#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-5.1                                                          
      Component:  symbolics                                            |    
Resolution:                                                                    
       Keywords:  lambert_w symbolics conversion maxima sd35.5 sd40.5  |   Work 
issues:                                                                    
Report Upstream:  N/A                                                  |     
Reviewers:  Keshav Kini, Karl-Dieter Crisman, Fredrik Johansson, Burcin Erocal
        Authors:  Benjamin Jones                                       |     
Merged in:                                                                    
   Dependencies:                                                       |      
Stopgaps:                                                                    
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Comment (by dsm):

 After some real-world discussions, I'd prefer to avoid falling into Python
 ints for (some of) the special values:

 {{{
 sage: parent(lambert_w(0))
 Integer Ring
 sage: parent(lambert_w(e))
 <type 'int'>
 sage: parent(lambert_w(-1/e))
 <type 'int'>
 sage: parent(lambert_w(SR(-1/e)))
 <type 'int'>
 sage: parent(lambert_w(SR(0)))
 Integer Ring
 }}}

 Mysteriously enough, instrumenting it reveals that `_eval_` is actually
 returning SR(1) which then in some part of the code I don't understand
 becomes int(1) before we get it back.  If we explicitly return Integer(1)
 then it seems to stay as Integer(1).  This isn't the biggest deal in the
 world but there have been several bug reports caused by something falling
 out of Sagespace into Pythonspace.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11888#comment:52>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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