage/quadratic_forms/quadratic_form__ternary_Tornaria.py # 2 doctests failed
 sage -t devel/sage/sage/quadratic_forms/quadratic_form__mass__Conway_Sloane_masses.py # 3 doctests failed
 sage -t devel/sage/sage/quadratic_forms/special_values.py # 8 doctests failed
 sage -t devel/sage/sage/misc/parser.pyx # 9 doctests failed
 sage -t devel/sage/sage/misc/prandom.py # 1 doctests failed
 sage -t devel/sage/sage/misc/preparser.py # 2 doctests failed
 sage -t devel/sage/sage/misc/citation.pyx # 1 doctests failed
 sage -t devel/sage/sage/numerical/optimize.py # 3 doctests failed
 sage -t devel/sage/sage/misc/functional.py # 8 doctests failed
 sage -t devel/sage/sage/modules/vector_real_double_dense.pyx # 7 doctests failed
 sage -t devel/sage/sage/matrix/matrix1.pyx # 0 doctests failed
 sage -t devel/sage/sage/matrix/tests.py # 1 doctests failed
 sage -t devel/sage/sage/rings/real_mpfi.pyx # 34 doctests failed
 sage -t devel/sage/sage/rings/arith.py # 10 doctests failed
 sage -t devel/sage/sage/databases/database.py # 1 doctests failed
 sage -t devel/sage/sage/rings/rational_field.py # 4 doctests failed
 sage -t devel/sage/sage/rings/integer.pyx # 2 doctests failed
 sage -t devel/sage/sage/rings/complex_double.pyx # 5 doctests failed
 sage -t devel/sage/sage/rings/complex_number.pyx # 2 doctests failed
 sage -t devel/sage/sage/matrix/matrix_symbolic_dense.pyx # 19 doctests failed
 sage -t devel/sage/sage/rings/complex_interval.pyx # 1 doctests failed
 sage -t devel/sage/sage/rings/infinity.py # Segfault
 sage -t devel/sage/sage/rings/real_lazy.pyx # 3 doctests failed
 sage -t devel/sage/sage/rings/power_series_ring.py # 1 doctests failed
 sage -t devel/sage/sage/rings/complex_interval_field.py # 1 doctests failed
 sage -t devel/sage/sage/rings/real_double.pyx # 2 doctests failed
 sage -t devel/sage/sage/rings/rational.pyx # 12 doctests failed
 sage -t devel/sage/sage/rings/real_mpfr.pyx # 5 doctests failed
 sage -t devel/sage/sage/rings/number_field/number_field_base.pyx # 8 doctests failed
 sage -t devel/sage/sage/rings/number_field/number_field_element.pyx # 4 doctests failed
 sage -t devel/sage/sage/rings/polynomial/polynomial_element.pyx # 3 doctests failed
 sage -t devel/sage/sage/matrix/matrix2.pyx # 3 doctests failed
 sage -t devel/sage/sage/structure/element.pyx # 2 doctests failed
 sage -t devel/sage/sage/structure/parent.pyx # 1 doctests failed
 sage -t devel/sage/sage/structure/sage_object.pyx # 1 doctests failed
 sage -t devel/sage/sage/gsl/dft.py # 1 doctests failed
 sage -t devel/sage/sage/tests/book_stein_ent.py # 8 doctests failed
 sage -t devel/sage/sage/combinat/species/series.py # 1 doctests failed
 sage -t devel/sage/sage/calculus/test_sympy.py # 15 doctests failed
 sage -t devel/sage/sage/calculus/var.pyx # 11 doctests failed
 sage -t devel/sage/sage/calculus/functions.py # 6 doctests failed
 sage -t devel/sage/sage/calculus/functional.py # 32 doctests failed
 sage -t devel/sage/sage/calculus/tests.py # 40 doctests failed
 sage -t devel/sage/sage/plot/line.py # 2 doctests failed
 sage -t devel/sage/sage/plot/density_plot.py # 3 doctests failed
 sage -t devel/sage/sage/plot/complex_plot.pyx # 4 doctests failed
 sage -t devel/sage/sage/plot/plot_field.py # 1 doctests failed
 sage -t devel/sage/sage/interfaces/gp.py # 2 doctests failed
 sage -t devel/sage/sage/plot/contour_plot.py # 11 doctests failed
 sage -t devel/sage/sage/plot/plot3d/transform.pyx # 1 doctests failed
 sage -t devel/sage/sage/interfaces/expect.py # 1 doctests failed
 sage -t devel/sage/sage/interfaces/qepcad.py # 29 doctests failed
 sage -t devel/sage/sage/calculus/calculus.py # 98 doctests failed
 sage -t devel/sage/sage/interfaces/maxima.py # 14 doctests failed
 sage -t devel/sage/sage/algebras/quatalg/quaternion_algebra.py # 1 doctests failed
 sage -t devel/sage/sage/graphs/graph_list.py # 2 doctests failed
 sage -t devel/sage/sage/schemes/elliptic_curves/lseries_ell.py # 13 doctests failed
 sage -t devel/sage/sage/schemes/elliptic_curves/padic_lseries.py # 101 doctests failed
 sage -t devel/sage/sage/schemes/elliptic_curves/ell_egros.py # 8 doctests failed
 sage -t devel/sage/sage/schemes/elliptic_curves/constructor.py # 8 doctests failed
 sage -t devel/sage/sage/schemes/elliptic_curves/padics.py # 25 doctests failed
 sage -t devel/sage/sage/schemes/plane_curves/affine_curve.py # 1 doctests failed
 sage -t devel/sage/sage/schemes/elliptic_curves/ell_modular_symbols.py # 66 doctests failed
 sage -t devel/sage/sage/schemes/elliptic_curves/ell_generic.py # 13 doctests failed
 sage -t devel/sage/sage/schemes/elliptic_curves/sha_tate.py # 41 doctests failed
 sage -t devel/sage/sage/plot/plot3d/parametric_plot3d.py # 4 doctests failed
 sage -t devel/sage/sage/graphs/graph.py # 3 doctests failed
 sage -t devel/sage/sage/ext/fast_eval.pyx # 1 doctests failed
 sage -t devel/sage/sage/coding/code_bounds.py # 2 doctests failed
 sage -t devel/sage/sage/sets/set.py # 2 doctests failed
 sage -t devel/sage/sage/functions/hyperbolic.py # 11 doctests failed
 sage -t devel/sage/sage/functions/other.py # 26 doctests failed
 sage -t devel/sage/sage/functions/log.py # 13 doctests failed
 sage -t devel/sage/sage/functions/functions.py # 15 doctests failed
 sage -t devel/sage/sage/functions/special.py # 12 doctests failed
 sage -t devel/sage/sage/functions/orthogonal_polys.py # 8 doctests failed
 sage -t devel/sage/sage/functions/trig.py # 22 doctests failed
 sage -t devel/sage/sage/symbolic/function.pyx # 4 doctests failed
 sage -t devel/sage/sage/symbolic/ring.pyx # 8 doctests failed
 sage -t devel/sage/sage/symbolic/callable.py # 2 doctests failed
 sage -t devel/sage/sage/symbolic/constants.py # 29 doctests failed
 sage -t devel/sage/sage/symbolic/expression_conversions.py # 1 doctests failed
 sage -t devel/sage/sage/ext/fast_callable.pyx # 3 doctests failed
 sage -t devel/sage/sage/schemes/elliptic_curves/ell_rational_field.py # 34 doctests failed
 sage -t devel/sage/sage/symbolic/expression.pyx # 136 doctests failed
 sage -t devel/sage/sage/calculus/desolvers.py # 0 doctests failed
 sage -t devel/sage/sage/calculus/wester.py # 37 doctests failed
 sage -t devel/sage/sage/calculus/equations.py # 0 doctests failed
 sage -t devel/sage/sage/plot/plot.py # 0 doctests failed
 sage -t devel/sage/sage/functions/piecewise.py # 6 doctests failed
----------------------------------------------------------------------
Total time for all tests: 734.9 seconds
}}}