#11888: Sage is missing the lambert_w function
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       Reporter:  benjaminfjones                                |         
Owner:  burcin                                                            
           Type:  defect                                        |        
Status:  needs_review                                                      
       Priority:  minor                                         |     
Milestone:  sage-5.0                                                          
      Component:  symbolics                                     |    
Resolution:                                                                    
       Keywords:  lambert_w symbolics conversion maxima sd35.5  |   Work 
issues:                                                                    
Report Upstream:  N/A                                           |     
Reviewers:  Keshav Kini, Karl-Dieter Crisman, Fredrik Johansson, Burcin Erocal
        Authors:  Benjamin Jones                                |     Merged 
in:                                                                    
   Dependencies:  #12507                                        |      
Stopgaps:                                                                    
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Changes (by benjaminfjones):

  * status:  needs_work => needs_review


Comment:

 Success!

 Symbolic and numerical integration now work as expected for the principle
 branch. I added doctests to indicate what is and is not implemented.

 ----

 One other comment, to indicate what causes errors, I want to add doctests
 to `lambert_w` such as:

 {{{
 sage: integral(lambert_w(1,x), x)
 ERROR: An unexpected error occurred while tokenizing input
 ...
 RuntimeError: ECL says: Error executing code in Maxima: lambert_w:
 expected exactly 1 arguments.
 }}}

 and

 {{{
 sage: numerical_integral(lambert_w(x), 0, 1)
 Exception TypeError: "function not supported for these types, and can't
 coerce safely to supported types" in 'sage.gsl.integration.c_ff' ignored
 ...
 (0.0, 0.0)
 }}}

 but the doctest framework doesn't recognize the `Exception TypeError` and
 it seems to automatically fail if a `RuntimeError` is raised. If I put the
 latter 4 lines in the docstring for `lambert_w`, it fails doctesting, the
 framework only sees the `(0.0, 0.0)` part at the end. Is there a way
 around either of these issues?

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11888#comment:38>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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