#8495: Regression: Many mathematica doctests now fail
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   Reporter:  flawrence                   |       Owner:  flawrence   
       Type:  defect                      |      Status:  needs_review
   Priority:  major                       |   Milestone:  sage-4.7    
  Component:  interfaces                  |    Keywords:              
     Author:  Felix Lawrence              |    Upstream:  N/A         
   Reviewer:  Mike Hansen, Burcin Erocal  |      Merged:              
Work_issues:                              |  
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Changes (by flawrence):

  * status:  needs_info => needs_review


Old description:

> Since #3587, which implements a _sage_() method for mathematica elements,
> many mathematica doctests fail.  E.g:
>
> {{{
> sage: def math_bessel_K(nu,x):
>      ...       return mathematica(nu).BesselK(x).N(20).sage()
>      ...
>      sage: math_bessel_K(2,I)
> NotImplementedError: Unable to parse
> Mathematica output:
> -2.5928861754911969781676606702635284285719718407749199115289`20.1494653502
> 82203
> +
> 0.1804899720669620266296208808560650432663536549483055754141`18.99213497581
> 376*i
>
> }}}

New description:

 Since #3587, which implements a _sage_() method for mathematica elements,
 many mathematica doctests fail.  E.g:

 {{{
 sage: def math_bessel_K(nu,x):
      ...       return mathematica(nu).BesselK(x).N(20).sage()
      ...
      sage: math_bessel_K(2,I)
 NotImplementedError: Unable to parse
 Mathematica output:
 -2.5928861754911969781676606702635284285719718407749199115289`20.1494653502
 82203
 +
 0.1804899720669620266296208808560650432663536549483055754141`18.99213497581
 376*i

 }}}

 apply only `trac_8495-rewrite-_sage_.patch`

--

Comment:

 ARGH! I upgraded to 4.6.2 (from 4.6.1), ran the tests and get the same
 errors as Dave.

 #9032 modified Sage's .n(), and added (in two files)
 {{{
 n = numerical_approx
 N = n
 }}}

 This means that Mathematica's `N[]` is no longer being called - instead
 Sage's `numerical_approx()` is being called, and it can't handle certain
 mma objects.  Furthermore the argument taken by `numerical_approx` is the
 number of bits (I think?) whereas `N[50]` gives 50 sig figs.

 I think that the way to fix this is by adjusting precedences so that on
 mathematica objects, mathematica functions take priority.  I also think
 that fixing this is beyond the scope of this ticket (which was a rewrite
 of `._sage_`).  I have created a new ticket regarding this issue: #10968

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8495#comment:22>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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